Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Bayesian inference”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3Linked to original sources
PubMed1998

Bayesian inference of genetic parameters and selection response for litter size components in pigs.

Three contemporary lines were formed from the progeny of 50 French Large White sows. In the first line, gilts were selected for ovulation rate at puberty. In the second line, they were selected for prenatal survival of the first two parities, corrected for ovulation rate. The control constituted the third line. Ovulation rate at puberty was analyzed using an animal model with a batch effect. Prenatal survival was analyzed with a repeatability animal model that included batch and parity effects. Flat priors were used to represent vague previous knowledge about parity and batch effects. Additive and residual effects were represented assuming that they were a priori normally distributed. Variance components were assumed to follow either uniform or inverted chi-square distributions, a priori. The use of different priors did not affect the results substantially. Heritabilities for ovulation rate ranged from 0.32 to 0.39, and from 0.11 to 0.16 for prenatal survival, depending on the prior used. The mean of the marginal posterior distribution of response to four generations of selection ranged from 0.38 to 0.40 ova per generation, and from 1.1 to 1.3% of the mean survival rate for average survival per generation.

Animals↗
PubMed1999

Bayesian inference for small-sample capture-recapture data.

We consider data on the survival of a population of Cephalorhynchus hectori, Hector's dolphins, in a marine area of New Zealand. To estimate survival probabilities of animal populations, a multiple capture-recapture sampling scheme can be used. In this paper, we propose a practical methodology to derive approximations to posterior distributions based on Laplace methods. We show how to calculate Bayes estimates and credible intervals in this setting.

Animals↗
PubMed2001

Bayesian inference on protective antibody levels using case-control data.

In the study of immune responses to infectious pathogens, the minimum protective antibody concentration (MPAC) is a quantity of great interest. We use case-control data to estimate the posterior distribution of the conditional risk of disease given a lower bound on antibody concentration in an at-risk subject. The concentration bound beyond which there is high credibility that infection risk is zero or nearly so is a candidate for the MPAC. A very simple Gibbs sampling procedure that permits inference on the risk of disease given antibody level is presented. In problems involving small numbers of patients, the procedure is shown to have favorable accuracy and robustness to choice/misspecification of priors. Frequentist evaluation indicates good coverage probabilities of credibility intervals for antibody-dependent risk, and rules for estimation of the MPAC are illustrated with epidemiological data.

Antibodies↗
PubMed1996

Practical Bayesian inference using mixtures of mixtures.

Discrete mixtures of normal distributions are widely used in modeling amplitude fluctuations of electrical potentials at synapses of human and other animal nervous systems. The usual framework has independent data values yj arising as yj = mu j + xn0 + j, where the means mu j come from some discrete prior G(mu) and the unknown xno + j's and observed xj, j = 1,...,n0, are Gaussian noise terms. A practically important development of the associated statistical methods is the issue of nonnormality of the noise terms, often the norm rather than the exception in the neurological context. We have recently developed models, based on convolutions of Dirichlet process mixtures, for such problems. Explicitly, we model the noise data values xj as arising from a Dirichlet process mixture of normals, in addition to modeling the location prior G(mu) as a Dirichlet process itself. This induces a Dirichlet mixture of mixtures of normals, whose analysis may be developed using Gibbs sampling techniques. We discuss these models and their analysis, and illustrate them in the context of neurological response analysis.

Animals↗
PubMed2000

Bayesian nonparametric inference on the dose level with specified response rate.

The richness of nonparametric Bayesian models has attracted many different applications. Its application in dose-finding studies has been hindered due to lack of methodologies on the nonparametric Bayesian inference on percentiles. The primary interest in dose-finding studies focuses inference on the unknown toxicity or efficacy dose level corresponding to a prespecified rate. This paper shows how this problem may generally be handled by deriving inference on percentiles of a distribution following a Dirichlet process prior. In particular, theoretical results are derived to obtain the nonparametric Bayesian inference of the unknown dose level. This is followed by a description of the numerical implementation of that theory. The method also allows efficient estimation of the entire potency curve. Finally, the usefulness of the approach is demonstrated via an experimental data example.

Animals↗
PubMed1993

Bayesian predictive inference for units with small sample sizes. The case of binary random variables.

The National Health Interview Survey is designed to produce precise estimates for the entire United States but not for individual states. In this study, Bayesian predictive inference is used to provide point estimates and measures of variability for the desired finite population quantities. The investigation reported here concerns binary random variables such as the occurrence of at least one doctor visit within the past 12 months. The specification is hierarchic. First, for each cluster, there is a separate logistic regression relating a patient's probability of a doctor visit with his or her characteristics. Second, there is a multivariate linear regression linking the (cluster) regression parameters to covariates measured at the cluster level. A fully Bayesian analysis is carried out; this technique provides gains over synthetic estimation and conventional randomization-based analysis. The reported approach is potentially useful for any situation when the sample size associated with a unit of interest (e.g., a hospital or small geographic area) is too small to permit satisfactory inference using only the data from that unit.

Bayes Theorem↗
PubMed1997

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method.

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.

Algorithms↗
PubMed2000

Bayesian predictive inference for time series count data.

Correlated count data arise often in practice, especially in repeated measures situations or instances in which observations are collected over time. In this paper, we consider a parametric model for a time series of counts by constructing a likelihood-based version of a model similar to that of Zeger (1988, Biometrika 75, 621-629). The model has the advantage of incorporating both overdispersion and autocorrelation. We consider a Bayesian approach and propose a class of informative prior distributions for the model parameters that are useful for prediction. The prior specification is motivated from the notion of the existence of data from similar previous studies, called historical data, which is then quantified into a prior distribution for the current study. We derive the Bayesian predictive distribution and use a Bayesian criterion, called the predictive L measure, for assessing the predictions for a given time series model. The distribution of the predictive L measure is also derived, which will enable us to compare the predictive ability for each model under consideration. Our methodology is motivated by a real data set involving yearly pollen counts, which is examined in some detail.

Bayes Theorem↗
PubMed1993

Bayesian analysis of mixtures applied to post-synaptic potential fluctuations.

Bayesian inference techniques have been applied to the analysis of fluctuation of post-synaptic potentials in the hippocampus. The underlying statistical model assumes that the varying synaptic signals are characterized by mixtures of (unknown) numbers of individual gaussian, or normal, component distributions. Each solution consists of a group of individual components with unique mean values and relative probabilities of occurrence and a predictive probability density. The advantages of bayesian inference techniques over the alternative method of maximum likelihood estimation (MLE) of the parameters of an unknown mixture distribution include the following: (1) prior information may be incorporated in the estimation of model parameters; (2) conditional probability estimates of the number of individual components in the mixture are calculated; (3) flexibility exists in the extent to which the estimated noise standard deviation indicates the width of each component; (4) posterior distributions for component means are calculated, including measures of uncertainty about the means; and (5) probability density functions of the component distributions and the overall mixture distribution are estimated in relation to the raw grouped data, together with measures of uncertainty about these estimates. This expository report describes this novel approach to the unconstrained identification of components within a mixture, and provides demonstration of the usefulness of the technique in the context of both simulations and the analysis of distributions of synaptic potential signals.

Action Potentials↗
PubMed2001

Bayesian spatiotemporal inference in functional magnetic resonance imaging.

Mapping of the human brain by means of functional magnetic resonance imaging (fMRI) is an emerging field in cognitive and clinical neuroscience. Current techniques to detect activated areas of the brain mostly proceed in two steps. First, conventional methods of correlation, regression, and time series analysis are used to assess activation by a separate, pixelwise comparison of the fMRI signal time courses to the reference function of a presented stimulus. Spatial aspects caused by correlations between neighboring pixels are considered in a separate second step, if at all. The aim of this article is to present hierarchical Bayesian approaches that allow one to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We introduce parametric and semiparametric spatial and spatiotemporal models that proved appropriate and illustrate their performance applied to visual fMRI data.

Bayes Theorem↗
PubMed1999

Bayesian phylogenetic inference via Markov chain Monte Carlo methods.

We derive a Markov chain to sample from the posterior distribution for a phylogenetic tree given sequence information from the corresponding set of organisms, a stochastic model for these data, and a prior distribution on the space of trees. A transformation of the tree into a canonical cophenetic matrix form suggests a simple and effective proposal distribution for selecting candidate trees close to the current tree in the chain. We illustrate the algorithm with restriction site data on 9 plant species, then extend to DNA sequences from 32 species of fish. The algorithm mixes well in both examples from random starting trees, generating reproducible estimates and credible sets for the path of evolution.

Algorithms↗
PubMed2000

Bayesian accelerated failure time analysis with application to veterinary epidemiology.

Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non-nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods.

Abortion, Veterinary↗
PubMed1997

Bayesian adaptive alignment and inference.

Sequence alignment without the specification of gap penalties or a scoring matrix is attained by using Bayesian inference and a recursive algorithm. This procedure's recursive algorithm sums over all possible alignments on the forward step to obtain normalizing constants essential to Bayesian inferences, and samples from the exact posterior distribution on the backward step. Since both terminal and intervening unrelated subsequences will often be excluded from an alignment, the resulting alignments may be seen as extensions of local alignments. An alignment's significance is assessed using the Bayesian evidence. A shuffling simulation shows that Bayesian evidence against the null hypothesis tends to be a conservative measure of significance compared to classical p-values. An application to proteins from the GTPase superfamily shows that the posterior distribution of the number of gaps is often flat and that the posterior distribution of the evolutionary distance is often flat and sometimes bimodal. An alignment of 1GIA with 1ETU shows good correspondence with a structural alignment.

Algorithms↗