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Practical applications of Bayesian reliability
Demonstrates how to solve reliability problems using practical applications of Bayesian models This self-contained reference provides fundamental knowledge of Bayesian reliability and utilizes numerous examples to show how Bayesian models can solve real life reliability problems. It teaches engineers and scientists exactly what Bayesian analysis is, what its benefits are, and how they can apply the methods to solve their own problems. To help readers get started quickly, the book presents many Bayesian models that use JAGS and which require fewer than 10 lines of command. It also offers a number of short R scripts consisting of simple functions to help them become familiar with R coding. Practical Applications of Bayesian Reliability starts by introducing basic concepts of reliability engineering, including random variables, discrete and continuous probability distributions, hazard function, and censored data. Basic concepts of Bayesian statistics, models, reasons, and theory are presented in the following chapter. Coverage of Bayesian computation, Metropolis-Hastings algorithm, and Gibbs Sampling comes next. The book then goes on to teach the concepts of design capability and design for reliability; introduce Bayesian models for estimating system reliability; discuss Bayesian Hierarchical Models and their applications; present linear and logistic regression models in Bayesian Perspective; and more.-Provides a step-by-step approach for developing advanced reliability models to solve complex problems, and does not require in-depth understanding of statistical methodology -Educates managers on the potential of Bayesian reliability models and associated impact -Introduces commonly used predictive reliability models and advanced Bayesian models based on real life applications -Includes practical guidelines to construct Bayesian reliability models along with computer codes for all of the case studies -JAGS and R codes are provided on an accompanying website to enable practitioners to easily copy them and tailor them to their own applications Practical Applications of Bayesian Reliability is a helpful book for industry practitioners such as reliability engineers, mechanical engineers, electrical engineers, product engineers, system engineers, and materials scientists whose work includes predicting design or product performance.
Book
A Bayesian Approach to Graphical Record Linkage and Deduplication
We propose an unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation involves the representation of the pattern of links between records as a bipartite graph, in which records are directly linked to latent true individuals, and only indirectly linked to other records. This flexible representation of the linkage structure naturally allows us to estimate the attributes of the unique observable people in the population, calculate transitive linkage probabilities across records (and represent this visually), and propagate the uncertainty of record linkage into later analyses. Our method makes it particularly easy to integrate record linkage with post-processing procedures such as logistic regression, capture-recapture, etc. Our linkage structure lends itself to an efficient, linear-time, hybrid Markov chain Monte Carlo algorithm, which overcomes many obstacles encountered by previously record linkage approaches, despite the high-dimensional parameter space. We illustrate our method using longitudinal data from the National Long Term Care Survey and with data from the Italian Survey on Household and Wealth, where we assess the accuracy of our method and show it to be better in terms of error rates and empirical scalability than other approaches in the literature. Supplementary materials for this article are available online.
Journal Article
Examining the Impact of Ranking on Consumer Behavior and Search Engine Revenue
In this paper, we study the effects of three different kinds of search engine rankings on consumer behavior and search engine revenues: direct ranking effect, interaction effect between ranking and product ratings, and personalized ranking effect. We combine a hierarchical Bayesian model estimated on approximately one million online sessions from Travelocity, together with randomized experiments using a real-world hotel search engine application. Our archival data analysis and randomized experiments are consistent in demonstrating the following: (1) A consumer-utility-based ranking mechanism can lead to a significant increase in overall search engine revenue. (2) Significant interplay occurs between search engine ranking and product ratings. An inferior position on the search engine affects \"higher-class\" hotels more adversely. On the other hand, hotels with a lower customer rating are more likely to benefit from being placed on the top of the screen. These findings illustrate that product search engines could benefit from directly incorporating signals from social media into their ranking algorithms. (3) Our randomized experiments also reveal that an \"active\" personalized ranking system (wherein users can interact with and customize the ranking algorithm) leads to higher clicks but lower purchase propensities and lower search engine revenue compared with a \"passive\" personalized ranking system (wherein users cannot interact with the ranking algorithm). This result suggests that providing more information during the decision-making process may lead to fewer consumer purchases because of information overload. Therefore, product search engines should not adopt personalized ranking systems by default. Overall, our study unravels the economic impact of ranking and its interaction with social media on product search engines.
This paper was accepted by Lorin Hitt, information systems.
Journal Article
Bayesian Spatial Quantile Regression
Tropospheric ozone is one of the six criteria pollutants regulated by the United States Environmental Protection Agency under the Clean Air Act and has been linked with several adverse health effects, including mortality. Due to the strong dependence on weather conditions, ozone may be sensitive to climate change and there is great interest in studying the potential effect of climate change on ozone, and how this change may affect public health. In this paper we develop a Bayesian spatial model to predict ozone under different meteorological conditions, and use this model to study spatial and temporal trends and to forecast ozone concentrations under different climate scenarios. We develop a spatial quantile regression model that does not assume normality and allows the covariates to affect the entire conditional distribution, rather than just the mean. The conditional distribution is allowed to vary from site-to-site and is smoothed with a spatial prior.For extremely large datasets our model is computationally infeasible, and we develop an approximate method. We apply the approximate version of our model to summer ozone from 1997-2005 in the Eastern U.S., and use deterministic climate models to project ozone under future climate conditions. Our analysis suggests that holding all other factors fixed, an increase in daily average temperature will lead to the largest increase in ozone in the Industrial Midwest and Northeast.
Journal Article
Everything is predictable : how Bayes' remarkable theorem explains the world
Thomas Bayes was an eighteenth-century Presbyterian minister and amateur mathematician whose obscure life belied the profound impact of his work. Like most research into probability at the time, his theorem was mainly seen as relevant to games of chance, like dice and cards. But its implications soon became clear, affecting fields as diverse as medicine, law and artificial intelligence. Bayes' theorem helps explain why highly accurate screening tests can lead to false positives, causing unnecessary anxiety for patients. A failure to account for it in court has put innocent people in jail. But its influence goes far beyond practical applications. Fusing biography, razor-sharp science communication and intellectual history, 'Everything Is Predictable' is a captivating tour of Bayes' theorem and its impact on modern life.
BOOK
The Bayesian bridge
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: a scale mixture of normal distributions with respect to an »-stable random variable; a mixture of Bartlett–Fejer kernels (or triangle densities) with respect to a two-component mixture of gamma random variables. Both lead to Markov chain Monte Carlo methods for posterior simulation, and these methods turn out to have complementary domains of maximum efficiency. The first representation is a well-known result due to West and is the better choice for collinear design matrices. The second representation is new and is more efficient for orthogonal problems, largely because it avoids the need to deal with exponentially tilted stable random variables. It also provides insight into the multimodality of the joint posterior distribution, which is a feature of the bridge model that is notably absent under ridge or lasso-type priors. We prove a theorem that extends this representation to a wider class of densities representable as scale mixtures of beta distributions, and we provide an explicit inversion formula for the mixing distribution. The connections with slice sampling and scale mixtures of normal distributions are explored. On the practical side, we find that the Bayesian bridge model outperforms its classical cousin in estimation and prediction across a variety of data sets, both simulated and real. We also show that the Markov chain Monte Carlo algorithm for fitting the bridge model exhibits excellent mixing properties, particularly for the global scale parameter. This makes for a favourable contrast with analogous Markov chain Monte Carlo algorithms for other sparse Bayesian models. All methods described in this paper are implemented in the R package BayesBridge. An extensive set of simulation results is provided in two on-line supplemental files.
Journal Article
Website Morphing
Virtual advisors often increase sales for those customers who find such online advice to be convenient and helpful. However, other customers take a more active role in their purchase decisions and prefer more detailed data. In general, we expect that websites are more preferred and increase sales if their characteristics (e.g., more detailed data) match customers' cognitive styles (e.g., more analytic). \"Morphing\" involves automatically matching the basic \"look and feel\" of a website, not just the content, to cognitive styles. We infer cognitive styles from clickstream data with Bayesian updating. We then balance exploration (learning how morphing affects purchase probabilities) with exploitation (maximizing short-term sales) by solving a dynamic program (partially observable Markov decision process). The solution is made feasible in real time with expected Gittins indices. We apply the Bayesian updating and dynamic programming to an experimental BT Group (formerly British Telecom) website using data from 835 priming respondents. If we had perfect information on cognitive styles, the optimal \"morph\" assignments would increase purchase intentions by 21%. When cognitive styles are partially observable, dynamic programming does almost as well—purchase intentions can increase by almost 20%. If implemented system-wide, such increases represent approximately $80 million in additional revenue.
Journal Article
Wavelet-based functional mixed models
Increasingly, scientific studies yield functional data, in which the ideal units of observation are curves and the observed data consist of sets of curves that are sampled on a fine grid. We present new methodology that generalizes the linear mixed model to the functional mixed model framework, with model fitting done by using a Bayesian wavelet-based approach. This method is flexible, allowing functions of arbitrary form and the full range of fixed effects structures and between-curve covariance structures that are available in the mixed model framework. It yields nonparametric estimates of the fixed and random-effects functions as well as the various between-curve and within-curve covariance matrices. The functional fixed effects are adaptively regularized as a result of the non-linear shrinkage prior that is imposed on the fixed effects' wavelet coefficients, and the random-effect functions experience a form of adaptive regularization because of the separately estimated variance components for each wavelet coefficient. Because we have posterior samples for all model quantities, we can perform pointwise or joint Bayesian inference or prediction on the quantities of the model. The adaptiveness of the method makes it especially appropriate for modelling irregular functional data that are characterized by numerous local features like peaks.
Journal Article