Non-linear regression models for Approximate Bayesian Computation

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the curse of dimensionality when the number of summary statistics is increased. Here we propose a machine-learning approach to the estimation of the posterior density by introducing two innovations. The new method fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics, and then adaptively improves estimation using importance sampling. The new algorithm is compared to the state-of-the-art approximate Bayesian methods, and achieves considerable reduction of the computational burden in two examples of inference in statistical genetics and in a queueing model.Comment: 4 figures; version 3 minor changes; to appear in Statistics and Computin

How Fitch-Margoliash Algorithm can Benefit from Multi Dimensional Scaling

Whatever the phylogenetic method, genetic sequences are often described as strings of characters, thus molecular sequences can be viewed as elements of a multi-dimensional space. As a consequence, studying motion in this space (ie, the evolutionary process) must deal with the amazing features of high-dimensional spaces like concentration of measured phenomenon

The genetic code can cause systematic bias in simple phylogenetic models

Phylogenetic analysis depends on inferential methodology estimating accurately the degree of divergence between sequences. Inaccurate estimates can lead to misleading evolutionary inferences, including incorrect tree topology estimates and poor dating of historical species divergence. Protein coding sequences are ubiquitous in phylogenetic inference, but many of the standard methods commonly used to describe their evolution do not explicitly account for the dependencies between sites in a codon induced by the genetic code. This study evaluates the performance of several standard methods on datasets simulated under a simple substitution model, describing codon evolution under a range of different types of selective pressures. This approach also offers insights into the relative performance of different phylogenetic methods when there are dependencies acting between the sites in the data. Methods based on statistical models performed well when there was no or limited purifying selection in the simulated sequences (low degree of dependency between sites in a codon), although more biologically realistic models tended to outperform simpler models. Phylogenetic methods exhibited greater variability in performance for sequences simulated under strong purifying selection (high degree of the dependencies between sites in a codon). Simple models substantially underestimate the degree of divergence between sequences, and underestimation was more pronounced on the internal branches of the tree. This underestimation resulted in some statistical methods performing poorly and exhibiting evidence for systematic bias in tree inference. Amino acid-based and nucleotide models that contained generic descriptions of spatial and temporal heterogeneity, such as mixture and temporal hidden Markov models, coped notably better, producing more accurate estimates of evolutionary divergence and the tree topology

A likelihood ratio test for species membership based on DNA sequence data

DNA barcoding as an approach for species identification is rapidly increasing in popularity. However, it remains unclear which statistical procedures should accompany the technique to provide a measure of uncertainty. Here we describe a likelihood ratio test which can be used to test if a sampled sequence is a member of an a priori specified species. We investigate the performance of the test using coalescence simulations, as well as using the real data from butterflies and frogs representing two kinds of challenge for DNA barcoding: extremely low and extremely high levels of sequence variability

Using the quantitative genetic threshold model for inferences between and within species

Sewall Wright's threshold model has been used in modelling discrete traits that may have a continuous trait underlying them, but it has proven difficult to make efficient statistical inferences with it. The availability of Markov chain Monte Carlo (MCMC) methods makes possible likelihood and Bayesian inference using this model. This paper discusses prospects for the use of the threshold model in morphological systematics to model the evolution of discrete all-or-none traits. There the threshold model has the advantage over 0/1 Markov process models in that it not only accommodates polymorphism within species, but can also allow for correlated evolution of traits with far fewer parameters that need to be inferred. The MCMC importance sampling methods needed to evaluate likelihood ratios for the threshold model are introduced and described in some detail