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

Experiments to determine the complete 3-dimensional structures of protein complexes are difficult to perform and only a limited range of such structures are available In contrast, large-scale screening experiments have identified thousands of pairwise interactions between proteins, but such experiments do not produce explicit structural information In addition, the data produced by these high through-put experiments contain large numbers of false positive results, and can be biased against detection of certain types of interaction Several methods exist that analyse such pairwise interaction data in terms of the constituent domains within proteins, scoring pairs of domain superfamilies according to their propensity to interact These scores can be used to predict the strongest domain-domain contact (the contact with the largest surface area) between interacting proteins for which the domain-level structures of the individual proteins are known We test this predictive approach on a set of pairwise protein interactions taken from the Protein Quaternary Structure (PQS) database for which the true domain-domain contacts are known ∗The authors would like to thank Emmanuel Levy of the MRC Laboratory of Molecular Biology for his help preparing this manuscript While the overall prediction success rate across the whole test data set is poor, we shown how interactions in the test data set for which the training data are not informative can be automatically excluded from the prediction process, giving improved prediction success rates at the expense of restricted coverage of the test data

Statistical Applications in Genetics and Molecular Biology

Do protein structures evolve around ‘anchor’ residues?

doi:10.1182/blood-2004-12-4642Prepublished online April 12, 2005;2005 106: 1003-1007€€€€Erber, Mark Bower, Brian Gazzard, Richard I. Christopherson and Mike A. ScottStephen P. Mulligan, Larissa Belov, Jeremy S. Chrisp, Will Errington, Adrian Wildfire, Wendy N. Adrian Woolfson, Justin Stebbing, Brian D. M. Tom, Kerryn J. Stoner, Walter R. Gilks, David P. Kreil,€

infected individuals - Conservation of unique cell-surface CD antigen mosaics in HIV-1

Phylogenetic trees describe evolutionary relationships between related organisms (taxa). One approach to estimating phylogenetic trees supposes that a matrix of estimated evolutionary distances between taxa is available. Agglomerative methods have been proposed in which closely related taxon-pairs are successively combined to form ancestral taxa. Several of these computationally efficient agglomerative algorithms involve steps to reduce the variance in estimated distances. We propose an agglomerative phylogenetic method which focuses on statistical modeling of variance components in distance estimates. We consider how these variance components evolve during the agglomerative process. Our method simultaneously produces two topologically identical rooted trees, one tree having branch lengths proportional to elapsed time, and the other having branch lengths proportional to underlying evolutionary divergence. The method models two major sources of variation which have been separately discussed in the literature: noise, reflecting inaccuracies in measuring divergences, and distortion, reflecting randomness in the amounts of divergence in different parts of the tree. The methodology is based on successive hierarchical generalized least-squares regressions. It involves only means, variances and covariances of distance estimates, thereby avoiding full distributional assumptions. Exploitation of the algebraic structure of the estimation leads to an algorithm with computational complexity comparable to the leading published agglomerative methods. A parametric bootstrap procedure allows full uncertainty in the phylogenetic reconstruction to be assessed. Software implementing the methodology may be freely downloaded from StatTree.

A Variance-Components Model for Distance-Matrix Phylogenetic Reconstruction

Abstract We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between the target density and a user-specified initial density, and exploits both wavelet theory and survival analysis. In practice, WMC can process only a finite range of wavelet scales. We prove that the resulting $$L_1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> approximation error converges to zero geometrically as the scale range tends to $$(-\infty ,+\infty )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>-</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>,</mml:mo> <mml:mo>+</mml:mo> <mml:mi>∞</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . This provides a principled approach to trading off accuracy against computational efficiency. We offer practical suggestions for addressing some issues of implementation, but further development is needed for a computationally efficient methodology. We illustrate the methodology in one- and two-dimensional examples, and discuss challenges and opportunities for application in higher dimensions. 

/pdf/wavelet-monte-carlo-a-principle-for-sampling-from-complex-1ripavmo.pdf

Walter R. Gilks

Papers

Statistical Applications in Genetics and Molecular Biology

Do protein structures evolve around ‘anchor’ residues?

infected individuals - Conservation of unique cell-surface CD antigen mosaics in HIV-1

A Variance-Components Model for Distance-Matrix Phylogenetic Reconstruction

Wavelet Monte Carlo: a principle for sampling from complex distributions