Bayesian Point Of View Research Articles

Gibbs sampling methods for Bayesian quantile regression

This paper considers quantile regression models using an asymmetric Laplace distribution from a Bayesian point of view. We develop a simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution. We also discuss some possible extensions of our approach, including the incorporation of a scale parameter, the use of double exponential prior, and a Bayesian analysis of Tobit quantile regression. The proposed methods are illustrated by both simulated and real data.

Z ′ bosons at colliders: a Bayesian viewpoint

We revisit the CDF data on di-muon production to impose constraints on a large class of Z' bosons occurring in a variety of E_6 GUT based models. We analyze the dependence of these limits on various factors contributing to the production cross-section, showing that currently systematic and theoretical uncertainties play a relatively minor role. Driven by this observation, we emphasize the use of the Bayesian statistical method, which allows us to straightforwardly (i) vary the gauge coupling strength, g', of the underlying U(1)'; (ii) include interference effects with the Z' amplitude (which are especially important for large g'); (iii) smoothly vary the U(1)' charges; (iv) combine these data with the electroweak precision constraints as well as with other observables obtained from colliders such as LEP 2 and the LHC; and (v) find preferred regions in parameter space once an excess is seen. We adopt this method as a complementary approach for a couple of sample models and find limits on the Z' mass, generally differing by only a few percent from the corresponding CDF ones when we follow their approach. Another general result is that the interference effects are quite relevant if one aims at discriminating between models. Finally, the Bayesian approach frees us of any ad hoc assumptions about the number of events needed to constitute a signal or exclusion limit for various actual and hypothetical reference energies and luminosities at the Tevatron and the LHC.

Bayes and Empirical Bayes Estimation of the Parameter n in a Binomial Distribution

The problem of estimating the total number of trials n in a binomial distribution is reconsidered in this article for both cases of known and unknown probability of success p from the Bayesian viewpoint. Bayes and empirical Bayes point estimates for n are proposed under the assumption of a left-truncated prior distribution for n and a beta prior distribution for p. Simulation studies are provided in this article in order to compare the proposed estimate with the most familiar n estimates.

Asymptotically Informative Prior for Bayesian Analysis

In classical Bayesian inference the prior is treated as fixed, it is asymptotically negligible, thus any information contained in the prior is ignored from the asymptotic first order result. However, in practice often an informative prior is summarized from previous similar or the same kind of studies, which contains non-negligible information for the current study. Here, different from traditional Bayesian point of view, we treat such prior to be non-fixed. In particular, we give the data sizes used in previous studies for the prior the same status as the size of the current dataset, viewing both sample sizes as increasing to infinity in the asymptotic study. Thus the prior is asymptotically non-negligible, and its original effects are ressumed under this view. Consequently, Bayesian inference using such prior is more efficient, as it should be, than that regarded under the existing setting. We study some basic properties of Bayesian estimators using such priors under convex losses and the 0—1 loss, and illustrate the method by an example via simulation.

Estimating a parameter of Burr type XII distribution using hybrid censored observations

PurposeBurr distribution has been proved to be a useful failure model. It can assume different shapes which allow it to be a good fit for various lifetimes data. Hybrid censoring is an important way of generating lifetimes data. The purpose of this paper is to estimate an unknown parameter of the Burr type XII distribution when data are hybrid censored.Design/methodology/approachThe problem is dealt with through both the classical and Bayesian point of view. Specifically, the methods of estimation used to tackle the problem are maximum likelihood estimation method and Bayesian method. Empirical Bayesian approach is also considered. The performance of all estimates is compared through their mean square error values. The paper employs Monte Carlo simulation to evaluate the mean square error values of all estimates.FindingsThe key findings of the paper are that the Bayesian estimates are superior to the maximum likelihood estimates (MLE).Practical implicationsThis work has practical importance. Indeed, the proposed methods are applied to real life data.Originality/valueThe paper is original and is quite applicable in lifetimes data analysis.

Semi-Supervised Logistic Discrimination via Regularized Gaussian Basis Expansions

The problem of constructing classification methods based on both labeled and unlabeled data sets is considered for analyzing data with complex structures. We introduce a semi-supervised logistic discriminant model with Gaussian basis expansions. Unknown parameters included in the logistic model are estimated by regularization method along with the technique of EM algorithm. For selection of adjusted parameters, we derive a model selection criterion from Bayesian viewpoints. Numerical studies are conducted to investigate the effectiveness of our proposed modeling procedures.

Is cefepime safe for clinical use? A Bayesian viewpoint

Cefepime hydrochloride is approved for pneumonia, empirical therapy for febrile neutropenia, uncomplicated and complicated urinary tract infections, uncomplicated skin and skin structure infections and complicated intra-abdominal infections. A recent meta-analysis by Yahav et al. (Lancet Infect Dis 2007; 7: 338-48) concluded that cefepime was associated with a statistically significant increase in mortality (risk ratio 1.26, 95% confidence interval 1.08-1.49) when compared with other antibiotics. The US FDA decided to re-evaluate the meta-analysis data in collaboration with the drug sponsor. Two years later the FDA Alert summarized that 'data do not indicate a higher rate of death in cefepime-treated patients. Cefepime remains an appropriate therapy for its approved indications.' However, a thorough evaluation of the 52-page FDA report still shows that safety remains an unresolved issue. A Bayesian re-appraisal of the findings by the FDA and by Yahav et al. indicates that there is a 90.9% (by FDA trial-level meta-analysis), 80.8% (by FDA patient-level meta-analysis) and 99.2% (by Yahav et al. meta-analysis) probability that cefepime raises mortality in neutropenic fever patients, which translates into the following numbers needed to harm (NNH), i.e. to cause one extra death with the use of cefepime: FDA trial-level meta-analysis, NNH = 109; FDA patient-level meta-analysis, NNH = 76; Yahav et al. meta-analysis, NNH = 54. A similar harmful probability was observed with skin structure infections but not with pneumonias, intra-abdominal infections and urinary tract infections. In conclusion, cefepime should be avoided in patients with neutropenic fever or with skin structure infections.

Bayesian mixture of parametric and nonparametric density estimation: A Misspecification Problem

In this paper we study the effect of model misspecifications for probabilitydensity function estimation. We use a mixture of a parametric and nonparametricdensity estimation. The former can be modeled by any suitable parametricprobability density function, including mixture of parametric models. The latteris given by the known B-spline estimation. The procedure also deals withthe situation when a highly structured data are collected so that it is difficultto propose a parametric model with a large number of mixture components.Then a nonparametric part would help to postulate an appropriate model. Inaddition, in order to reduce the computational cost of getting a nonparametricdensity for high dimensional data a parametric mixture of densities could beused as the starting point for modeling such dataset. Our procedure is computedby using EM-type algorithm for a non-Bayesian approach and MCMCalgorithm under a Bayesian point of view. Simulations and real data analysisshow that our proposed procedure have performed quite well even for nonstructured datasets.

Bayesian inference in a correlated random coefficients model: Modeling causal effect heterogeneity with an application to heterogeneous returns to schooling

We consider the problem of causal effect heterogeneity from a Bayesian point of view. This is accomplished by introducing a three-equation system, similar in spirit to the work of Heckman and Vytlacil (1998), describing the joint determination of a scalar outcome, an endogenous “treatment” variable, and an individual-specific causal return to that treatment. We describe a Bayesian posterior simulator for fitting this model which recovers far more than the average causal effect in the population, the object which has been the focus of most previous work. Parameter identification and generalized methods for flexibly modeling the outcome and return heterogeneity distributions are also discussed. Combining data sets from High School and Beyond (HSB) and the 1980 Census, we illustrate our methods in practice and investigate heterogeneity in returns to education. Our analysis decomposes the impact of key HSB covariates on log wages into three parts: a “direct” effect and two separate indirect effects through educational attainment and returns to education. Our results strongly suggest that the quantity of schooling attained is determined, at least in part, by the individual’s own return to education. Specifically, a one percentage point increase in the return to schooling parameter is associated with the receipt of (approximately) 0.14 more years of schooling. Furthermore, when we control for variation in returns to education across individuals, we find no difference in predicted schooling levels for men and women. However, women are predicted to attain approximately 1/4 of a year more schooling than men on average as a result of higher rates of return to investments in education.

Bayesian Reproduction Number Estimation for Dengue Virus Transmission

The estimation of the reproduction number of dengue viral transmission is an active area of research owing to the importance of the reproduction number as an epidemiological quantity. It determines, among others, the intensity of intervention and control measures necessary to contain an outbreak. This study uses the reproduction number proposed by Favier, Degallier, Rosa-Freitas, Boulanger, Costa Lima, Luitgards-Moura, Menkes, Mondet, Oliveira, Weimann, & Tsouris (2006) but employs a Bayesian estimation procedure to estimate the parameters found in the reproduction number. Earlier studies by Chowell, Rivas, Smith, & Hyman (2006) showed that reproduction numbers computed from this basic formula overestimates the viral transmissibility and hence, also overestimates the control mechanisms employed to control the outbreak. The present study essentially deflates the reproduction number by the prior distribution of the parameters in a Bayesian viewpoint. The new estimation procedure is tried out for selected cases in Central Visayas and Bukidnon where outbreaks of dengue cases were noted for 2010. Â Keywords - reproduction number, Bayesian estimation, dengue flavivirus, incubation period

Statistical Inferences from Formaldehyde DNA–Protein Cross-Link Data: Improving Methods for Characterization of Uncertainty

Physiologically based pharmacokinetic (PBPK) modeling has reached considerable sophistication in its application to pharmacological and environmental health problems. Yet, mature methodologies for making statistical inferences have not been routinely incorporated in these applications except in a few data-rich cases. This paper demonstrates how improved statistical inference on estimated model parameters from both frequentist and Bayesian points of view can be routinely carried out. We work with a previously developed PBPK model for the formation and disposition of DNA–protein cross-links formed by inhaled formaldehyde in the nasal lining of rats and rhesus monkeys. We purposefully choose this model because it is based on sparse time-course data.

Bayesian neural networks for bridge integrity assessment

In recent years, neural network models have been widely used in the Civil Engineering field. Interesting enhancements may be obtained by re-examining this model from the Bayesian probability logic viewpoint. Using this approach, it will be shown that the conventional regularized learning approach can be derived as a particular approximation of the Bayesian framework. Network training is only a first level where Bayesian inference can be applied to neural networks. It can also be utilized in another three levels in a hierarchical fashion: for the optimization of the regularization terms, for data-based model selection, and to evaluate the relative importance of different inputs. In this paper, after a historical overview of the probability logic approach and its application in the field of neural network models, the existing literature is revisited and reorganized according to the enunciated four levels. Then, this framework is applied to develop a two-step strategy for the assessment of the integrity of a long-suspension bridge under ambient vibrations. In the first step of the proposed strategy, the occurrence of damage is detected and the damaged portion of the bridge is identified. In the second step, the specific damaged element is recognized and the intensity of damage is evaluated. The Bayesian framework is applied in both steps and the improvements in the results are discussed.

Estimation and Prediction for Exponentiated Family of Distributions Based on Records

In this article, a family of distributions, namely the exponentiated family of distributions, is defined and for the unknown parameters, different point estimates are derived based on record statistics. Prediction for future record values is presented from a Bayesian view point. Two numerical examples and a Monte Carlo simulation study are presented to illustrate the results.

Exact Bayesian Prediction in a Class of Markov-switching Models

Jump-Markov state-space systems (JMSS) are widely used in statistical signal processing. However as is well known Bayesian restoration in JMSS is an NP-hard problem, so in practice all inference algorithms need to resort to some approximations. In this paper we focus on the computation of the conditional expectation of the hidden variable of interest given the available observations, which is optimal from the Bayesian quadratic risk viewpoint. We show that in some stochastic systems, namely the Partially Pairwise Markov-switching Chains (PPMSC) and Trees (PPMST), no approximation scheme is actually needed since the conditional expectation of interest (be it either in a filtering or prediction problem) can be computed exactly and in a number of operations linear in the number of observations.

Bootstrap of deviation probabilities with applications

We show that under different moment bounds on the underlying variables, bootstrap approximation to the large deviation probabilities of standardized sample sum, based on independent random variables, is valid for a wider zone of n , the sample size, compared to the classical normal tail probability approximation. As an application, different notions of efficiency for statistical tests are considered from Bayesian point of view. In particular, efficiency due to Pitman (1938) [11], Chernoff (1952) [1], and Bayes risk efficiency due to Rubin and Sethuraman (1965) [12] turn out to be special cases with the choice of the weight function; i.e., prior density times loss.

On posterior distribution of Bayesian wavelet thresholding

We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior distribution itself from a nonparametric Bayesian asymptotics point of view and study its rate of convergence. We obtain the same rate as in Abramovich et al. (2004) where the authors studied the convergence of several Bayesian estimators.

A Bayesian Approach for Zero-Inflated Count Regression Models by Using the Reversible Jump Markov Chain Monte Carlo Method and an Application

In this study, estimation of the parameters of the zero-inflated count regression models and computations of posterior model probabilities of the log-linear models defined for each zero-inflated count regression models are investigated from the Bayesian point of view. In addition, determinations of the most suitable log-linear and regression models are investigated. It is known that zero-inflated count regression models cover zero-inflated Poisson, zero-inflated negative binomial, and zero-inflated generalized Poisson regression models. The classical approach has some problematic points but the Bayesian approach does not have similar flaws. This work points out the reasons for using the Bayesian approach. It also lists advantages and disadvantages of the classical and Bayesian approaches. As an application, a zoological data set, including structural and sampling zeros, is used in the presence of extra zeros. In this work, it is observed that fitting a zero-inflated negative binomial regression model creates no problems at all, even though it is known that fitting a zero-inflated negative binomial regression model is the most problematic procedure in the classical approach. Additionally, it is found that the best fitting model is the log-linear model under the negative binomial regression model, which does not include three-way interactions of factors.

Paid–incurred chain claims reserving method

We present a novel stochastic model for claims reserving that allows us to combine claims payments and incurred losses information. The main idea is to combine two claims reserving models ( Hertig’s ( 1985) model and Gogol’s ( 1993) model ) leading to a log-normal paid–incurred chain (PIC) model. Using a Bayesian point of view for the parameter modelling we derive in this Bayesian PIC model the full predictive distribution of the outstanding loss liabilities. On the one hand, this allows for an analytical calculation of the claims reserves and the corresponding conditional mean square error of prediction. On the other hand, simulation algorithms provide any other statistics and risk measure on these claims reserves.

Bayesian functional {ANOVA} modeling using Gaussian process prior distributions

Functional analysis of variance (ANOVA) models partition a func- tional response according to the main efiects and interactions of various factors. This article develops a general framework for functional ANOVA modeling from a Bayesian viewpoint, assigning Gaussian process prior distributions to each batch of functional efiects. We discuss the choices to be made in specifying such a model, advocating the treatment of levels within a given factor as dependent but exchangeable quantities, and we suggest weakly informative prior distributions for higher level parameters that may be appropriate in many situations. We discuss computationally e-cient strategies for posterior sampling using Markov Chain Monte Carlo algorithms, and we emphasize useful graphical summaries based on the posterior distribution of model-based analogues of traditional ANOVA decom- positions of variance. We illustrate this process of model speciflcation, posterior sampling, and graphical posterior summaries in two examples. The flrst consid- ers the efiect of geographic region on the temperature proflles at weather stations in Canada. The second example examines sources of variability in the output of regional climate models from a designed experiment.

R×s tables from a Bayesian viewpoint

The display of the data by means of contingency tables is used for dis- cussing different approaches to statistical inference. We develop a Bayesian proce- dure for the homogeneity testing problem of r populations using r × s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated us- ing a mixed prior distribution. The methodology consists of assigning an appropriate prior mass, π0, to the null and spreading the remainder, 1 − π0, over the alternative according to a density function. With this method, it is possible to prove a theorem which shows when the p-value and the posterior probability can give rise to the same conclusion.