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

Third international workshop on lung tumor and differentiation antigens : overview of the results of the central data analysis

We describe Bayesian hierarchical-spatial models for disease mapping with imprecisely observed ecological covariates. We posit smoothing priors for both the disease submodel and the covariate submodel. We apply the models to an analysis of insulin Dependent Diabetes Mellitus incidence in Sardinia, with malaria prevalence as a covariate.

Disease mapping with errors in covariates.

Model checking and model improvement

Motivation: Several methods have recently been developed to analyse large-scale sets of physical interactions between proteins in terms of physical contacts between the constituent domains, often with a view to predicting new pairwise interactions. Our aim is to combine genomic interaction data, in which domain--domain contacts are not explicitly reported, with the domain-level structure of individual proteins, in order to learn about the structure of interacting protein pairs. Our approach is driven by the need to assess the evidence for physical contacts between domains in a statistically rigorous way.

Results: We develop a statistical approach that assigns p-values to pairs of domain superfamilies, measuring the strength of evidence within a set of protein interactions that domains from these superfamilies form contacts. A set of p-values is calculated for SCOP superfamily pairs, based on a pooled data set of interactions from yeast. These p-values can be used to predict which domains come into contact in an interacting protein pair. This predictive scheme is tested against protein complexes in the Protein Quaternary Structure (PQS) database, and is used to predict domain--domain contacts within 705 interacting protein pairs taken from our pooled data set.

Contact: thomas.nye@mrc-bsu.cam.ac.uk

https://www.mrc-lmb.cam.ac.uk/genomes/mkayikci/MendeleyMadanPapers/2005_Bioinformatics%20(Oxford,%20England)_Nye%20et%20al._Statistical%20analysis%20of%20domains%20in%20interacting%20protein%20pairs.pdf

Walter R. Gilks

Papers

Third international workshop on lung tumor and differentiation antigens : overview of the results of the central data analysis

Disease mapping with errors in covariates.

Model checking and model improvement

Statistical analysis of domains in interacting protein pairs

Defining a genomic radius for long-range enhancer action: duplicated conserved non-coding elements hold the key