8,428 research outputs found
An alternative marginal likelihood estimator for phylogenetic models
Bayesian phylogenetic methods are generating noticeable enthusiasm in the
field of molecular systematics. Many phylogenetic models are often at stake and
different approaches are used to compare them within a Bayesian framework. The
Bayes factor, defined as the ratio of the marginal likelihoods of two competing
models, plays a key role in Bayesian model selection. We focus on an
alternative estimator of the marginal likelihood whose computation is still a
challenging problem. Several computational solutions have been proposed none of
which can be considered outperforming the others simultaneously in terms of
simplicity of implementation, computational burden and precision of the
estimates. Practitioners and researchers, often led by available software, have
privileged so far the simplicity of the harmonic mean estimator (HM) and the
arithmetic mean estimator (AM). However it is known that the resulting
estimates of the Bayesian evidence in favor of one model are biased and often
inaccurate up to having an infinite variance so that the reliability of the
corresponding conclusions is doubtful. Our new implementation of the
generalized harmonic mean (GHM) idea recycles MCMC simulations from the
posterior, shares the computational simplicity of the original HM estimator,
but, unlike it, overcomes the infinite variance issue. The alternative
estimator is applied to simulated phylogenetic data and produces fully
satisfactory results outperforming those simple estimators currently provided
by most of the publicly available software
RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.
Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]
Differential Evolution Markov Chain with snooker updater and fewer chains
Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t 3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the mode
Parallel Tempering with Equi-Energy Moves
The Equi-Energy Sampler (EES) introduced by Kou et al [2006] is based on a
population of chains which are updated by local moves and global moves, also
called equi-energy jumps. The state space is partitioned into energy rings, and
the current state of a chain can jump to a past state of an adjacent chain that
has energy level close to its level. This algorithm has been developed to
facilitate global moves between different chains, resulting in a good
exploration of the state space by the target chain. This method seems to be
more efficient than the classical Parallel Tempering (PT) algorithm. However it
is difficult to use in combination with a Gibbs sampler and it necessitates
increased storage. In this paper we propose an adaptation of this EES that
combines PT with the principle of swapping between chains with same levels of
energy. This adaptation, that we shall call Parallel Tempering with Equi-Energy
Moves (PTEEM), keeps the original idea of the EES method while ensuring good
theoretical properties, and practical implementation even if combined with a
Gibbs sampler. Performances of the PTEEM algorithm are compared with those of
the EES and of the standard PT algorithms in the context of mixture models, and
in a problem of identification of gene regulatory binding motifs
Efficiency Analysis of Swarm Intelligence and Randomization Techniques
Swarm intelligence has becoming a powerful technique in solving design and
scheduling tasks. Metaheuristic algorithms are an integrated part of this
paradigm, and particle swarm optimization is often viewed as an important
landmark. The outstanding performance and efficiency of swarm-based algorithms
inspired many new developments, though mathematical understanding of
metaheuristics remains partly a mystery. In contrast to the classic
deterministic algorithms, metaheuristics such as PSO always use some form of
randomness, and such randomization now employs various techniques. This paper
intends to review and analyze some of the convergence and efficiency associated
with metaheuristics such as firefly algorithm, random walks, and L\'evy
flights. We will discuss how these techniques are used and their implications
for further research.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:1212.0220, arXiv:1208.0527, arXiv:1003.146
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