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Bayesian Markov Chain (bayesian + markov_chain)
Selected AbstractsData cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methodsECOLOGY LETTERS, Issue 7 2007Subhash R. Lele Abstract We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as the maximum likelihood estimates and their standard errors. The inferences are completely invariant to the choice of the prior distributions and therefore avoid the inherent subjectivity of the Bayesian approach. The data cloning method is easily implemented using standard MCMC software. Data cloning is particularly useful for analysing ecological situations in which hierarchical statistical models, such as state-space models and mixed effects models, are appropriate. We illustrate the method by fitting two nonlinear population dynamics models to data in the presence of process and observation noise. [source] Spatio-temporal point process filtering methods with an applicationENVIRONMETRICS, Issue 3-4 2010ena Frcalová Abstract The paper deals with point processes in space and time and the problem of filtering. Real data monitoring the spiking activity of a place cell of hippocampus of a rat moving in an environment are evaluated. Two approaches to the modelling and methodology are discussed. The first one (known from literature) is based on recursive equations which enable to describe an adaptive system. Sequential Monte Carlo methods including particle filter algorithm are available for the solution. The second approach makes use of a continuous time shot-noise Cox point process model. The inference of the driving intensity leads to a nonlinear filtering problem. Parametric models support the solution by means of the Bayesian Markov chain Monte Carlo methods, moreover the Cox model enables to detect adaptivness. Model selection is discussed, numerical results are presented and interpreted. Copyright © 2009 John Wiley & Sons, Ltd. [source] Low level of gene flow from cultivated beets (Beta vulgaris L. ssp. vulgaris) into Danish populations of sea beet (Beta vulgaris L. ssp. maritima (L.) Arcangeli)MOLECULAR ECOLOGY, Issue 5 2005N. S. ANDERSEN Abstract Gene flow from sugar beets to sea beets occurs in the seed propagation areas in southern Europe. Some seed propagation also takes place in Denmark, but here the crop,wild gene flow has not been investigated. Hence, we studied gene flow to sea beet populations from sugar beet lines used in Danish seed propagation areas. A set of 12 Danish, two Swedish, one French, one Italian, one Dutch, and one Irish populations of sea beets, and four lines of sugar beet were analysed. To evaluate the genetic variation and gene flow, eight microsatellite loci were screened. This analysis revealed hybridization with cultivated beet in one of the sea beet populations from the centre of the Danish seed propagation area. Triploid hybrids found in this population were verified with flow cytometry. Possible hybrids or introgressed plants were also found in the French and Italian populations. However, individual assignment test using a Bayesian method provided 100% assignment success of diploid individuals into their correct subspecies of origin, and a Bayesian Markov chain Monte Carlo (MC MC) approach revealed clear distinction of individuals into groups according to their subspecies of origin, with a zero level of genetic admixture among subspecies. This underlines that introgression beyond the first hybridization is not extensive. The overall pattern of genetic distance and structure showed that Danish and Swedish sea beet populations were closely related to each other, and they are both more closely related to the population from Ireland than to the populations from France, the Netherlands, and Italy. [source] SCALE MIXTURES DISTRIBUTIONS IN STATISTICAL MODELLINGAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2008S.T. Boris Choy Summary This paper presents two types of symmetric scale mixture probability distributions which include the normal, Student t, Pearson Type VII, variance gamma, exponential power, uniform power and generalized t (GT) distributions. Expressing a symmetric distribution into a scale mixture form enables efficient Bayesian Markov chain Monte Carlo (MCMC) algorithms in the implementation of complicated statistical models. Moreover, the mixing parameters, a by-product of the scale mixture representation, can be used to identify possible outliers. This paper also proposes a uniform scale mixture representation for the GT density, and demonstrates how this density representation alleviates the computational burden of the Gibbs sampler. [source] Survival of Bowhead Whales, Balaena mysticetus, Estimated from 1981,1998 Photoidentification DataBIOMETRICS, Issue 4 2002Judith Zeh Summary. Annual survival probability of bowhead whales, Balaena mysticetus, was estimated using both Bayesian and maximum likelihood implementations of Cormack and Jolly-Seber (JS) models for capture-recapture estimation in open populations and reduced-parameter generalizations of these models. Aerial photographs of naturally marked bowheads collected between 1981 and 1998 provided the data. The marked whales first photographed in a particular year provided the initial ,capture' and ,release' of those marked whales and photographs in subsequent years the ,recaptures'. The Cormack model, often called the Cormack-Jolly-Seber (CJS) model, and the program MARK were used to identify the model with a single survival and time-varying capture probabilities as the most appropriate for these data. When survival was constrained to be one or less, the maximum likelihood estimate computed by MARK was one, invalidating confidence interval computations based on the asymptotic standard error or profile likelihood. A Bayesian Markov chain Monte Carlo (MCMC) implementation of the model was used to produce a posterior distribution for annual survival. The corresponding reduced-parameter JS model was also fit via MCMC because it is the more appropriate of the two models for these photoidentification data. Because the CJS model ignores much of the information on capture probabilities provided by the data, its results are less precise and more sensitive to the prior distributions used than results from the JS model. With priors for annual survival and capture probabilities uniform from 0 to 1, the posterior mean for bowhead survival rate from the JS model is 0.984, and 95% of the posterior probability lies between 0.948 and 1. This high estimated survival rate is consistent with other bowhead life history data. [source] | |||||||||||||