Bayesian Point Of View Research Articles

Bayesian model comparison and selection in energy decay analysis of acoustically coupled spaces

The use of Bayesian inference in problems of parameter estimation from noisy data and in uncertain environments has been well discussed in the acoustical signal processing literature. In many acoustical problems where it is uncertain which suitable model among a set of competing ones should be used, the model comparison and selection become crucial prior to the actual parameter estimation. However, tools for model selection in Bayesian inference have received less attention. In problems of model comparison and selection, the Bayesian methodology is most different from orthodox statistical methods. We present several methods for model comparison and selection from a Bayesian viewpoint and demonstrate their application to the problem of estimating the number of decay rates present in acoustically coupled spaces.

On Estimating Burr Type XII Parameter Based on General Type II Progressive Censoring

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

Local regularization method applied to estimating oxygen consumption during muscle activities

In this paper, we consider a one-dimensional inverse problem of estimating an input signal that a priori is known to be a smooth function with a few jump discontinuities. A popular method of regularizing the inverse problem with such prior information is to use a total variation (TV) penalty as a regularizing functional. In this paper, we adopt a different approach, considering the problem from the Bayesian statistics viewpoint and using a hierarchical Gaussian smoothness prior. We demonstrate that the approach allows us to construct a local regularization scheme that is computationally effective and reproduces well the jump discontinuities. The approach avoids the non-differentiability problems encountered by TV methods. Once discretized, the algorithm is completely data driven, the parameter selections requiring no user intervention. The method is applied to an inverse problem in metabolic modelling, where the objective is to estimate the mitochondrial oxygen consumption during muscle activities based on noisy observations of the time decay of the oxygen concentration on the muscle surface.

Non-normal path analysis in the presence of measurement error and missing data: a Bayesian analysis of nursing homes' structure and outcomes

Path analytic models are useful tools in quantitative nursing research. They allow researchers to hypothesize causal inferential paths and test the significance of these paths both directly and indirectly through a mediating variable. A standard statistical method in the path analysis literature is to treat the variables as having a normal distribution and to estimate paths using several least squares regression equations. The parameters corresponding to the direct paths have point and interval estimates based on normal distribution theory. Indirect paths are a product of the direct path from the independent variable to the mediating variable and the direct path of the mediating variable to the dependent variable. However, in the case of non-normal distributions, the point and interval estimates of the indirect path become much more difficult to estimate. We address the issue of calculating indirect point and interval estimates in the case of non-normally distributed data. Our substantive application is a nursing home research problem in which the variables in the path analysis of interest involve variables with normal, Bernoulli, or Poisson distributions. Additionally, one of the Poisson variables is observed with error. This paper addresses estimating point and interval estimation of indirect paths for variables with non-normal distributions in the presence of missing data and measurement error. We handle these difficulties from a fully Bayesian point of view. We present our substantive path analysis motivated from a nursing home structure, process, and outcomes model. Our results focus on the impact job turnover in the nursing homes has on nursing home outcomes.

A Bayesian determination of threshold for identifying differentially expressed genes in microarray experiments

The original definitions of false discovery rate (FDR) and false non-discovery rate (FNR) can be understood as the frequentist risks of false rejections and false non-rejections, respectively, conditional on the unknown parameter, while the Bayesian posterior FDR and posterior FNR are conditioned on the data. From a Bayesian point of view, it seems natural to take into account the uncertainties in both the parameter and the data. In this spirit, we propose averaging out the frequentist risks of false rejections and false non-rejections with respect to some prior distribution of the parameters to obtain the average FDR (AFDR) and average FNR (AFNR), respectively. A linear combination of the AFDR and AFNR, called the average Bayes error rate (ABER), is considered as an overall risk. Some useful formulas for the AFDR, AFNR and ABER are developed for normal samples with hierarchical mixture priors. The idea of finding threshold values by minimizing the ABER or controlling the AFDR is illustrated using a gene expression data set. Simulation studies show that the proposed approaches are more powerful and robust than the widely used FDR method.

Neighborhood Level Spatial Analysis of the Relationship Between Alcohol Outlet Density and Criminal Violence

Misuse of alcohol is a significant public health problem, potentially resulting in unintentional injuries, motor vehicle crashes, drownings, and, perhaps of greatest concern, serious acts of violence, including assaults, rapes, suicides, and homicides. Although previous research establishes a link between alcohol consumption increased levels of violence, studies relating the density of alcohol outlets (e.g., restaurants, bars, liquor stores) and the likelihood of violent crime have been less common. In this paper we test for such a relationship at the small area level, using data from 79 neighborhoods in the city of Minneapolis, Minnesota. We adopt a fully Bayesian point of view using Markov chain Monte Carlo (MCMC) computational methods as available in the popular and freely available WinBUGS language. Our models control for important covariates (e.g., neighborhood racial heterogeneity, age heterogeneity) and also account for spatial association in unexplained variability using conditionally autoregressive (CAR) random effects. Our results indicate a significant positive relationship between alcohol outlet density and violent crime, while also permitting easy mapping of neighborhood-level predicted and residual values, the former useful for intervention in the most at-risk neighborhoods and the latter potentially useful in identifying covariates still missing from the fixed effects portion of the model.

Probability matching property of adjusted likelihoods

For models characterized by a scalar parameter, it is well known that Jeffrey's prior ensures approximate frequentist validity of posterior quantiles. We examine how far this result remains robust in the presence of nuisance parameters, when the interest parameter θ 1 is scalar, a prior on θ 1 alone is considered, and the analysis is based on an adjusted version of the profile likelihood, rather than the true likelihood. This provides justification, from a Bayesian viewpoint, for some popular adjustments in term of their ability to neutralize unknown nuisance parameters. The dual problem of identifying adjustments that make a given prior on θ 1 probability matching in the above sense is also addressed.

Sample size determination of binomial data with the presence of misclassification

We propose a double sampling scheme with two classifiers to address the problem of optimal sample size when misclassification among binomial observations is observed. The classifiers vary with respect to the classifying cost and precision. Furthermore, since the data are unknown, an additional constraint is set on the probability of observing ``undesirable'' data. The method is developed following the Bayesian point of view.

Connectionist-Based Dempster–Shafer Evidential Reasoning for Data Fusion

Dempster-Shafer evidence theory (DSET) is a popular paradigm for dealing with uncertainty and imprecision. Its corresponding evidential reasoning framework is theoretically attractive. However, there are outstanding issues that hinder its use in real-life applications. Two prominent issues in this regard are 1) the issue of basic probability assignments (masses) and 2) the issue of dependence among information sources. This paper attempts to deal with these issues by utilizing neural networks in the context of pattern classification application. First, a multilayer perceptron neural network with the mean squared error as a cost function is implemented to calculate, for each information source, posteriori probabilities for all classes. Second, an evidence structure construction scheme is developed for transferring the estimated posteriori probabilities to a set of masses along with the corresponding focal elements, from a Bayesian decision point of view. Third, a network realization of the Dempster-Shafer evidential reasoning is designed and analyzed, and it is further extended to a DSET-based neural network, referred to as DSETNN, to manipulate the evidence structures. In order to tackle the issue of dependence between sources, DSETNN is tuned for optimal performance through a supervised learning process. To demonstrate the effectiveness of the proposed approach, we apply it to three benchmark pattern classification problems. Experiments reveal that the DSETNN out-performs DSET and provide encouraging results in terms of classification accuracy and the speed of learning convergence.

Target detection from a classical and a Bayesian viewpoint

Two approaches have been used for designing spatial surveys to detect a target. The classical approach controls the probability of missing a target that exists; a Bayesian approach controls the probability that a target exists given that none was seen. In both cases, information about the likely size of the target can reduce sampling requirements. In this paper, previous results are summarized and then used to assess the risk that Roman remains could be present at sites scheduled for development in Greater London.

Bayesian approach to feature selection and parameter tuning for support vector machine classifiers

A Bayesian point of view of SVM classifiers allows the definition of a quantity analogous to the evidence in probabilistic models. By maximizing this one can systematically tune hyperparameters and, via automatic relevance determination (ARD), select relevant input features. Evidence gradients are expressed as averages over the associated posterior and can be approximated using Hybrid Monte Carlo (HMC) sampling. We describe how a Nyström approximation of the Gram matrix can be used to speed up sampling times significantly while maintaining almost unchanged classification accuracy. In experiments on classification problems with a significant number of irrelevant features this approach to ARD can give a significant improvement in classification performance over more traditional, non-ARD, SVM systems. The final tuned hyperparameter values provide a useful criterion for pruning irrelevant features, and we define a measure of relevance with which to determine systematically how many features should be removed. This use of ARD for hard feature selection can improve classification accuracy in non-ARD SVMs. In the majority of cases, however, we find that in data sets constructed by human domain experts the performance of non-ARD SVMs is largely insensitive to the presence of some less relevant features. Eliminating such features via ARD then does not improve classification accuracy, but leads to impressive reductions in the number of features required, by up to 75%. 1 1 An abbreviated version of some portions of this article appeared in ( Gold & Sollich, 2005), published under the IEEE copyright.

Quantitative magnetic resonance spectroscopy: Semi‐parametric modeling and determination of uncertainties

A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramér-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline. The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramér-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Crémer-Rao lower bounds, which tend to overestimate accuracy.

Estimation and Prediction in a Two-Parameter Exponential Distribution Based on k-Record Values under LINEX Loss Function

ABSTRACT There are many situations where experimental outcomes are a sequence of record-breaking observations. In this article, Bayesian estimation for the two parameters of the exponential distribution are obtained based on k-record values under Linear-Exponential LINEX loss function. The admissibility of some estimators are discussed. Prediction, either point or interval, for future k-record values are also presented from a Bayesian view point. Numerical computations are given for an empirical comparison.

BAYESIAN STUDY OF A TWO-COMPONENT SYSTEM WITH COMMON-CAUSE SHOCK FAILURES

The steady-state availability of a two-component system in series and parallel subject to individual failures (I-failures) and common-cause shock (CCS) failures is studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters in the system. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and subsequently the highest posterior density intervals. A numerical example illustrates the results.

Random effects survival models gave a better understanding of heterogeneity in individual patient data meta-analyses

Background and objectiveIndividual patient data meta-analysis consists in combining data from all available trials dealing with a therapeutic problem in order to increase the power of statistical analyses. A key issue when analyzing these pooled data sets is intertrial heterogeneity. In survival data, heterogeneity manifests itself either by differing treatment effects between the included trials or by a baseline hazard that differs between studies. One way to investigate and accommodate this heterogeneity is to use models that include random effects. MethodsWe apply this class of models to the Meta-Analysis of Chemotherapy in Head and Neck Cancers, in which strong heterogeneity is exhibited. This meta-analysis pooled 63 trials involving 10,741 patients. ResultsWe show that such modeling permits a better understanding of heterogeneity in the MACH-NC data, both from a frequentist and from a Bayesian point of view. In particular, the modeling suggests the presence of two outlying sets of trials whose baseline risk could explain the apparent efficacy or inefficacy of some treatment protocols. ConclusionWe conclude that this family of random-effects models is a useful tool for exploring heterogeneity in meta-analyses of time-to-event data, and that its features can be applied to a very wide range of studies.

A new approach to influence diagnostics in superpopulations

Influence analysis on a model is one of the most studied topics from a frequentist viewpoint. Basically, disturbances are introduced into the model in order to measure the influence that one or a set of observations has on statistical analysis. The most common disturbance pattern is that of the omission of the observations whose influence is to be studied. In our model, we assume that there are only one or a few outliers because they may often be detected by deletion methods associated with regression diagnostics. However, these methods may fail in the presence of multiple outliers. In this case, the forward search can be used to avoid the masking and swamping problems. This article presents a Bayes approach for the influence analysis on a model in finite populations. Particularly, we develop a new approach to the study of influence in prediction theory, based on the given data rather than on the sampling design for data collection. We propose that the influence analysis on the superpopulation normal regression model and a measure based on the conditional bias from a Bayesian viewpoint is analyzed. Forward deletion formulae based on our influence measure can be defined, but this topic is beyond the scope of this article. Finally, we apply our proposed influence measure in a classic example for water contents of soil specimens. Copyright © 2005 John Wiley & Sons, Ltd.

Bayesian Analysis of an Additive Survival Model with Frailty

There has been some interest in survival models with additive hazard function (e.g., the Aalen's linear model), which is considered an alternative or supplementary model to the most common Cox model in analysis of censored data. One advantage of the Aalen's model is to allow the influence of each covariate to vary separately over time. In this article, an additive survival model, based on counting processes, is presented introducing additive frailties into the intensity in order to account for the heterogeneity of the data due to unobserved risk factors or dependence among individuals in study. The additive frailty model is analyzed under a Bayesian point of view and illustrated by two well-known data sets.

応用科学哲学の問題としてのリスク

The practice of risk analysis and its validity have invited heated controversies for many years. In this paper, I approach this issue from the point of view of "an applied philosophy of science". Two common models of risk analysis, i.e. the positivist and the social constructivist models, seem untenable because they reflect positions already refuted in the philosophy of science. Kristine Shrader-Frechette and Deborah Mayo offer alternative post-positivistic models of the risk analysis (scientific proceduralism and a metascientific analysis, respectively). Although I agree with them in many respects, their images of uncertainty in the risk analysis seem to be somewhat coarse-grained. I introduce a Bayesian point of view as a refinement in the post-positivistic model.

BAYESIAN DETECTION AND ANALYSIS OF CHANGING TRANSITION MATRICES OF STATIONARY MARKOV CHAINS

SummaryThis paper considers the detection of abrupt changes in the transition matrix of a Markov chain from a Bayesian viewpoint. It derives Bayes factors and posterior probabilities for unknown numbers of change‐points, as well as the positions of the change‐points, assuming non‐informative but proper priors on the parameters and fixed upper bound. The Markov chain Monte Carlo approach proposed by Chib in 1998 for estimating multiple change‐points models is adapted for the Markov chain model. It is especially useful when there are many possible change‐points. The method can be applied in a wide variety of disciplines and is particularly relevant in the social and behavioural sciences, for analysing the effects of events on the attitudes of people.

Particle Filtering Equalization Method for a Satellite Communication Channel

We propose the use of particle filtering techniques and Monte Carlo methods to tackle the in-line and blind equalization of a satellite communication channel. The main difficulties encountered are the nonlinear distortions caused by the amplifier stage in the satellite. Several processing methods manage to take into account these nonlinearities but they require the knowledge of a training input sequence for updating the equalizer parameters. Blind equalization methods also exist but they require a Volterra modelization of the system which is not suited for equalization purpose for the present model. The aim of the method proposed in the paper is also to blindly restore the emitted message. To reach this goal, a Bayesian point of view is adopted. Prior knowledge of the emitted symbols and of the nonlinear amplification model, as well as the information available from the received signal, is jointly used by considering the posterior distribution of the input sequence. Such a probability distribution is very difficult to study and thus motivates the implementation of Monte Carlo simulation methods. The presentation of the equalization method is cut into two parts. The first part solves the problem for a simplified model, focusing on the nonlinearities of the model. The second part deals with the complete model, using sampling approaches previously developed. The algorithms are illustrated and their performance is evaluated using bit error rate versus signal-to-noise ratio curves.