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Full Likelihood (full + likelihood)

Distribution by Scientific Domains
Mathematics and Statistics100%

Selected Abstracts

Inference in molecular population genetics

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2000
Matthew Stephens
Full likelihood-based inference for modern population genetics data presents methodological and computational challenges. The problem is of considerable practical importance and has attracted recent attention, with the development of algorithms based on importance sampling (IS) and Markov chain Monte Carlo (MCMC) sampling. Here we introduce a new IS algorithm. The optimal proposal distribution for these problems can be characterized, and we exploit a detailed analysis of genealogical processes to develop a practicable approximation to it. We compare the new method with existing algorithms on a variety of genetic examples. Our approach substantially outperforms existing IS algorithms, with efficiency typically improved by several orders of magnitude. The new method also compares favourably with existing MCMC methods in some problems, and less favourably in others, suggesting that both IS and MCMC methods have a continuing role to play in this area. We offer insights into the relative advantages of each approach, and we discuss diagnostics in the IS framework. [source]

Linkage Disequilibrium Mapping of Disease Susceptibility Genes in Human Populations

INTERNATIONAL STATISTICAL REVIEW, Issue 1 2000
David Clayton
Summary The paper reviews recent work on statistical methods for using linkage disequilibrium to locate disease susceptibility genes, given a set of marker genes at known positions in the genome. The paper starts by considering a simple deterministic model for linkage disequilibrium and discusses recent attempts to elaborate it to include the effects of stochastic influences, of "drift", by the use of either Writht-Fisher models or by approaches based on the coalescence of the genealogy of the sample of disease chromosomes. Most of this first part of the paper concerns a series of diallelic markers and, in this case, the models so far proposed are hierarchical probability models for multivariate binary data. Likelihoods are intractable and most approaches to linkage disequilibrium mapping amount to marginal models for pairwise associations between individual markers and the disease susceptibility locus. Approaches to evalutation of a full likelihood require Monte Carlo methods in order to integrate over the large number of unknowns. The fact that the initial state of the stochastic process which has led to present-day allele frequencies is unknown is noted and its implications for the hierarchical probability model is discussed. Difficulties and opportunities arising as a result of more polymorphic markers and extended marker haplotypes are indicated. Connections between the hierarchical modelling approach and methods based upon identity by descent and haplotype sharing by seemingly unrelated case are explored. Finally problems resulting from unknown modes of inheritance, incomplete penetrance, and "phenocopies" are briefly reviewed. Résumé Ce papier est une revue des travaux récents, protant sur les méthodes statistiques qui utilisent I'étude, des liaisons désé, quilib rées, pour identifer les génes, de susceptibilité des maladies,ápartir d'une série, de marqueurs de géncs á des positions définies du génome,. Le papier commence par considérer, un modéle, détéministe, simple pour liaisons déséquilibr,ées, puis nous discutons les améliorations, ré centes proposées, de ce modéle, dans but de tenir compte des effects des influences stochastiques soit en utilisant les modéles, de wright-fisher, soit par des approches basées, sur la coalescence de la géné alogic de I'échantillon, des chromosomes malades. La plupart de cette premiére, partie porte sur une série, de marqueurs dialléliques et, dans ce cas, les modéles, proposés, sont des modéles, hiérerchiques, probabilistes pour dinnées, binaires multivariées. Les viaisemblances n'ont pas de forme analytique et la plupart des approches pour la cartographie des liaisons déséquilibrées, sont équivalentes aux modéles, marginaux pour dinnées, appariées, entre des marqueurs individuels et le géne, de susceptibilité de la maladie.Pour évaluer, la vriausemblance compléte, des méthodes de Monte carlo sont nécessaires, afin d'intégrer, le large nombre d; inconnues. Le fait que l'état, initial du process stochastique qui a conduit éla fré, quence, allélique, actuel soit inconnu est á noter et ses implications pour le modéle, hiérarchique, probabiliste sont discutées.Les difficultés, et implications issues de marqueurs polumorphiques et de marquers haplotypes sont dévéloppées.Les liens entire l'approche de modélisation, hiérerchique, et les méthodes, d'analyse d'identite pardescendance et les haplotypes partagés, par des cas apparement non apparentés, sont explorés. Enfin les problémes, relatifs à des modes de transmission inconnus,à des pénétrances, incomplé, tes, et aux "phénocopies" sont briévenment evoqués. [source]

Estimating the effect of treatment in a proportional hazards model in the presence of non-compliance and contamination

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 4 2007
Jack Cuzick
Summary., Methods for adjusting for non-compliance and contamination, which respect the randomization, are extended from binary outcomes to time-to-event analyses by using a proportional hazards model. A simple non-iterative method is developed when there are no covariates, which is a generalization of the Mantel,Haenszel estimator. More generally, a ,partial likelihood' is developed which accommodates covariates under the assumption that they are independent of compliance. A key feature is that the proportion of contaminators and non-compliers in the risk set is updated at each failure time. When covariates are not independent of compliance, a full likelihood is developed and explored, but this leads to a complex estimator. Estimating equations and information matrices are derived for these estimators and they are evaluated by simulation studies. [source]

ESTIMATING COMPONENTS IN FINITE MIXTURES AND HIDDEN MARKOV MODELS

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2005
D.S. Poskitt
Summary When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests the number of states of the unobservable Markov chain can be estimated by determining the number of mixture components in the marginal distribution. This paper presents new methods for estimating the number of states in a hidden Markov model, and coincidentally the unknown number of components in a finite mixture, based on penalized quasi-likelihood and generalized quasi-likelihood ratio methods constructed from the marginal distribution. The procedures advocated are simple to calculate, and results obtained in empirical applications indicate that they are as effective as current available methods based on the full likelihood. Under fairly general regularity conditions, the methods proposed generate strongly consistent estimates of the unknown number of states or components. [source]

Partial-Likelihood Analysis of Spatio-Temporal Point-Process Data

BIOMETRICS, Issue 2 2010
Peter J. Diggle
Summary We investigate the use of a partial likelihood for estimation of the parameters of interest in spatio-temporal point-process models. We identify an important distinction between spatially discrete and spatially continuous models. We focus our attention on the spatially continuous case, which has not previously been considered. We use an inhomogeneous Poisson process and an infectious disease process, for which maximum-likelihood estimation is tractable, to assess the relative efficiency of partial versus full likelihood, and to illustrate the relative ease of implementation of the former. We apply the partial-likelihood method to a study of the nesting pattern of common terns in the Ebro Delta Natural Park, Spain. [source]

Analysis of Matched Case,Control Data in Presence of Nonignorable Missing Exposure

BIOMETRICS, Issue 1 2008
Samiran Sinha
Summary. The present article deals with informative missing (IM) exposure data in matched case,control studies. When the missingness mechanism depends on the unobserved exposure values, modeling the missing data mechanism is inevitable. Therefore, a full likelihood-based approach for handling IM data has been proposed by positing a model for selection probability, and a parametric model for the partially missing exposure variable among the control population along with a disease risk model. We develop an EM algorithm to estimate the model parameters. Three special cases: (a) binary exposure variable, (b) normally distributed exposure variable, and (c) lognormally distributed exposure variable are discussed in detail. The method is illustrated by analyzing a real matched case,control data with missing exposure variable. The performance of the proposed method is evaluated through simulation studies, and the robustness of the proposed method for violation of different types of model assumptions has been considered. [source]