We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis±Hastings algorithm.

The following paper is a pre-print and the final publication can be found in Accident Analysis and Prevention, 40 (3):964-975, 2008. Presented at the 86 th Annual Meeting of the Transportation Research Board, January 2007 ABSTRACT Numerous efforts have been devoted to investigating crash occurrence as related to roadway design features, environmental and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models injuries by severity. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses some questions that are difficult to answer by estimating them separately. With recent advancements in crash modeling and Bayesian statistics, the parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis-Hastings (M-H) algorithms for crashes on Washington State rural two-lane highways.The estimation results from the MVPLN approach did show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggested overdispersion in crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves. KEY WORDS INTRODUCTIONRoadway safety is a major concern for the general public and public agencies. Roadway crashes claim many lives and cause substantial economic losses each year. In the U.S. traffic crashes bring about more loss of human life (as measured in human-years) than almost any other causefalling behind only cancer and heart disease (NHTSA, 2005). The situation is of particular interest on rural two-lane roadways, which experience significantly higher fatality rates than urban roads. The annual cost of traffic crashes is estimated to be $231 billion, or $820 per capita in 2000(Blincoe et al., 2000. These costs do not include the cost of delays imposed on other travelers, which also are significant, particularly when crashes occur on busy roadways. Schrank and Lomax (2002) estimate that over half of all traffic delays are due to non-recurring events, such as crashes, costing on the order of $1,000 per peak-period driver per year, particularly in urban areas. Thus, while vehicle and roadway design are improving, and growing congestion may be reducing impact speeds, crashes are becoming more critical in many ways, particularly in societies that continue to motorize. Given the importance of roadways safety, there has been considerable crash prediction research (see, e.g., Hauer, 1986Hauer, , 1997Hauer,...

In recent years, Bayesian nonparametric inference, both theoretical and computational, has witnessed considerable advances. However, these advances have not received a full critical and comparative analysis of their scope, impact and limitations in statistical modelling; many aspects of the theory and methods remain a mystery to practitioners and many open questions remain. In this paper, we discuss and illustrate the rich modelling and analytic possibilities that are available to the statistician within the Bayesian nonparametric and/or semiparametric framework.

In this paper, we study the drivers of customer satisfaction for financial services. We discuss a full Bayesian analysis based on data collected from customers of a leading financial services company. Our approach allows us to explicitly accommodate missing data and enables quantitative assessment of the impact of the drivers of satisfaction across the customer population. We find that satisfaction with product offerings is a primary driver of overall customer satisfaction. The quality of customer service with respect to financial statements and services provided through different channels of delivery, such as information technology enabled call centers and traditional branch offices, are also important in determining overall satisfaction. However, our analysis indicates that the impact of these service delivery factors may differ substantially across customer segments. In order to facilitate managerial action, we discuss how specific operational quality attributes for designing and delivering financial services can be leveraged to enhance satisfaction with product offerings and service delivery. Our approach and findings have significant implications for managing customer satisfaction in the financial services industry.financial services, customer satisfaction, Bayesian analysis, information technology

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