Bayesian quantile regression for skew-normal linear mixed models

Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples.     

An intuitive risk factors search algorithm: usage of the Bayesian network technique in personalized medicine

The article focuses on the application of the Bayesian networks (BN) technique to problems of personalized medicine. The simple (intuitive) algorithm of BN optimization with respect to the number of nodes using naive network topology is developed. This algorithm allows to increase the BN prediction quality and to identify the most important variables of the network. The parallel program implementing the algorithm has demonstrated good scalability with an increase in the computational cores number, and it can be applied to the large patients database containing thousands of variables. This program is applied for the prediction for the unfavorable outcome of coronary artery disease (CAD) for patients who survived the acute coronary syndrome (ACS). As a result, the quality of the predictions of the investigated networks was significantly improved and the most important risk factors were detected. The significance of the tumor necrosis factor-alpha gene polymorphism for the prediction of the unfavorable outcome of CAD for patients survived after ACS was revealed for the first time.     

A Bayesian Approach for Analyzing Results of Vehicle Collision Tests

Certain motor vehicle safety standards stipulate a collision test speed and a set of performance criteria that vehicles must satisfy during or after the collision test. For example, Federal Motor Vehicle Safety Standard 301 requires a 30 mile per hour (mph) barrier collision and specifies a certain maximum allowable limit on the total spillage of fuel. Vehicle designs are required to meet this standard; however, when collision tests are conducted at speeds higher than the standard, vehicles do not always satisfy the performance criteria. This paper develops a mathematical model for estimating the probability of meeting the standard by using a Bayesian framework to incorporate engineering judgment with collision test results. The model is based on the idea that there are random features to a vehicle's ability to meet performance standards in a collision, especially at such elevated speeds. Example calculations are included to illustrate the estimation of the probability of meeting the standard and to compare it with a maximum likelihood approach.     

MAP segmentation in Bayesian hidden Markov models: a case study

We consider the problem of estimating the maximum posterior probability (MAP) state sequence for a finite state and finite emission alphabet hidden Markov model (HMM) in the Bayesian setup, where both emission and transition matrices have Dirichlet priors. We study a training set consisting of thousands of protein alignment pairs. The training data is used to set the prior hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is not applicable any more, there is no simple procedure to find the MAP path, and several iterative algorithms are considered and compared. The main goal of the paper is to test the Bayesian setup against the frequentist one, where the parameters of HMM are estimated using the training data.     

Risk Analysis for U.S. Offshore Wind Farms: The Need for an Integrated Approach

Wind power is becoming an increasingly important part of the global energy portfolio, and there is growing interest in developing offshore wind farms in the United States to better utilize this resource. Wind farms have certain environmental benefits, notably near‐zero emissions of greenhouse gases, particulates, and other contaminants of concern. However, there are significant challenges ahead in achieving large‐scale integration of wind power in the United States, particularly offshore wind. Environmental impacts from wind farms are a concern, and these are subject to a number of on‐going studies focused on risks to the environment. However, once a wind farm is built, the farm itself will face a number of risks from a variety of hazards, and managing these risks is critical to the ultimate achievement of long‐term reductions in pollutant emissions from clean energy sources such as wind. No integrated framework currently exists for assessing risks to offshore wind farms in the United States, which poses a challenge for wind farm risk management. In this “Perspective”, we provide an overview of the risks faced by an offshore wind farm, argue that an integrated framework is needed, and give a preliminary starting point for such a framework to illustrate what it might look like. This is not a final framework; substantial work remains. Our intention here is to highlight the research need in this area in the hope of spurring additional research about the risks to wind farms to complement the substantial amount of on‐going research on the risks from wind farms.     

A Bayesian analysis of a change in the parameters of autoregressive time series

In this article, we consider a Bayesian analysis of a possible change in the parameters of autoregressive time series of known order p, AR(p). An unconditional Bayesian test based on highest posterior density (HPD) credible sets is determined. The test is useful to detect a change in any one of the parameters separately. Using the Gibbs sampler algorithm, we approximate the posterior densities of the change point and other parameters to calculate the p-values that define our test.     

Objective Bayesian analysis of counting experiments with correlated sources of background

Searches for faint signals in counting experiments are often encountered in particle physics and astrophysics, as well as in other fields. Many problems can be reduced to the case of a model with independent and Poisson-distributed signal and background. Often several background contributions are present at the same time, possibly correlated. We provide the analytic solution of the statistical inference problem of estimating the signal in the presence of multiple backgrounds, in the framework of objective Bayes statistics. The model can be written in the form of a product of a single Poisson distribution with a multinomial distribution. The first is related to the total number of events, whereas the latter describes the fraction of events coming from each individual source. Correlations among different backgrounds can be included in the inference problem by a suitable choice of the priors.     

Efficient Bayesian sampling plans for exponential distributions with type-I-censored samples

The aim of this paper is to introduce an efficient Bayesian sampling procedure for exponential distribution with type-I censoring. An online inspection method is suggested to reach a Bayes decision prior the termination time of life test. Bayesian sampling plans (BSPs) with quadratic loss function are established to illustrate the use of the proposed method. Some BSPs are tabulated, and the performance of the proposed BSPs is compared with two existing competitive methods. Numerical results indicate that a significant reduction in the experimental time over the conventional BSP can be achieved when the online inspection method is applied.     

Bayesian testing of restrictions on vector autoregressive models

In this study, we propose a prior on restricted Vector Autoregressive (VAR) models. The prior setting permits efficient Markov Chain Monte Carlo (MCMC) sampling from the posterior of the VAR parameters and estimation of the Bayes factor. Numerical simulations show that when the sample size is small, the Bayes factor is more effective in selecting the correct model than the commonly used Schwarz criterion. We conduct Bayesian hypothesis testing of VAR models on the macroeconomic, state-, and sector-specific effects of employment growth.