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Results for “Bayesian inference”

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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↗
PubMedDate not supplied

Interim analyses in clinical trials: classical vs. Bayesian approaches.

This paper concerns interim analysis in clinical trials involving two treatments from the points of view of both classical and Bayesian inference. I criticize classical hypothesis testing in this setting and describe and recommend a Bayesian approach in which sampling stops when the probability that one treatment is the better exceeds a specified value. I consider application to normal sampling analysed in stages and evaluate the gain in average sample number as a function of the number of interim analyses.

Bayes Theorem↗
PubMed1999

Toward evidence-based medical statistics. 2: The Bayes factor.

Bayesian inference is usually presented as a method for determining how scientific belief should be modified by data. Although Bayesian methodology has been one of the most active areas of statistical development in the past 20 years, medical researchers have been reluctant to embrace what they perceive as a subjective approach to data analysis. It is little understood that Bayesian methods have a data-based core, which can be used as a calculus of evidence. This core is the Bayes factor, which in its simplest form is also called a likelihood ratio. The minimum Bayes factor is objective and can be used in lieu of the P value as a measure of the evidential strength. Unlike P values, Bayes factors have a sound theoretical foundation and an interpretation that allows their use in both inference and decision making. Bayes factors show that P values greatly overstate the evidence against the null hypothesis. Most important, Bayes factors require the addition of background knowledge to be transformed into inferences--probabilities that a given conclusion is right or wrong. They make the distinction clear between experimental evidence and inferential conclusions while providing a framework in which to combine prior with current evidence.

Bayes Theorem↗
PubMed1995

A Bayesian group sequential design for a multiple arm randomized clinical trial.

Group sequential designs for randomized clinical trials allow analyses of accruing data. Most group sequential designs in the literature concern the comparison of two treatments and maintain an overall prespecified type I error. As the number of treatments increases, however, so does the probability of falsely rejecting the null hypothesis. Bayesian statisticians concern themselves with the observed data and abide by the likelihood principle. As long as previous analyses do not change the likelihood, these analyses do not change Bayesian inference. In this paper, we discuss a group sequential design for a proposed randomized clinical trial comparing four treatment regimens. Bayesian ideas underlie the design and posterior probability calculations determine the criteria for stopping accrual to one or more of the treatments. We use computer simulation to estimate the frequentists properties of the design, information of interest to many of our collaborators. We show that relatively simple posterior probability calculations, along with simulations to calculate power under alternative hypotheses, can produce appealing designs for randomized clinical trials.

Bayes Theorem↗
PubMedDate not supplied

Bayesian approaches to meta-analysis of ROC curves.

A comparative review of important classic and Bayesian approaches to fixed-effects and random-effects meta-analysis of binormal ROC curves and areas underneath them is presented. The ROC analyses results of seven evaluation studies concerning the dexamethasone suppression test provide the basis for a worked example. Particular attention is given to fully Bayesian inference, a novelty in the ROC context, based on Gibbs samples from posterior distributions of hierarchical model parameters and related quantities. Fully Bayesian meta-analysis may properly account for the uncertainty associated with the model parameters, possibly incorporating prior knowledge and beliefs, and allows clinically intuitive predictions of unobserved study effects via calculation of posterior predictive densities. The effects of various different prior specifications (six noninformative as well as one informative) on the posterior estimates are investigated (sensitivity-analysis). Recommendations and suggestions for further research are made. Computer code for the more advanced methods may either be downloaded via the Internet or be found elsewhere.

Bayes Theorem↗
PubMed2000

Accommodating phylogenetic uncertainty in evolutionary studies.

Many evolutionary studies use comparisons across species to detect evidence of natural selection and to examine the rate of character evolution. Statistical analyses in these studies are usually performed by means of a species phylogeny to accommodate the effects of shared evolutionary history. The phylogeny is usually treated as known without error; this assumption is problematic because inferred phylogenies are subject to both stochastic and systematic errors. We describe methods for accommodating phylogenetic uncertainty in evolutionary studies by means of Bayesian inference. The methods are computationally intensive but general enough to be applied in most comparative evolutionary studies.

Animals↗
PubMed1998

Bayesian protein family classifier.

A Bayesian procedure for the simultaneous alignment and classification of sequences into subclasses is described. This Gibbs sampling algorithm iterates between an alignment step and a classification step. It employs Bayesian inference for the identification of the number of conserved columns, the number of motifs in each class, their size, and the size of the classes. Using Bayesian prediction, inter-class differences in all these variables are brought to bare on the classification. Application to a superfamily of cyclic nucleotide-binding proteins identifies both similarities and differences in the sequence characteristics of the five subclasses identified by the procedure: 1) cNMP-dependent kinases, 2) prokaryotic cAMP-dependent regulatory proteins, CRP-type, 3) prokaryotic regulatory proteins, FNR-type, 4) cAMP gated ion channel proteins of animals, and 5) cAMP gated ion channels of plants.

Algorithms↗
PubMed2001

Directed Convergence in Stable Percept Acquisition.

We view a perceptual capacity as a nondeductive inference, represented as a function from a set of premises to a set of conclusions. The application of the function to a single premise to produce a single conclusion is called a "percept" or "instantaneous percept." We define a stable percept as a convergent sequence of instantaneous percepts. Assuming that the sets of premises and conclusions are metric spaces, we introduce a strategy for acquiring stable percepts, called directed convergence. We consider probabilistic inferences, where the premise and conclusion sets are spaces of probability measures, and in this context we study Bayesian probabilistic/recursive inference. In this type of Bayesian inference the premises are probability measures, and the prior as well as the posterior is updated nontrivially at each iteration. This type of Bayesian inference is distinguished from classical Bayesian statistical inference where the prior remains fixed, and the posterior evolves by conditioning on successively more punctual premises. We indicate how the directed convergence procedure may be implemented in the context of Bayesian probabilistic/recursive inference. We discuss how the L(infinity) metric can be used to give numerical control of this type of Bayesian directed convergence. Copyright 2001 Academic Press.

Journal Article↗
PubMed1993

An introduction to the Bayesian analysis of clinical trials.

Although most clinical trials comparing therapies are analyzed using classical hypothesis testing and P values, such methods do not yield the information most useful to the clinician, that is, the probability that one treatment is more efficacious than another. Bayesian inference can yield this probability but only if we quantify our prior beliefs about the possible efficacies of the treatments studied. This article gives a brief introduction to Bayesian methods and contrasts them with classical hypothesis testing. It shows that the quantification of prior beliefs is a common and necessary part of the interpretation of clinical information, whether from a laboratory test or published clinical trial. Advantages of Bayesian analysis over classical analysis of clinical trials include the ability to incorporate prior information regarding treatment efficacies into the analysis; the ability to make multiple unscheduled inspections of accumulating data without increasing the error rate of the study; and the ability to calculate the probability that one treatment is more effective than another. Because it is likely that Bayesian methods will be used more often in the analysis of future clinical trials, investigators and readers should be aware of the two schools of statistical thought and the strengths and weaknesses of each.

Bayes Theorem↗
PubMed2000

Bayesian estimation of range for microsatellite loci.

Microsatellite loci have become important in population genetics because of their high level of polymorphism in natural populations, very frequent occurrence throughout the genome, and apparently high mutation rate. Observed repeat numbers (alleles size) in natural populations and expectations based on computer simulations suggest that the range of repeat numbers at a microsatellite locus is restricted. This range is a key parameter that should be properly estimated in order to proceed with calculations of divergence times in phylogenetic studies and to better investigate the within- and between-population variability. The 'plug-in' estimate of range based on the minimum and maximum value observed in a sample is not satisfactory because of the relatively large number of alleles in comparison with typical sample sizes. In this paper, a set of data from 30 dinucleotide microsatellite loci is analysed under the assumption of independence among loci. Bayesian inference on range for one locus is obtained by assuming that constraints on range values exist as sharp bounds. Closed-form calculations and robustness revealed by our analysis suggest that the proposed Bayesian approach might be routinely used by researchers to classify microsatellite loci according to the estimated value of their allelic range.

Bayes Theorem↗
PubMed2000

The Bayesian approach improves the electrocardiographic diagnosis of broad complex tachycardia.

Despite numerous attempts at devising algorithms for diagnosing broad complex tachycardia (BCT) on the basis of the electrocardiogram (ECG), misdiagnosis is still common. The reason for this may lie with difficulty in implementing existent algorithms in practice, due to imperfect ascertainment of ECG features within them. An attempt was made to approach the problem afresh with the Bayesian inference by the construction of a diagnostic algorithm centered around the likelihood ratio (LR). Previously studied ECG features most effective in discriminating ventricular tachycardia (VT) from supraventricular tachycardia with aberrant conduction (SVTAC), according to their LR values, were selected for inclusion into a Bayesian diagnostic algorithm. A test set of 244 BCT ECGs was assembled and shown to three independent observers who were blinded to the diagnoses made at electrophysiological study. Their diagnostic accuracy by the Bayesian algorithm was compared against that by clinical judgement with the diagnoses from EPS as the criterial standard. Clinical judgement correctly diagnosed 35% of SVTAC, 85% of VT, and 47% of fascicular tachycardia. In comparison, by the Bayesian algorithm devised, 52% of SVTAC, 95% of VT, and 97% of fascicular tachycardia were correctly diagnosed. The Bayesian algorithm devised has proved to be superior to the clinical judgement of the observers who participated in this study, and theoretically will obviate the problem of imperfect ascertainment of ECG features. Hence, it holds the promise for being an effective tool for routine use in clinical practice.

Algorithms↗
PubMed1988

The diagnosis of polyarteritis nodosa. I. A literature-based decision analysis approach.

We investigated diagnostic testing in polyarteritis nodosa (PAN) by calculating, from published data, the sensitivity and specificity of visceral angiography and muscle, nerve, testicle, kidney, and liver biopsy. Test sequence strategies were constructed by Bayesian inference using a computer program written for this purpose. Test sequences were compared with an aggressive strategy consisting of repeated tests until there was a positive finding or until the available tests were exhausted, and a conservative strategy consisting of 1 biopsy procedure plus angiography. The Bayesian analysis agreed most closely with the conservative approach for most prior probabilities (degree of suspicion) that a patient had PAN. The aggressive strategy had an overall sensitivity of 90% and specificity of 91%, whereas the conservative strategy was 85% sensitive and 96% specific. Furthermore, the aggressive strategy was more costly ($2,986 versus $1,961) and had a higher rate of morbidity (3.8 versus 2.7 days of hospitalization per patient evaluated) than did the conservative strategy. The mortality rates of both strategies were equivalent (approximately 0.05 deaths per hundred patients evaluated). The per-case cost of diagnosis increased as prevalence decreased, and at 10% prevalence, the aggressive strategy cost more than $17,000 per case diagnosed. Sensitivity analysis revealed that the strategies were moderately affected by the test characteristics, within reasonable assumptions, but that the differences in conservative and aggressive approaches remained. Thus, our analysis based on available data and the assumption of test independence suggests that the preferred diagnostic evaluation of patients with symptoms suggestive of PAN consists, in most cases, of a single biopsy procedure, with angiographic evaluation if necessary.

Costs and Cost Analysis↗
PubMed1998

Generalized linear mixed models in dairy cattle breeding.

Fitness and fertility traits of dairy cattle are of increasing importance and are often measured on a discrete scale. The development and application of generalized linear mixed models to the genetic analysis of these traits are reviewed. Because current genetic evaluation systems are predominantly based on animal models, the inferential challenges of highly parameterized generalized linear mixed models are discussed. Development and adoption of new methods for drawing appropriate inferences on dispersion parameters are essential. Recent hierarchical extensions have been proposed for generalized linear mixed models, allowing for complex dispersion patterns that accommodate heteroscedasticity and outlier robustness. Steady advances in available computing power have facilitated multiple-trait analyses involving continuous and discrete measures. Full Bayesian inference via the development of Markov Chain Monte Carlo methods will continue to allow even greater generality and dimensions in the genetic model.

Animals↗
PubMed2000

Baseline risk as predictor of treatment benefit: three clinical meta-re-analyses.

A relationship between baseline risk and treatment effect is increasingly investigated as a possible explanation of between-study heterogeneity in clinical trial meta-analysis. An approach that is still often applied in the medical literature is to plot the estimated treatment effects against the estimated measures of risk in the control groups (as a measure of baseline risk), and to compute the ordinary weighted least squares regression line. However, it has been pointed out by several authors that this approach can be seriously flawed. The main problem is that the observed treatment effect and baseline risk measures should be viewed as estimates rather than the true values. In recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates. In this article we propose a vague priors Bayesian solution to the problem which can be carried out using the 'Bayesian inference using Gibbs sampling' (BUGS) implementation of Markov chain Monte Carlo numerical integration techniques. Different from other proposed methods, it uses the exact rather than an approximate likelihood, while it can handle many different treatment effect measures and baseline risk measures. The method differs from a recently proposed Bayesian method in that it explicitly models the distribution of the underlying baseline risks. We apply the method to three meta-analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods. In particular we compare our approach to McIntosh's method, for which we show how it can be carried out using standard statistical software. We conclude that our proposed method offers a very general and flexible solution to the problem, which can be carried out relatively easily with existing Bayesian analysis software. A confidence band for the underlying relationship between true effect measure and baseline risk and a confidence interval for the value of the baseline risk measure for which there is no treatment effect are easily obtained by-products of our approach.

Bayes Theorem↗