A Bayes Linear Bayes Method for Estimation of Correlated Event Rates

Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well‐known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates.     

Inference in Dynamic Discrete Choice Models With Serially orrelated Unobserved State Variables

This paper develops a method for inference in dynamic discrete choice models with serially correlated unobserved state variables. Estimation of these models involves computing high‐dimensional integrals that are present in the solution to the dynamic program and in the likelihood function. First, the paper proposes a Bayesian Markov chain Monte Carlo estimation procedure that can handle the problem of multidimensional integration in the likelihood function. Second, the paper presents an efficient algorithm for solving the dynamic program suitable for use in conjunction with the proposed estimation procedure.     

An Efficient Dynamic Mechanism

This paper constructs an efficient, budget‐balanced, Bayesian incentive‐compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods. First, under the assumption of “private values” (other agents' private information does not directly affect an agent's payoffs), we construct an efficient, ex post incentive‐compatible mechanism, which is not budget‐balanced. Second, under the assumption of “independent types” (the distribution of each agent's private information is not directly affected by other agents' private information), we show how the budget can be balanced without compromising agents' incentives. Finally, we show that the mechanism can be made self‐enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite Markov chain.     

基于多子样的贝叶斯动态过程能力估计与评价方法研究

针对参数随机化情况下生产过程能力的评价问题,提出了新的过程能力指数估计与评价方法。通过质量控制模型的统计结构分析,研究了扩散先验分布下参数后验分布,据此构造了过程能力指数的贝叶斯点估计和区间估计;在此基础上,将前一阶段模型参数后验分布作为下一阶段的参数先验分布,充分利用历史数据信息,建立了过程能力指数及其下限的贝叶斯动态评价模型。研究结果表明:与现有的贝叶斯过程能力指数估计方法比较,贝叶斯动态过程能力指数的预测精度优于前者,更能反映实际生产过程能力水平。     

供应链信息结构与控制结构绩效研究

本文应用Bayesian推断原理构建信息结构与控制结构组合决策模型,考察了信息预测精度、市场风险、信息分布以及中心化与分散化结构对系统绩效的影响,识别了市场信息共享与决策控制的有效匹配结构,为供应链信息管理提出了建议。     

Demonstrating the Benefits of Predictive Bayesian Dose–Response Relationships Using Six Exposure Studies of Cryptosporidium parvum

A conventional dose–response function can be refitted as additional data become available. A predictive dose–response function in contrast does not require a curve-fitting step, only additional data and presents the unconditional probabilities of illness, reflecting the level of information it contains. In contrast, the predictive Bayesian dose–response function becomes progressively less conservative as more information is included. This investigation evaluated the potential for using predictive Bayesian methods to develop a dose–response for human infection that improves on existing models, to show how predictive Bayesian statistical methods can utilize additional data, and expand the Bayesian methods for a broad audience including those concerned about an oversimplification of dose–response curve use in quantitative microbial risk assessment (QMRA). This study used a dose–response relationship incorporating six separate data sets for Cryptosporidium parvum. A Pareto II distribution with known priors was applied to one of the six data sets to calibrate the model, while the others were used for subsequent updating. While epidemiological principles indicate that local variations, host susceptibility, and organism strain virulence may vary, the six data sets all appear to be well characterized using the Bayesian approach. The adaptable model was applied to an existing data set for Campylobacter jejuni for model validation purposes, which yielded results that demonstrate the ability to analyze a dose–response function with limited data using and update those relationships with new data. An analysis of the goodness of fit compared to the beta-Poisson methods also demonstrated correlation between the predictive Bayesian model and the data.     

基于贝叶斯网络的并发型突发事件链建模方法

现实情形中，由于致灾因子和作用对象的相似性，初始突发事件的发生易引发多个次生事件并发及耦合，致使事件的演化发展及可能造成的损失具有更大的不确定性。然而，现有的突发事件链式演化分析多运用串发型事件链，对于并发型突发事件存在适用性较低的问题。针对上述问题，本文将突发事件抽象描述为以输入、状态和输出属性为组成要素，通过属性要素间的作用关系构成的复杂系统，进而从属性层面分析事件间的关联关系；以贝叶斯网络为建模工具，识别并发型突发事件间具有的因果关系和耦合关系，给出事件贝叶斯网络关联方法，构建并发型突发事件链模型；基于历史数据获取网络节点间的先验概率信息，运用贝叶斯网络推理算法实现并发型突发事件的演化分析；最后，通过实例验证本文方法在实际应用中的科学性及可行性，并通过对比分析阐明其在提高灾害损失预测精度方面具有一定的优势。     

Domino Effect Analysis Using Bayesian Networks

A new methodology is introduced based on Bayesian network both to model domino effect propagation patterns and to estimate the domino effect probability at different levels. The flexible structure and the unique modeling techniques offered by Bayesian network make it possible to analyze domino effects through a probabilistic framework, considering synergistic effects, noisy probabilities, and common cause failures. Further, the uncertainties and the complex interactions among the domino effect components are captured using Bayesian network. The probabilities of events are updated in the light of new information, and the most probable path of the domino effect is determined on the basis of the new data gathered. This study shows how probability updating helps to update the domino effect model either qualitatively or quantitatively. The methodology is applied to a hypothetical example and also to an earlier‐studied case study. These examples accentuate the effectiveness of Bayesian network in modeling domino effects in processing facility.     

A Bayesian Evidence Synthesis for Estimating Campylobacteriosis Prevalence

Stakeholders making decisions in public health and world trade need improved estimations of the burden‐of‐illness of foodborne infectious diseases. In this article, we propose a Bayesian meta‐analysis or more precisely a Bayesian evidence synthesis to assess the burden‐of‐illness of campylobacteriosis in France. Using this case study, we investigate campylobacteriosis prevalence, as well as the probabilities of different events that guide the disease pathway, by (i) employing a Bayesian approach on French and foreign human studies (from active surveillance systems, laboratory surveys, physician surveys, epidemiological surveys, and so on) through the chain of events that occur during an episode of illness and (ii) including expert knowledge about this chain of events. We split the target population using an exhaustive and exclusive partition based on health status and the level of disease investigation. We assume an approximate multinomial model over this population partition. Thereby, each observed data set related to the partition brings information on the parameters of the multinomial model, improving burden‐of‐illness parameter estimates that can be deduced from the parameters of the basic multinomial model. This multinomial model serves as a core model to perform a Bayesian evidence synthesis. Expert knowledge is introduced by way of pseudo‐data. The result is a global estimation of the burden‐of‐illness parameters with their accompanying uncertainty.     

Application of Bayesian Networks in Quantitative Risk Assessment of Subsea Blowout Preventer Operations

This article proposes a methodology for the application of Bayesian networks in conducting quantitative risk assessment of operations in offshore oil and gas industry. The method involves translating a flow chart of operations into the Bayesian network directly. The proposed methodology consists of five steps. First, the flow chart is translated into a Bayesian network. Second, the influencing factors of the network nodes are classified. Third, the Bayesian network for each factor is established. Fourth, the entire Bayesian network model is established. Lastly, the Bayesian network model is analyzed. Subsequently, five categories of influencing factors, namely, human, hardware, software, mechanical, and hydraulic, are modeled and then added to the main Bayesian network. The methodology is demonstrated through the evaluation of a case study that shows the probability of failure on demand in closing subsea ram blowout preventer operations. The results show that mechanical and hydraulic factors have the most important effects on operation safety. Software and hardware factors have almost no influence, whereas human factors are in between. The results of the sensitivity analysis agree with the findings of the quantitative analysis. The three‐axiom‐based analysis partially validates the correctness and rationality of the proposed Bayesian network model.     

A Bayesian Network Estimation of the Service‐Profit Chain for Transport Service Satisfaction

Bayesian network methodology is used to model key linkages of the service‐profit chain within the context of transportation service satisfaction. Bayesian networks offer some advantages for implementing managerially focused models over other statistical techniques designed primarily for evaluating theoretical models. These advantages are (1) providing a causal explanation using observable variables within a single multivariate model, (2) analysis of nonlinear relationships contained in ordinal measurements, (3) accommodation of branching patterns that occur in data collection, and (4) the ability to conduct probabilistic inference for prediction and diagnostics with an output metric that can be understood by managers and academics. Sample data from 1,101 recent transport service customers are utilized to select and validate a Bayesian network and conduct probabilistic inference.     

Bayesian Network for Risk of Diarrhea Associated with the Use of Recycled Water

Estimating potential health risks associated with recycled (reused) water is highly complex given the multiple factors affecting water quality. We take a conceptual model, which represents the factors and pathways by which recycled water may pose a risk of contracting gastroenteritis, convert the conceptual model to a Bayesian net, and quantify the model using one expert's opinion. This allows us to make various predictions as to the risks posed under various scenarios. Bayesian nets provide an additional way of modeling the determinants of recycled water quality and elucidating their relative influence on a given disease outcome. The important contribution to Bayesian net methodology is that all model predictions, whether risk or relative risk estimates, are expressed as credible intervals.     

Bayesian and Frequentist Inference in Partially Identified Models

A large‐sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by an identifiable finite‐dimensional reduced‐form parameter vector. It is used to analyze the differences between Bayesian credible sets and frequentist confidence sets. We define a plug‐in estimator of the identified set and show that asymptotically Bayesian highest‐posterior‐density sets exclude parts of the estimated identified set, whereas it is well known that frequentist confidence sets extend beyond the boundaries of the estimated identified set. We recommend reporting estimates of the identified set and information about the conditional prior along with Bayesian credible sets. A numerical illustration for a two‐player entry game is provided.     

Determining the expected value of information for new product introduction

Bayesian analysis is an important technique for marketing decision-making. To this point, however, these procedures have been used infrequently by practicing managers. Two major obstacles to the application of Bayesian analysis are the difficulties associated with generating input values and with performing the necessary calculations. In this paper a procedure is presented which, in most cases, removes both of these obstacles. The procedure has assessment needs with which the practicing manager may be more familiar. Tables are developed to alleviate computational difficulties.     

Inferring an Augmented Bayesian Network to Confront a Complex Quantitative Microbial Risk Assessment Model with Durability Studies: Application to Bacillus Cereus on a Courgette Purée Production Chain

The Monte Carlo (MC) simulation approach is traditionally used in food safety risk assessment to study quantitative microbial risk assessment (QMRA) models. When experimental data are available, performing Bayesian inference is a good alternative approach that allows backward calculation in a stochastic QMRA model to update the experts’ knowledge about the microbial dynamics of a given food‐borne pathogen. In this article, we propose a complex example where Bayesian inference is applied to a high‐dimensional second‐order QMRA model. The case study is a farm‐to‐fork QMRA model considering genetic diversity of Bacillus cereus in a cooked, pasteurized, and chilled courgette purée. Experimental data are Bacillus cereus concentrations measured in packages of courgette purées stored at different time‐temperature profiles after pasteurization. To perform a Bayesian inference, we first built an augmented Bayesian network by linking a second‐order QMRA model to the available contamination data. We then ran a Markov chain Monte Carlo (MCMC) algorithm to update all the unknown concentrations and unknown quantities of the augmented model. About 25% of the prior beliefs are strongly updated, leading to a reduction in uncertainty. Some updates interestingly question the QMRA model.     

Truthful Equilibria in Dynamic Bayesian Games

This paper characterizes an equilibrium payoff subset for dynamic Bayesian games as discounting vanishes. Monitoring is imperfect, transitions may depend on actions, types may be correlated, and values may be interdependent. The focus is on equilibria in which players report truthfully. The characterization generalizes that for repeated games, reducing the analysis to static Bayesian games with transfers. With independent private values, the restriction to truthful equilibria is without loss, except for the punishment level: if players withhold their information during punishment‐like phases, a folk theorem obtains.     

A Mechanism‐Design Approach to Speculative Trade

When two parties have different prior beliefs about some future event, they can realize gains through speculative trade. Can these gains be realized when the parties' prior beliefs are not common knowledge? We examine a simple example in which two parties having heterogeneous prior beliefs, independently drawn from some distribution, bet on what future action one of them will choose. We define a notion of “constrained interim‐efficient” best and ask whether they can be implemented in Bayesian equilibrium by some mechanism. Our main result establishes that as the costs of unilaterally manipulating the bet's outcome become more symmetric across states, implementation becomes easier. In particular, when these costs are equal in both states, implementation is possible for any distribution.     

On the Equivalence of Bayesian and Dominant Strategy Implementation

We consider a standard social choice environment with linear utilities and independent, one‐dimensional, private types. We prove that for any Bayesian incentive compatible mechanism there exists an equivalent dominant strategy incentive compatible mechanism that delivers the same interim expected utilities for all agents and the same ex ante expected social surplus. The short proof is based on an extension of an elegant result due to Gutmann, Kemperman, Reeds, and Shepp (1991). We also show that the equivalence between Bayesian and dominant strategy implementation generally breaks down when the main assumptions underlying the social choice model are relaxed or when the equivalence concept is strengthened to apply to interim expected allocations.     

基于GLM的贝叶斯变量与模型选择

针对非正态响应的部分因子试验,当筛选试验所涉及的因子数目较大时,提出了基于广义线性模型(generalized linear models,GLM)的贝叶斯变量与模型选择方法.首先,针对模型参数的不确定性,选择了经验贝叶斯先验.其次,在广义线性模型的线性预测器中对每个变量设置了二元变量指示器,并建立起变量指示器与模型指示器之间的转换关系.然后,利用变量指示器与模型指示器的后验概率来识别显著性因子与选择最佳模型.最后,以实际的工业案例说明此方法能够有效地识别非正态响应部分因子试验的显著性因子.     

Decision Making Under Risk: A Comparison of Bayesian and Fuzzy Set Methods

A classical decision problem is considered where a decision maker is to choose one of a number of actions each offering different consequences. The outcome from a choice of action is uncertain because it depends on the existing state of Nature. Also, the outcome, once an action and state of Nature are specified, may be a vector or a random vector. The decision maker employs both Bayesian methods and fuzzy set techniques to handle the uncertainties. The decision maker is also allowed to use multiple, possibly conflicting, goals in order to determine his best strategy. The Bayesian method produces a set of undominated strategies to choose from, whereas the fuzzy set technique usually produces a unique optimal strategy.