Model selection

Gorm — Wed, 15 Apr 2026 18:27:05 GMT

Bayesian Phylogeny

Gorm — Thu, 19 Mar 2026 14:59:53 GMT

Windows software installation

Gorm — Thu, 19 Mar 2026 08:46:43 GMT

R + RStudio: install versions for Windows instead of Linux

← Older revision		Revision as of 10:46, 19 March 2026
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	* Instead of installing the Linux version of R and RStudio, you should install the Windows versions:		* Instead of installing the Linux version of R and RStudio, you should install the Windows versions:
	** https://posit.co/download/rstudio-desktop/		** https://posit.co/download/rstudio-desktop/
			* Also install the following R-packages:
			** install.packages("tidyverse")
			** install.packages("bayesplot")
			** install.packages("hexbin")
	* NOTE: this means you will have to access files on the Linux file system from the Windows file system.		* NOTE: this means you will have to access files on the Linux file system from the Windows file system.
	** Your Linux files should be accessible at a file path similar to this: <code>\\wsl$\Ubuntu\home\user\whatever</code> (where <code>user</code> is your username, and <code>whatever</code> is the path to where your files are located.		** Your Linux files should be accessible at a file path similar to this: <code>\\wsl$\Ubuntu\home\user\whatever</code> (where <code>user</code> is your username, and <code>whatever</code> is the path to where your files are located.

Linux software installation

Gorm — Thu, 19 Mar 2026 08:45:50 GMT

← Older revision		Revision as of 10:45, 19 March 2026
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	install.packages("tidyverse")		install.packages("tidyverse")
	install.packages("bayesplot")		install.packages("bayesplot")
			install.packages("hexbin")

MacOS software installation

Gorm — Thu, 19 Mar 2026 08:44:54 GMT

← Older revision		Revision as of 10:44, 19 March 2026
Line 125:		Line 125:
	install.packages("tidyverse")		install.packages("tidyverse")
	install.packages("bayesplot")		install.packages("bayesplot")
			install.packages("hexbin")

Bayesian Phylogeny

Gorm — Thu, 19 Mar 2026 08:39:39 GMT

Overview

← Older revision		Revision as of 10:39, 19 March 2026
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	Today's exercise will focus on phylogenetic analysis using Bayesian methods.		Today's exercise will focus on phylogenetic analysis using Bayesian methods.

	As was the case for likelihood methods, Bayesian analysis is founded on having a probabilistic model of how the observed data is produced. This means that, for a given set of parameter values, you can compute the probability or [https://www.statlect.com/glossary/probability-density-function probability density] of any possible observation. For a full dataset, you then obtain the likelihood by multiplying these values across all observations. You will recall from the lecture that in Bayesian statistics the goal is to obtain a full ~~so-called~~ posterior probability distribution over all possible parameter values. The posterior distribution quantifies our degree of belief in any possible parameter value, after seeing the data. ~~The posterior probability distribution~~ is obtained by updating the prior probability distribution using the likelihood of the observed data.		As was the case for likelihood methods, Bayesian analysis is founded on having a probabilistic model of how the observed data is produced. This means that, for a given set of parameter values, you can compute the probability or [https://www.statlect.com/glossary/probability-density-function probability density] of any possible observation. For a full dataset, you then obtain the likelihood by multiplying these values across all observations. You will recall from the lecture that in Bayesian statistics the goal is to obtain a full posterior probability distribution over all possible parameter values. The posterior distribution quantifies our degree of belief in any possible parameter value after seeing the data. It is obtained by updating the prior probability distribution using the likelihood of the observed data.

	The prior probability distribution expresses your beliefs about the parameters before seeing any data, while the likelihood expresses what the observed data are telling you about the parameters~~, and is used to update the prior into the posterior~~. Specifically, the likelihood of a parameter value is the probability of the observed data given that parameter value. We regard a parameter value as more plausible the more probable it makes the observed data. This is the measure we have previously used to find the maximum likelihood estimate. If the prior probability distribution is flat (i.e., if all possible parameter values have the same prior probability) then the posterior distribution is proportional to the likelihood, and the parameter value with the maximum likelihood also has the maximum posterior probability. However, even in this case, using a Bayesian approach still lets you interpret the result as a probability distribution over parameter values.		The prior probability distribution expresses your beliefs about the parameters before seeing any data, while the likelihood expresses what the observed data are telling you about the parameters. Specifically, the likelihood of a parameter value is the probability of the observed data given that parameter value. We regard a parameter value as more plausible the more probable it makes the observed data. This is the same measure we have previously used to find the maximum likelihood estimate. If the prior probability distribution is flat (i.e., if all possible parameter values have the same prior probability), then the posterior distribution is proportional to the likelihood, and the parameter value with the maximum likelihood also has the maximum posterior probability. However, even in this case, using a Bayesian approach still lets you interpret the result as a probability distribution over parameter values.

	If the prior is not flat, then it may have a substantial impact on the posterior, although this effect will usually diminish as the amount of data increases. A prior should ideally be based on domain knowledge and results from previous experiments. For instance one can use the posterior from one analysis as the prior in a new, independent analysis. Often a prior is chosen to be weakly informative, meaning that it places reasonable bounds on the parameter values without constraining them too narrowly. For instance the transition/transversion rate ratio kappa is typically 1.5-10. Values such as 100, 1,000 or 1,000,000 would be extremely unlikely, so a weakly informative prior for this parameter could be chosen to place 95% of its probability mass in the 0.5-20 range, slightly wider than what we think of as ~~typical~~ values. For instance one could use a lognormal distribution with suitable parameters.		If the prior is not flat, then it may have a substantial impact on the posterior, although this effect will usually diminish as the amount of data increases. A prior should ideally be based on domain knowledge and results from previous experiments. For instance one can use the posterior from one analysis as the prior in a new, independent analysis. Often a prior is chosen to be weakly informative, meaning that it places reasonable bounds on the parameter values without constraining them too narrowly. For instance the transition/transversion rate ratio kappa is typically 1.5-10. Values such as 100, 1,000 or 1,000,000 would be extremely unlikely, so a weakly informative prior for this parameter could be chosen to place 95% of its probability mass in the 0.5-20 range, slightly wider than what we think of as plausible values. For instance one could use a lognormal distribution with suitable parameters.

	In Bayesian phylogeny the parameters are of the same kind as in maximum likelihood phylogeny. Typical parameters include tree topology, branch lengths, nucleotide frequencies, and substitution model parameters such as the transition/transversion rate ratio or the gamma shape parameter. The difference is that, whereas in maximum likelihood phylogeny we seek the best point estimates of the parameter values, in Bayesian phylogeny the goal is instead to infer a full probability distribution over the possible parameter values. The observed data are again usually taken to be the alignment, although strictly speaking it would be more reasonable to say that the sequences are what have been observed, and that the alignment should then be inferred jointly with the phylogeny.		In Bayesian phylogeny the parameters are of the same kind as in maximum likelihood phylogeny. Typical parameters include tree topology, branch lengths, nucleotide frequencies, and substitution model parameters such as the transition/transversion rate ratio or the gamma shape parameter. The difference is that, whereas in maximum likelihood phylogeny we seek the best point estimates of the parameter values, in Bayesian phylogeny the goal is instead to infer a full probability distribution over the possible parameter values. The observed data are again usually taken to be the alignment, although strictly speaking it would be more reasonable to say that the sequences are what have been observed, and that the alignment should then be inferred jointly with the phylogeny.

22115 - Recent changes [en]

Model selection

Bayesian Phylogeny

Windows software installation

Linux software installation

MacOS software installation

Bayesian Phylogeny