Lagged couplings diagnose Markov chain Monte Carlo phylogenetic inference

Bayesian phylogenetic inference via Markov chain Monte Carlo methods.

We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees cl...

Markov Chain Monte Carlo for Statistical Inference

Markov chain Monte Carlo for Bayesian inference

The chord length transform (CLT) is a useful tool to analyze fibre structures. Assuming e.g. arandom process of straight fibres then a realization of such a process can be observed in a binaryimage. The CLT maps to each point in the foreground of a binary image and to each direction thelength of the related chord, where the chord is the connecting part of a line in the direction...

Bayesian Phylogenetic Model Selection Using Reversible Jump Markov Chain Monte Carlo R.H. Substitution model selection Key words: Bayesian phylogenetic inference, Markov chain Monte Carlo, maximum likelihood, reversible jump Markov chain Monte Carlo, substitution models

A common problem in molecular phylogenetics is choosing a model of DNA substitution that does a good job of explaining the DNA sequence alignment without introducing superfluous parameters. A number of methods have been used to choose among a small set of candidate substitution models, such as the likelihood ratio test, the Akaike Information Criterion (AIC), the Bayesian Information Criterion ...

Markov Chain Monte Carlo

Markov chain Monte Carlo is an umbrella term for algorithms that use Markov chains to sample from a given probability distribution. This paper is a brief examination of Markov chain Monte Carlo and its usage. We begin by discussing Markov chains and the ergodicity, convergence, and reversibility thereof before proceeding to a short overview of Markov chain Monte Carlo and the use of mixing time...