Nial Friel

Classical model selection via simulated annealing

Summary. The classical approach to statistical analysis is usually based upon finding values for model parameters that maximize the likelihood function. Model choice in this context is often also based on the likelihood function, but with the addition of a penalty term for the number of parameters. Though models may be compared pairwise by using likelihood ratio tests for example, various criteria such as the Akaike information criterion have been proposed as alternatives when multiple models need to be compared. In practical terms, the classical approach to model selection usually involves maximizing the likelihood function associated with each competing model and then calculating the corresponding criteria value(s). However, when large numbers of models are possible, this quickly becomes infeasible unless a method that simultaneously maximizes over both parameter and model space is available. We propose an extension to the traditional simulated annealing algorithm that allows for moves that not only change parameter values but also move between competing models. This transdimensional simulated annealing algorithm can therefore be used to locate models and parameters that minimize criteria such as the Akaike information criterion, but within a single algorithm, removing the need for large numbers of simulations to be run. We discuss the implementation of the transdimensional simulated annealing algorithm and use simulation studies to examine its performance in realistically complex modelling situations. We illustrate our ideas with a pedagogic example based on the analysis of an autoregressive time series and two more detailed examples: one on variable selection for logistic regression and the other on model selection for the analysis of integrated recapture–recovery data.

Bayesian inference in hidden Markov random fields for binary data defined on large lattices.

Hidden Markov random fields represent a complex hierarchical model, where the hidden latent process is an undirected graphical structure. Performing inference for such models is difficult primarily because the likelihood of the hidden states is often unavailable. The main contribution of this article is to present approximate methods to calculate the likelihood for large lattices based on exact methods for smaller lattices. We introduce approximate likelihood methods by relaxing some of the dependencies in the latent model, and also by extending tractable approximations to the likelihood, the so-called pseudolikelihood approximations, for a large lattice partitioned into smaller sublattices. Results are presented based on simulated data as well as inference for the temporal-spatial structure of the interaction between up- and down-regulated states within the mitochondrial chromosome of the Plasmodium falciparum organism. Supplemental material for this article is available online.

Sequencing and analysis of an Irish human genome

BackgroundRecent studies generating complete human sequences from Asian, African and European subgroups have revealed population-specific variation and disease susceptibility loci. Here, choosing a DNA sample from a population of interest due to its relative geographical isolation and genetic impact on further populations, we extend the above studies through the generation of 11-fold coverage of the first Irish human genome sequence.ResultsUsing sequence data from a branch of the European ancestral tree as yet unsequenced, we identify variants that may be specific to this population. Through comparisons with HapMap and previous genetic association studies, we identified novel disease-associated variants, including a novel nonsense variant putatively associated with inflammatory bowel disease. We describe a novel method for improving SNP calling accuracy at low genome coverage using haplotype information. This analysis has implications for future re-sequencing studies and validates the imputation of Irish haplotypes using data from the current Human Genome Diversity Cell Line Panel (HGDP-CEPH). Finally, we identify gene duplication events as constituting significant targets of recent positive selection in the human lineage.ConclusionsOur findings show that there remains utility in generating whole genome sequences to illustrate both general principles and reveal specific instances of human biology. With increasing access to low cost sequencing we would predict that even armed with the resources of a small research group a number of similar initiatives geared towards answering specific biological questions will emerge.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution

Efficient calculation of the normalizing constant of the autologistic and related models on the cylinder and lattice

\pi

Tuning tempered transitions

π by simulating a Markov chain with transition kernel

A new thresholding technique based on random sets

P