https://teaching.healthtech.dtu.dk/22115/index.php?action=history&feed=atom&title=Bayesian_Phylogeny
Bayesian Phylogeny - Revision history
2026-04-08T01:12:55Z
Revision history for this page on the wiki
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https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=256&oldid=prev
Gorm at 14:59, 19 March 2026
2026-03-19T14:59:53Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:59, 19 March 2026</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== Posterior probability of trees ==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== Posterior <ins style="font-weight: bold; text-decoration: none;">samples and posterior </ins>probability of trees ==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 1'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 1'''</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del style="font-weight: bold; text-decoration: none;">Analysis of </del>Neanderthal data <del style="font-weight: bold; text-decoration: none;">(</del>posterior probability of clades<del style="font-weight: bold; text-decoration: none;">) </del>==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== Neanderthal data<ins style="font-weight: bold; text-decoration: none;">: </ins>posterior probability of clades ==</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 5'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 5'''</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== <del style="font-weight: bold; text-decoration: none;">Probability </del>distributions over other parameters ==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>== <ins style="font-weight: bold; text-decoration: none;">Posterior </ins>distributions over other parameters ==</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 6'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 6'''</div></td></tr>
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Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=255&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T11:40:05Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:40, 19 March 2026</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 8'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 8'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Marginal <del style="font-weight: bold; text-decoration: none;">vs. joint </del>distributions'''</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Marginal distributions'''</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del style="font-weight: bold; text-decoration: none;">Strictly speaking </del>the <del style="font-weight: bold; text-decoration: none;">comparison above was </del>not <del style="font-weight: bold; text-decoration: none;">entirely appropriate</del>. <del style="font-weight: bold; text-decoration: none;">We first found the overall distribution </del>of the <del style="font-weight: bold; text-decoration: none;">r(CG) parameter and then compared its mean to the mean </del>of <del style="font-weight: bold; text-decoration: none;">the overall distribution of the r(AC) parameter. By doing things this way, we are ignoring the possibility </del>that <del style="font-weight: bold; text-decoration: none;">the two parameters might be associated in some way. For instance</del>, <del style="font-weight: bold; text-decoration: none;">one </del>parameter <del style="font-weight: bold; text-decoration: none;">might always be larger than the other in any individual sample, even though the total distributions overlap</del>. We <del style="font-weight: bold; text-decoration: none;">should instead be looking at the distribution over both parameters simultaneously. A probability distribution over several parameters simultaneously is called </del>a <del style="font-weight: bold; text-decoration: none;">"joint distribution" over </del>the parameters.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: <ins style="font-weight: bold; text-decoration: none;">Comparing posterior means gives a useful first summary of </ins>the <ins style="font-weight: bold; text-decoration: none;">two parameters, but it does </ins>not <ins style="font-weight: bold; text-decoration: none;">show how uncertain these estimates are</ins>. <ins style="font-weight: bold; text-decoration: none;">One </ins>of the <ins style="font-weight: bold; text-decoration: none;">strengths </ins>of <ins style="font-weight: bold; text-decoration: none;">Bayesian analysis is precisely </ins>that <ins style="font-weight: bold; text-decoration: none;">it gives us access not just to a single best estimate</ins>, <ins style="font-weight: bold; text-decoration: none;">but to a full posterior probability distribution over possible </ins>parameter <ins style="font-weight: bold; text-decoration: none;">values</ins>. We <ins style="font-weight: bold; text-decoration: none;">will now use this to get </ins>a <ins style="font-weight: bold; text-decoration: none;">fuller picture of </ins>the <ins style="font-weight: bold; text-decoration: none;">two substitution-rate </ins>parameters.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: <del style="font-weight: bold; text-decoration: none;">By </del>looking at one parameter <del style="font-weight: bold; text-decoration: none;">at a time, we are summing its probability over all values of the other parameters. This </del>is called <del style="font-weight: bold; text-decoration: none;">the </del>marginal distribution.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: <ins style="font-weight: bold; text-decoration: none;">We start by </ins>looking at <ins style="font-weight: bold; text-decoration: none;">the posterior distribution of each parameter separately. Such a distribution for </ins>one parameter <ins style="font-weight: bold; text-decoration: none;">alone </ins>is called <ins style="font-weight: bold; text-decoration: none;">its </ins>marginal distribution.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Examine marginal distributions'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Examine marginal distributions'''</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 9'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 9'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''<del style="font-weight: bold; text-decoration: none;">Examine </del>joint distributions'''</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''<ins style="font-weight: bold; text-decoration: none;">Marginal vs. </ins>joint distributions'''</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: Looking at the marginal distributions gives us a fuller understanding of the uncertainty in each parameter separately. However, it still does not directly answer the question of whether r(AC) is larger than r(CG) in most posterior samples, because the two parameters may be associated with each other across samples. For instance, one parameter might be larger than the other in almost every individual sample, even though the two overall marginal distributions overlap. To answer such questions, we must examine the two parameters simultaneously. A probability distribution over several parameters at the same time is called a "joint distribution", whereas a distribution for one parameter considered by itself is called a "marginal distribution".</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: These plots and results explore the relationship between the A<->C and C<->G rates.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: These plots and results explore the relationship between the A<->C and C<->G rates.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ggplot(df_hcv2, aes(x=CG, y=AC)) + </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ggplot(df_hcv2, aes(x=CG, y=AC)) + </div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''Based on the two different ways to plot the joint distribution and based on the unfiltered and filtered row counts, what is the posterior probability that r(AC) > r(CG)?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''Based on the two different ways to plot the joint distribution and based on the unfiltered and filtered row counts, what is the posterior probability that r(AC) > r(CG)?</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">----</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: Note how examining the joint distribution provides information that you could not obtain by simply comparing the marginal distributions. In particular, it lets you answer direct questions about how parameters relate to each other, for instance whether one is larger than another in most posterior samples. The same idea can be used to answer many other questions about posterior distributions.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 10'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question 10'''</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">: Note how examining the joint distribution provides you with information that you could not get from simply comparing the marginal distributions. This very simple procedure can be used to answer many different questions.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Now, plot the relative substitution rates at the first, second, and third codon positions:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Now, plot the relative substitution rates at the first, second, and third codon positions:</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=254&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T11:09:13Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:09, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l252">Line 252:</td>
<td colspan="2" class="diff-lineno">Line 252:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>'''Question 7: ''' Based on the reported posterior means, <del style="font-weight: bold; text-decoration: none;">does </del>r(CG) <del style="font-weight: bold; text-decoration: none;">appear </del>to be larger <del style="font-weight: bold; text-decoration: none;">than r(AC)</del>?</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>'''Question 7: '''Based on the reported posterior means, <ins style="font-weight: bold; text-decoration: none;">which of the two parameters, r(AC) or </ins>r(CG)<ins style="font-weight: bold; text-decoration: none;">, appears </ins>to be larger <ins style="font-weight: bold; text-decoration: none;">on average</ins>?</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>----</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=253&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T10:44:37Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:44, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l246">Line 246:</td>
<td colspan="2" class="diff-lineno">Line 246:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Secondly, the posterior probability distribution of each parameter is summarized by giving the mean, variance, median, and 95% credible interval.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Secondly, the posterior probability distribution of each parameter is summarized by giving the mean, variance, median, and 95% credible interval.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: The last columns contain values indicating <del style="font-weight: bold; text-decoration: none;">if </del>the run has converged. Specifically ESS means Effective Sample Size, and <del style="font-weight: bold; text-decoration: none;">is a measure of </del>how many independent samples you have from the posterior <del style="font-weight: bold; text-decoration: none;">- </del>the higher the better, but this should be at least 100. The column labeled PSRF+ <del style="font-weight: bold; text-decoration: none;">is a measure </del>(also known as <del style="font-weight: bold; text-decoration: none;">"R</del>-<del style="font-weight: bold; text-decoration: none;">hat"</del>) <del style="font-weight: bold; text-decoration: none;">which </del>should be close to 1 if the runs have converged. Specifically <del style="font-weight: bold; text-decoration: none;">this </del>measures whether different chains (and different parts of <del style="font-weight: bold; text-decoration: none;">different </del>chains) <del style="font-weight: bold; text-decoration: none;">converge to sample </del>the same <del style="font-weight: bold; text-decoration: none;">set </del>of values. As a rule of thumb<del style="font-weight: bold; text-decoration: none;">: </del>values less than 1.05 are good, between 1.05 and 1.10 are <del style="font-weight: bold; text-decoration: none;">ok</del>, and above 1.10 <del style="font-weight: bold; text-decoration: none;">have not converged well</del>.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: The last columns contain values indicating <ins style="font-weight: bold; text-decoration: none;">whether </ins>the run has converged. Specifically<ins style="font-weight: bold; text-decoration: none;">, </ins>ESS means Effective Sample Size, and <ins style="font-weight: bold; text-decoration: none;">measures </ins>how many <ins style="font-weight: bold; text-decoration: none;">effectively </ins>independent samples you have from the posterior <ins style="font-weight: bold; text-decoration: none;">— </ins>the higher the better, but this should be at least 100. <ins style="font-weight: bold; text-decoration: none;">[https://sites.stat.columbia.edu/gelman/research/published/brooksgelman2.pdf </ins>The column labeled PSRF+ <ins style="font-weight: bold; text-decoration: none;">gives another convergence diagnostic </ins>(also known as <ins style="font-weight: bold; text-decoration: none;">“R</ins>-<ins style="font-weight: bold; text-decoration: none;">hat”</ins>)<ins style="font-weight: bold; text-decoration: none;">] and </ins>should be close to 1 if the runs have converged. Specifically<ins style="font-weight: bold; text-decoration: none;">, it </ins>measures whether different chains (and different parts of <ins style="font-weight: bold; text-decoration: none;">the </ins>chains) <ins style="font-weight: bold; text-decoration: none;">are sampling </ins>the same <ins style="font-weight: bold; text-decoration: none;">distribution </ins>of values. As a rule of thumb<ins style="font-weight: bold; text-decoration: none;">, </ins>values less than 1.05 are good, <ins style="font-weight: bold; text-decoration: none;">values </ins>between 1.05 and 1.10 are <ins style="font-weight: bold; text-decoration: none;">acceptable</ins>, and <ins style="font-weight: bold; text-decoration: none;">values </ins>above 1.10 <ins style="font-weight: bold; text-decoration: none;">suggest poor convergence</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''What are the posterior mean values of the relative substitution rate parameters r(AC) and r(CG)?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''What are the posterior mean values of the relative substitution rate parameters r(AC) and r(CG)?</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=252&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T10:37:00Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:37, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l246">Line 246:</td>
<td colspan="2" class="diff-lineno">Line 246:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Secondly, the posterior probability distribution of each parameter is summarized by giving the mean, variance, median, and 95% credible interval.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Secondly, the posterior probability distribution of each parameter is summarized by giving the mean, variance, median, and 95% credible interval.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: The last columns contain values indicating if the run has converged. Specifically ESS means Effective Sample Size, and is a measure of how many independent samples you have from the posterior - the higher the better, but this should be at least 100. The column labeled PSRF+ is a measure (also known as "R-hat") which should be close to 1 if the runs have converged. Specifically this measures whether different chains (and different parts of different chains) converge to sample the same set of values. </div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: The last columns contain values indicating if the run has converged. Specifically ESS means Effective Sample Size, and is a measure of how many independent samples you have from the posterior - the higher the better, but this should be at least 100. The column labeled PSRF+ is a measure (also known as "R-hat") which should be close to 1 if the runs have converged. Specifically this measures whether different chains (and different parts of different chains) converge to sample the same set of values<ins style="font-weight: bold; text-decoration: none;">. As a rule of thumb: values less than 1.05 are good, between 1.05 and 1.10 are ok, and above 1.10 have not converged well</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''What are the posterior mean values of the relative substitution rate parameters r(AC) and r(CG)?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Question: '''What are the posterior mean values of the relative substitution rate parameters r(AC) and r(CG)?</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=251&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T10:32:45Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:32, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l230">Line 230:</td>
<td colspan="2" class="diff-lineno">Line 230:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Inspect model details'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Inspect model details'''</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> showmodel</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> showmodel</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: This command gives you a summary of the current model settings. You will also get a summary of how the prior probabilities of all model parameters are set. You will for instance notice that the nucleotide frequencies (parameter labeled "Statefreq") have a "Dirichlet" prior. Without going into details, the Dirichlet distribution is a probability distribution over frequency vectors (i.e., vectors of positive values that sum to 1). Depending on the exact parameters the distribution can be more or less flat (flat here means that all sum-1 vectors are equally probable). The Dirichlet distribution is a handy way of specifying the prior probability distribution of nucleotide (or amino acid) frequency vectors. The default statefreq prior in MrBayes is the flat or un-informative prior dirichlet(1,1,1,1).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: This command gives you a summary of the current model settings. You will also get a summary of how the prior probabilities of all model parameters are set. You will for instance notice that the nucleotide frequencies (parameter labeled "Statefreq") have a "Dirichlet" prior. Without going into details, the Dirichlet distribution is a probability distribution over frequency vectors (i.e., vectors of positive values that sum to 1). Depending on the exact parameters the distribution can be more or less flat (flat here means that all sum<ins style="font-weight: bold; text-decoration: none;">-to</ins>-1 vectors are equally probable). The Dirichlet distribution is a handy way of specifying the prior probability distribution of nucleotide (or amino acid) frequency vectors. The default statefreq prior in MrBayes is the flat or un-informative prior dirichlet(1,1,1,1).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: We will not go into the priors for the remaining parameters in any detail, but you may notice that by default all topologies are taken to be equally likely (a flat prior on trees).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: We will not go into the priors for the remaining parameters in any detail, but you may notice that by default all topologies are taken to be equally likely (a flat prior on trees).</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=250&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T10:31:39Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:31, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l226">Line 226:</td>
<td colspan="2" class="diff-lineno">Line 226:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: This specifies that we want to use a model of the General Time Reversible (GTR) type, where all 6 substitution types have separate rate parameters.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: This specifies that we want to use a model of the General Time Reversible (GTR) type, where all 6 substitution types have separate rate parameters.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: When the lset command was discussed previously, a few issues were glossed over. Importantly, and unlike PAUP, the lset command in MrBayes gives no information about whether nucleotide frequencies are equal or not, and whether they should be estimated from the data or not. In MrBayes this is instead controlled by defining the prior probability of the nucleotide frequencies (the command prset can be used to set priors). For instance, a model with equal nucleotide frequencies corresponds to having prior probability 1 (one) for the frequency vector (A=0.25, C=0.25, G=0.25, T=0.25), and zero prior probability for the infinitely many other possible vectors. As you will see below, the default prior is not this limited, and the program will therefore estimate the frequencies from the data.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: When the lset command was discussed previously, a few issues were glossed over. Importantly, and unlike PAUP, the lset command in MrBayes gives no information about whether nucleotide frequencies are equal or not, and whether they should be estimated from the data or not. In MrBayes this is instead controlled by defining the prior probability of the nucleotide frequencies (the command prset can be used to set priors). For instance, a model with equal nucleotide frequencies corresponds to having prior probability 1 (one) for the frequency vector (A=0.25, C=0.25, G=0.25, T=0.25), and zero prior probability for the infinitely many other possible <ins style="font-weight: bold; text-decoration: none;">frequency </ins>vectors. As you will see below, the default prior is not this limited, and the program will therefore estimate the frequencies from the data.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Inspect model details'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Inspect model details'''</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=249&oldid=prev
Gorm: /* Probability distributions over other parameters */
2026-03-19T10:29:25Z
<p><span dir="auto"><span class="autocomment">Probability distributions over other parameters</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 12:29, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l220">Line 220:</td>
<td colspan="2" class="diff-lineno">Line 220:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> set partition=bycodon</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> set partition=bycodon</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> prset ratepr=variable</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> prset ratepr=variable</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>: This is an alternative way of specifying that different sites <del style="font-weight: bold; text-decoration: none;">have </del>different rates. <del style="font-weight: bold; text-decoration: none;">Instead of using </del>a gamma <del style="font-weight: bold; text-decoration: none;">distribution and learning about site-specific </del>rates from the data<del style="font-weight: bold; text-decoration: none;">, </del>we <del style="font-weight: bold; text-decoration: none;">are </del>instead <del style="font-weight: bold; text-decoration: none;">using our </del>prior knowledge about the structure of the genetic code to <del style="font-weight: bold; text-decoration: none;">specify </del>that all 1st <del style="font-weight: bold; text-decoration: none;">codon </del>positions <del style="font-weight: bold; text-decoration: none;">have the same </del>rate, all 2nd <del style="font-weight: bold; text-decoration: none;">codon </del>positions <del style="font-weight: bold; text-decoration: none;">have the same rate</del>, and all 3rd <del style="font-weight: bold; text-decoration: none;">codon </del>positions <del style="font-weight: bold; text-decoration: none;">have the same rate</del>. Specifically, charset 1stpos=1-.\3 <del style="font-weight: bold; text-decoration: none;">means that we define </del>a character set named <del style="font-weight: bold; text-decoration: none;">"</del>1stpos<del style="font-weight: bold; text-decoration: none;">" which includes </del>site 1 <del style="font-weight: bold; text-decoration: none;">in the alignment </del>followed by every third site (<del style="font-weight: bold; text-decoration: none;">"</del>\3<del style="font-weight: bold; text-decoration: none;">"</del>, <del style="font-weight: bold; text-decoration: none;">meaning it includes </del>sites 1, 4, 7, <del style="font-weight: bold; text-decoration: none;">11</del>, <del style="font-weight: bold; text-decoration: none;">...</del>) until the end of the alignment (<del style="font-weight: bold; text-decoration: none;">here </del>denoted <del style="font-weight: bold; text-decoration: none;">"</del>.<del style="font-weight: bold; text-decoration: none;">"</del>).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>: This is an alternative way of specifying that different sites <ins style="font-weight: bold; text-decoration: none;">may evolve at </ins>different rates. <ins style="font-weight: bold; text-decoration: none;">With </ins>a gamma <ins style="font-weight: bold; text-decoration: none;">model, we allow </ins>rates <ins style="font-weight: bold; text-decoration: none;">to vary across sites but do not specify in advance which sites are fast or slow; instead, that pattern is inferred </ins>from the data<ins style="font-weight: bold; text-decoration: none;">. Here </ins>we instead <ins style="font-weight: bold; text-decoration: none;">use </ins>prior <ins style="font-weight: bold; text-decoration: none;">biological </ins>knowledge about the structure of the genetic code to <ins style="font-weight: bold; text-decoration: none;">divide sites into three classes: 1st, 2nd, and 3rd codon positions. We then allow each class to have its own rate, so </ins>that all 1st positions <ins style="font-weight: bold; text-decoration: none;">share one </ins>rate, all 2nd positions <ins style="font-weight: bold; text-decoration: none;">another</ins>, and all 3rd positions <ins style="font-weight: bold; text-decoration: none;">a third</ins>. Specifically, charset 1stpos=1-.\3 <ins style="font-weight: bold; text-decoration: none;">defines </ins>a character set named 1stpos <ins style="font-weight: bold; text-decoration: none;">consisting of </ins>site 1 followed by every third site (\3, <ins style="font-weight: bold; text-decoration: none;">i.e. </ins>sites 1, 4, 7, <ins style="font-weight: bold; text-decoration: none;">10</ins>, <ins style="font-weight: bold; text-decoration: none;">…</ins>)<ins style="font-weight: bold; text-decoration: none;">, continuing </ins>until the end of the alignment (denoted .).</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Specify model'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Specify model'''</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=248&oldid=prev
Gorm: /* Analysis of Neanderthal data (posterior probability of clades) */
2026-03-19T09:56:56Z
<p><span dir="auto"><span class="autocomment">Analysis of Neanderthal data (posterior probability of clades)</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:56, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l197">Line 197:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Find posterior probability of clades'''</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Find posterior probability of clades'''</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">: When the run has finished, issue this command to compute a consensus tree:</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> sumt contype=halfcompat showtreeprobs=no relburnin=yes burninfrac=0.25</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> sumt contype=halfcompat showtreeprobs=no relburnin=yes burninfrac=0.25</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Examine the consensus tree that is plotted to screen: On the branches that are resolved, you will notice that numbers have been plotted. These are clade-credibility values, and are in fact the posterior probability that the clade is real (based on the present data set).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: Examine the consensus tree that is plotted to screen: On the branches that are resolved, you will notice that numbers have been plotted. These are clade-credibility values, and are in fact the posterior probability that the clade is real (based on the present data set).</div></td></tr>
</table>
Gorm
https://teaching.healthtech.dtu.dk/22115/index.php?title=Bayesian_Phylogeny&diff=247&oldid=prev
Gorm: /* Analysis of Neanderthal data (posterior probability of clades) */
2026-03-19T09:53:42Z
<p><span dir="auto"><span class="autocomment">Analysis of Neanderthal data (posterior probability of clades)</span></span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:53, 19 March 2026</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l183">Line 183:</td>
<td colspan="2" class="diff-lineno">Line 183:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>delete 5-40</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>delete 5-40</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></pre></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></pre></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">: As we did for the maximum likelihood analysis, we will discard some of the human sequences in order to speed up the analysis. The command delete 5-40 removes sequence number 5 to sequence number 40 from the active data set.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: As we did for the maximum likelihood analysis, we will discard some of the human sequences in order to speed up the analysis. The command delete 5-40 removes sequence number 5 to sequence number 40 from the active data set.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: As we did for the maximum likelihood analysis, we will discard some of the human sequences in order to speed up the analysis. The command delete 5-40 removes sequence number 5 to sequence number 40 from the active data set.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Gorm