We describe a model-based clustering method for using multilocus genotype data to infer population structure and assign individuals to populations. We assume a model in which there are K populations (where K may be unknown), each of which is characterized by a set of allele frequencies at each locus. Individuals in the sample are assigned (probabilistically) to populations, or jointly to two or more populations if their genotypes indicate that they are admixed. Our model does not assume a particular mutation process, and it can be applied to most of the commonly used genetic markers, provided that they are not closely linked. Applications of our method include demonstrating the presence of population structure, assigning individuals to populations, studying hybrid zones, and identifying migrants and admixed individuals. We show that the method can produce highly accurate assignments using modest numbers of loci— e.g. , seven microsatellite loci in an example using genotype data from an endangered bird species. The software used for this article is available from http://www.stats.ox.ac.uk/~pritch/home.html.

/pdf/inference-of-population-structure-using-multilocus-genotype-1x75ku6urs.pdf

Inference of population structure using multilocus genotype data

The Gibbs sampler, the algorithm of Metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give misleading answers. Our methods are simple and generally applicable to the output of any iterative simulation; they are designed for researchers primarily interested in the science underlying the data and models they are analyzing, rather than for researchers interested in the probability theory underlying the iterative simulations themselves. Our recommended strategy is to use several independent sequences, with starting points sampled from an overdispersed distribution. At each step of the iterative simulation, we obtain, for each univariate estimand of interest, a distributional estimate and an estimate of how much sharper the distributional estimate might become if the simulations were continued indefinitely. Because our focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normality after transformations and marginalization, we derive our results as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations. The methods are illustrated on a random-effects mixture model applied to experimental measurements of reaction times of normal and schizophrenic patients.

/pdf/inference-from-iterative-simulation-using-multiple-sequences-f65bwr81f3.pdf

Inference from Iterative Simulation Using Multiple Sequences

Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.

/pdf/bayesian-measures-of-model-complexity-and-fit-1ouzmtfu7x.pdf

Bayesian measures of model complexity and fit

Increasingly, for many application areas, it is becoming important to include elements of nonlinearity and non-Gaussianity in order to model accurately the underlying dynamics of a physical system. Moreover, it is typically crucial to process data on-line as it arrives, both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics. In this paper, we review both optimal and suboptimal Bayesian algorithms for nonlinear/non-Gaussian tracking problems, with a focus on particle filters. Particle filters are sequential Monte Carlo methods based on point mass (or "particle") representations of probability densities, which can be applied to any state-space model and which generalize the traditional Kalman filtering methods. Several variants of the particle filter such as SIR, ASIR, and RPF are introduced within a generic framework of the sequential importance sampling (SIS) algorithm. These are discussed and compared with the standard EKF through an illustrative example.

/pdf/a-tutorial-on-particle-filters-for-online-nonlinear-non-1rzkwgk2pp.pdf

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking

Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

/pdf/information-theory-inference-and-learning-algorithms-gbv6i2zu22.pdf

Information Theory, Inference and Learning Algorithms

A total of 3653 first cadaver kidney transplants in nondiabetic recipients over 15 years of age, performed in 30 transplant centers throughout the United Kingdom between 1978 and 1983, were analyzed to discover which of many recorded recipient, donor, surgical, and tissue-matching variables were important for graft survival, and in which postoperative period they exerted their maximum influence. A considerable effort was invested in checking the validity of the data and the appropriateness of the statistical methods. The duration of dialysis prior to transplantation was associated with a substantially reduced risk of graft failure, particularly at later postoperative times. Good HLA-B locus matching was also found to enhance graft survival--but, by contrast, HLA-A locus matching showed no significant effect on survival. Recipient age over 45 years, high serum reactivity, and grafts with anoxia time (the interval between circulatory arrest and perfusion with ice) exceeding 10 min were found to be associated with poor graft survival. Trends in survival were identified across calendar years of transplant, such that early graft failure (0-15 days) had increased in recent years, whereas later graft failure (greater than 15 days) had declined.

Immunogenetic and clinical factors affecting renal transplantation. A rigorous analysis of data recorded by the UK Transplant Service.

One of the main goals of analysing DNA sequences is to understand the temporal and positional information that specifies gene expression. An important step in this process is the recognition of gene expression regulatory elements. Experimental procedures for this are slow and costly. In this paper we present a computational non-supervised algorithm that facilitates the process by statistically identifying the most likely regions within a putative regulatory sequence. A probabilistic technique is presented, based on the approximation of regulatory DNA with a Markov chain, for the location of putative transcription factor binding sites in a single stretch of DNA. Hereto we developed a procedure to approximate the order of Markov model for a given DNA sequence that circumvents some of the prohibitive assumptions underlying Markov modeling. Application of the algorithm to data from 55 genes in five species shows the high sensitivity of this Markov search algorithm. Our algorithm does not require any prior knowledge in the form of description or cross-genomic comparison; it is context sensitive and takes DNA heterogeneity into account.

Transcription binding site prediction using markov models

This paper reviews recent computational approaches to the understanding of gene regulation in eukaryotes. Cis-regulation of gene expression by the binding of transcription factors is a critical component of cellular physiology. In eukaryotes, a number of transcription factors often work together in a combinatorial fashion to enable cells to respond to a wide spectrum of environmental and developmental signals. Integration of genome sequences and/or Chromatin Immunoprecipitation on chip data with gene-expression data has facilitated in silico discovery of how the combinatorics and positioning of transcription factors binding sites underlie gene activation in a variety of cellular processes.The process of gene regulation is extremely complex and intriguing, therefore all possible points of view and related links should be carefully considered. Here we attempt to collect an inventory, not claiming it to be comprehensive and complete, of related computational biological topics covering gene regulation, which may en-lighten the process, and briefly review what is currently occurring in these areas.We will consider the following computational areas:o gene regulatory network construction;o evolution of regulatory DNA;o studies of its structural and statistical informational properties;o and finally, regulatory RNA.

Recent computational approaches to understand gene regulation: mining gene regulation in silico.

Particle filtering methods for dynamic and static Bayesian problems

Experiments to determine the complete 3-dimensional structures ofprotein complexes are difficult to perform and only a limited range of suchstructures are available.In contrast, large-scale screening experiments haveidentified thousands of pairwise interactions between proteins, but suchexperiments do not produce explicit structural information. In addition, thedata produced by these high through-put experiments contain large numbers offalse positive results, and can be biased against detection of certain typesof interaction.Several methods exist that analyse such pairwise interactiondata in terms of the constituent domains within proteins, scoring pairs ofdomain superfamilies according to their propensity to interact. These scorescan be used to predict the strongest domain-domain contact (the contact withthe largest surface area) between interacting proteins for which the domain-levelstructures of the individual proteins are known.We test this predictive approachon a set of pairwise protein interactions taken from the Protein QuaternaryStructure (PQS) database for which the true domain-domain contacts are known.While the overall prediction success rate across the whole test data set ispoor, we shown how interactions in the test data set for which the trainingdata are not informative can be automatically excluded from the predictionprocess, giving improved prediction success rates at the expense ofrestricted coverage of the test data.

/pdf/predicting-the-strongest-domain-domain-contact-in-3us9d8ipep.pdf

Walter R. Gilks

Papers

Immunogenetic and clinical factors affecting renal transplantation. A rigorous analysis of data recorded by the UK Transplant Service.

Transcription binding site prediction using markov models

Recent computational approaches to understand gene regulation: mining gene regulation in silico.

Particle filtering methods for dynamic and static Bayesian problems

Predicting the strongest domain-domain contact in interacting protein pairs.