Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

An Introduction to RevBayes and Graphical Models

1,400 views

Published on

An introduction to the Bayesian phylogenetics software program RevBayes. Tutorials for RevBayes can be found at http://revbayes.github.io/

Edited July 20, 2016

Published in: Science
  • Be the first to comment

An Introduction to RevBayes and Graphical Models

  1. 1. I  P I  RB Tracy A. Heath Iowa State University @trayc7 Michael J. Landis Yale University @landismj 2016 Workshop on Molecular Evolution Woods Hole, MA
  2. 2. O Overview – Heath Introduction to RevBayes • Motivation • Probabilistic graphical models • The Rev language and demo short break Demo & Tutorial – Landis Phylogenetic reconstruction in RevBayes • Demo: tree reconstruction using MCMC under JC • Tutorial (on your own): specify the HKY model, sample using MCMC, summarize the tree beer(s)
  3. 3. C  S P Prior options in MrBayes v3.2
  4. 4. C  S P Prior options in MrBayes v3.2
  5. 5. M B P S Several software packages in phylogenetics are moving toward a more modular framework • reuse code • easier to extend existing models and implement new models through a rich, language-based interface • provides a unified framework for analyses under complex models RevBayes Bali-Phy BEAST2
  6. 6. RB Höhna et al. 2016. RevBayes: Bayesian phylogenetic inference using graphical models and an interactive model-specification language. Systematic Biology. (doi: 10.1093/sysbio/syw021) http://revbayes.com Development team Höhna Lartillot Huelsenbeck Ronquist Landis Heath Boussau & others... (Höhna et al. 2016. Systematic Biology, 65:726-736.)
  7. 7. G M  RB Graphical models provide tools for visually & computationally representing complex, parameter-rich probabilistic models We can depict the conditional dependence structure of various parameters and other random variables Höhna, Heath, Boussau, Landis, Ronquist, Huelsenbeck. 2014. Probabilistic Graphical Model Representation in Phylogenetics. Systematic Biology. (doi: 10.1093/sysbio/syu039)
  8. 8. M  C V What is the distribution of heights in a population of penguins? 4.098 2.867 3.756 1.693 3.251 2.516 3.998 2.606 2.744 3.463 4.20 3.058 4.559 3.55 2.852 (silhouette from http://phylopic.org/)
  9. 9. M  C V To estimate the distribution of a variable (like the heights of all individuals within a population of penguins), we need a prior model of that parameter For a parameter like height, we want a distribution with properties that match our biological knowledge 3.756 The Lognormal distribution is an asymmetric probability distribution on positive values (silhouette from http://phylopic.org/)
  10. 10. T L D A variable that is lognormally distributed matches a normal distribution when on a log scale χ ∼ LN(μ,σ) log(χ) ∼ Norm(μ,σ) 3.756 χ must be a positive real number & is the product of a large number of independent, identically-distributed variables (silhouette from http://phylopic.org/)
  11. 11. T L D 0 1 2 3 4 5 6 7 8 mean = exp(µ + σ/2) mean = 1.11 mean = 1.29 mean = 1.65 Density Variable σ=0.2, µ=0 σ=0.5, µ=0 σ=1.0, µ=0
  12. 12. T L D 0 1 2 3 4 5 6 7 8 Density Variable σ=0.2, µ=0 σ=0.5, µ=0 σ=1.0, µ=0 σ=0.2, µ=1 σ=0.5, µ=1 σ=1.0, µ=1
  13. 13. M  C V 3.756 (silhouette from http://phylopic.org/)
  14. 14. M  C V 3.756 (silhouette from http://phylopic.org/)
  15. 15. M  C V 3.756 (silhouette from http://phylopic.org/)
  16. 16. M  C V 3.756 4.098 2.867 3.756 1.693 3.251 2.516 3.998 2.606 2.744 3.463 4.20 3.058 4.559 3.55 2.852 (silhouette from http://phylopic.org/)
  17. 17. G M  RB
  18. 18. G M  RB
  19. 19. G M  RB
  20. 20. G M  RB
  21. 21. G M  RB Defining the model in the Rev language xi µ observations = [<your data go here>]
  22. 22. G M  RB Defining the model in the Rev language xi µ M α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0
  23. 23. G M  RB Defining the model in the Rev language xi µ M α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta)
  24. 24. G M  RB Defining the model in the Rev language xi µ σ M λ α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta) lambda <- 1.0
  25. 25. G M  RB Defining the model in the Rev language xi µ σ M λ α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta) lambda <- 1.0 sigma ∼ dnExponential(lambda)
  26. 26. G M  RB Defining the model in the Rev language xi µ σ M λ α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta) lambda <- 1.0 sigma ∼ dnExponential(lambda) mu := ln(M) - (power(sigma, 2.0) / 2.0)
  27. 27. G M  RB Defining the model in the Rev language xi µ σ M i ∈ N λ α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta) lambda <- 1.0 sigma ∼ dnExponential(lambda) mu := ln(M) - (power(sigma, 2.0) / 2.0) N <- observations.size() for( i in 1:N ){ x[i] ∼ dnLnorm(mu, sigma) }
  28. 28. G M  RB Defining the model in the Rev language xi µ σ M i ∈ N λ α β observations = [<your data go here>] alpha <- 3.0 beta <- 1.0 M ∼ dnGamma(alpha, beta) lambda <- 1.0 sigma ∼ dnExponential(lambda) mu := ln(M) - (power(sigma, 2.0) / 2.0) N <- observations.size() for( i in 1:N ){ x[i] ∼ dnLnorm(mu, sigma) x[i].clamp(observations[i]) }
  29. 29. RB D: A S M Use MCMC to approximate the posterior distributions of stochastic and deterministic variables
  30. 30. RB http://revbayes.com • Downloads • Tutorials • Help documentation • User forum • Source code: https://github.com/revbayes/revbayes
  31. 31. I B M  RB

×