Aeroengine performance is determined by temperature and pressure profiles along various axial stations within an engine. Given limited sensor measurements both along and between axial stations, we require a statistically principled approach to inferring these profiles. In this paper we detail a Bayesian methodology for interpolating the spatial temperature or pressure profile at axial stations within an aeroengine. The profile at any given axial station is represented as a spatial Gaussian random field on an annulus, with circumferential variations modelled using a Fourier basis and radial variations modelled with a squared exponential kernel. This Gaussian random field is extended to ingest data from multiple axial measurement planes, with the aim of transferring information across the planes. To facilitate this type of transfer learning, a novel planar covariance kernel is proposed, with hyperparameters that characterise the correlation between any two measurement planes. In the scenario where precise frequencies comprising the temperature field are unknown, we utilise a sparsity-promoting prior on the frequencies to encourage sparse representations. This easily extends to cases with multiple engine planes whilst accommodating frequency variations between the planes. The main quantity of interest, the spatial area average is readily obtained in closed form. We term this the Bayesian area average and demonstrate how this metric offers far more precise averages than a sector area average -- a widely used area averaging approach. Furthermore, the Bayesian area average naturally decomposes the posterior uncertainty into terms characterising insufficient sampling and sensor measurement error respectively. This too provides a significant improvement over prior standard deviation based uncertainty breakdowns.
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose two types of Bayesian model criticism approaches to identify potentially irreproducible results in scientific experiments. They are motivated by established Bayesian prior and posterior predictive model-checking procedures and generalize many existing replicability assessment methods. Finally, we discuss the statistical properties of the proposed replicabilit…
The likelihood ratio (LR) is largely used to evaluate the relative weight of forensic data regarding two hypotheses and for its assessment Bayesian methods are widespread in the forensic field. However, the Bayesian `recipe' for the LR presented in most of literature consists in plugging-in Bayesian estimates of the involved nuisance parameters into a frequentist-defined LR: frequentist and Bayesian methods are thus mixed, giving rise to solutions obtained by hybrid reasoning. This paper provides the derivation of a proper Bayesian approach to assess LR for the `rare type match problem', the s…
Recent advances in machine learning have led to increased deployment of black-box classifiers across a wide variety of applications. In many such situations there is a critical need to both reliably assess the performance of these pre-trained models and to perform this assessment in a label-efficient manner (given that labels may be scarce and costly to collect). In this paper, we introduce an active Bayesian approach for assessment of classifier performance to satisfy the desiderata of both reliability and label-efficiency. We begin by developing inference strategies to quantify uncertainty f…
In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of the analyst and the particular forms chosen for the prior specification and the likelihood for the analysis. In order to do this, we propose performing a finite collection of additional Bayesian analyses under alternative collections of prior and likelihood modelling judgements that we may also view as representative of our prior knowledge and the problem st…
Within path sampling framework, we show that probability distribution divergences, such as the Chernoff information, can be estimated via thermodynamic integration. The Boltzmann-Gibbs distribution pertaining to different Hamiltonians is implemented to derive tempered transitions along the path, linking the distributions of interest at the endpoints. Under this perspective, a geometric approach is feasible, which prompts intuition and facilitates tuning the error sources. Additionally, there are direct applications in Bayesian model evaluation. Existing marginal likelihood and Bayes factor est…
Geostatistical modeling of the reservoir intrinsic properties starts only with sparse data available. These estimates will depend largely on the number of wells and their location. The drilling costs are so high that they do not allow new wells to be placed for uncertainty assessment. Besides that difficulty, usual geostatistical models do not account for the uncertainty of conceptual models, which should be considered. Spatial bootstrap is applied to assess the estimate reliability when resampling from original field is not an option. Considering different realities (conceptual models) and di…
The paper proposes a novel model assessment paradigm aiming to address shortcoming of posterior predictive $p-$values, which provide the default metric of fit for Bayesian structural equation modelling (BSEM). The model framework of the paper focuses on the approximate zero approach, according to which parameters that would before set to zero (e.g. factor loadings) are now formulated to be approximate zero via informative priors (Muthen and Asparouhov, 2012). The introduced model assessment procedure monitors the out-of-sample predictive performance of the fitted model, and together with a lis…
Fossil-based palaeoclimate reconstruction is an important area of ecological science that has gained momentum in the backdrop of the global climate change debate. The hierarchical Bayesian paradigm provides an interesting platform for studying such important scientific issue. However, our cross-validation based assessment of the existing Bayesian hierarchical models with respect to two modern proxy data sets based on chironomid and pollen, respectively, revealed that the models are inadequate for the data sets. In this paper, we model the species assemblages (compositional data) by the zero-in…
The Bayesian expected power (BEP) has become increasingly popular in sample size determination and assessment of the probability of success (POS) for a future trial. The BEP takes into consideration the uncertainty around the parameters assumed by a power analysis and is thus more robust compared to the traditional power that assumes a single set of parameters. Current methods for assessing BEP are often based in a parametric framework by imposing a model on the pilot data to derive and sample from the posterior distributions of the parameters. Implementation of the model-based approaches can …
Queen Mary University of London（伦敦玛丽女王大学）；Agena Ltd（Agena有限公司）
Product risk assessment is the overall process of determining whether a product, which could be anything from a type of washing machine to a type of teddy bear, is judged safe for consumers to use. There are several methods used for product risk assessment, including RAPEX, which is the primary method used by regulators in the UK and EU. However, despite its widespread use, we identify several limitations of RAPEX including a limited approach to handling uncertainty and the inability to incorporate causal explanations for using and interpreting test data. In contrast, Bayesian Networks (BNs) a…
Managing risk at the aggregate level is crucial for banks and financial institutions as required by the Basel III framework. In this paper, we introduce discrete time Bayesian state space models with Poisson measurements to model aggregate mortgage default rate. We discuss parameter updating, filtering, smoothing, forecasting and estimation using Markov chain Monte Carlo methods. In addition, we investigate the dynamic behavior of the default rate and the effects of macroeconomic variables. We illustrate the use of the proposed models using actual U.S. residential mortgage data and discuss ins…
Few models have been more ubiquitous in their respective fields than Bayesian knowledge tracing and item response theory. Both of these models were developed to analyze data on learners. However, the study designs that these models are designed for differ; Bayesian knowledge tracing is designed to analyze longitudinal data while item response theory is built for cross-sectional data. This paper illustrates a fundamental connection between these two models. Specifically, the stationary distribution of the latent variable and the observed response variable in Bayesian knowledge Tracing are relat…
This paper is an invited commentary on Tamas Budavari's presentation, "On statistical cross-identification in astronomy," for the Statistical Challenges in Modern Astronomy V conference held at Pennsylvania State University in June 2011. I begin with a brief review of previous work on probabilistic (Bayesian) assessment of directional and spatio-temporal coincidences in astronomy (e.g., cross-matching or cross-identification of objects across multiple catalogs). Then I discuss an open issue in the recent innovative work of Budavari and his colleagues on large-scale probabilistic cross-identifi…
The evaluation of a match between the DNA profile of a stain found on a crime scene and that of a suspect (previously identified) involves the use of the unknown parameter $p=(p_1, p_2, ...)$, (the ordered vector which represents the proportions of the different DNA profiles in the population of potential donors) and the names of the different DNA types. We propose a Bayesian non parametric method which considers $P$ as a random variable distributed according to the two-parameter Poisson Dirichlet distribution, and discard information about names of DNA types. The ultimate goal of this model i…
We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sam…
Risk assessment instruments are used across the criminal justice system to estimate the probability of some future behavior given covariates. The estimated probabilities are then used in making decisions at the individual level. In the past, there has been controversy about whether the probabilities derived from group-level calculations can meaningfully be applied to individuals. Using Bayesian hierarchical models applied to a large longitudinal dataset from the court system in the state of Kentucky, we analyze variation in individual-level probabilities of failing to appear for court and the …
The aim of this paper is to explore and develop advanced spatial Bayesian assessment methods and techniques for land use modeling. The paper provides a comprehensive guide for assessing additional informational entropy value of model predictions at the spatially explicit domain of knowledge, and proposes a few alternative metrics and indicators for extracting higher-order information dynamics from simulation tournaments. A seven-county study area in South-Eastern Wisconsin (SEWI) has been used to simulate and assess the accuracy of historical land use changes (1963-1990) using artificial neura…
Neural Architectures for Amortized Bayesian Inference: Statistical Foundations and Empirical Assessments
Department of Mathematics and Statistics, Indian Institute of Technology Kanpur（数学与统计学系，印度理工学院坎浦尔分校）；Marshall School of Business, University of Southern California（马歇尔商学院，南加州大学）
This paper develops a Bayesian approach for assessing equivalence and non-inferiority hypotheses in two-arm trials using relative belief ratios. A relative belief ratio is a measure of statistical evidence and can indicate evidence either for or against a hypothesis. In addition to the relative belief ratio, we also compute a measure of the strength of this evidence as a calibration of the relative belief ratio. Furthermore, we make use of the relative belief ratio as a measure of evidence, to assess whether a given prior induces bias either for or against a hypothesis. Prior elicitation, mode…
Fueled by the call for formative assessments, diagnostic classification models (DCMs) have recently gained popularity in psychometrics. Despite their potential for providing diagnostic information that aids in classroom instruction and students' learning, empirical applications of DCMs to classroom assessments have been highly limited. This is partly because how DCMs with different estimation methods perform in small sample contexts is not yet well-explored. Hence, this study aims to investigate the performance of respondent classification and item parameter estimation with a comprehensive sim…
Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor are present in the data (i.e. the population of factor levels has been exhausted). Random and mixed effects models are used for more elaborate cases, but require distinct nomenclature, concepts and theory, as well as distinct inferential procedures. Following a hierarchical Bayesian approach, a comprehensive ANOVA framework is shown, which unifies the above s…
The distribution of deaths by cause provides crucial information for public health planning, response, and evaluation. About 60% of deaths globally are not registered or given a cause, limiting our ability to understand disease epidemiology. Verbal autopsy (VA) surveys are increasingly used in such settings to collect information on the signs, symptoms, and medical history of people who have recently died. This article develops a novel Bayesian method for estimation of population distributions of deaths by cause using verbal autopsy data. The proposed approach is based on a multivariate probit…
We propose a modification of the improved cross entropy (iCE) method to enhance its performance for network reliability assessment. The iCE method performs a transition from the nominal density to the optimal importance sampling (IS) density via a parametric distribution model whose cross entropy with the optimal IS is minimized. The efficiency and accuracy of the iCE method are largely influenced by the choice of the parametric model. In the context of reliability of systems with independent multi-state components, the obvious choice of the parametric family is the categorical distribution. W…
A method for conducting Bayesian elicitation and learning in risk assessment is presented. It assumes that the risk process can be described as a fault tree. This is viewed as a belief network, for which prior distributions on primary event probabilities are elicited by means of a pairwise comparison approach. A Bayesian updating procedure, following observation of some or all of the events in the fault tree, is described. The application is illustrated through the motivating example of risk assessment of spacecraft explosion during controlled re-entry.
The enhanced Bayesian network (eBN) methodology described in the companion paper facilitates the assessment of reliability and risk of engineering systems when information about the system evolves in time. We present the application of the eBN (a) to the assessment of the life-cycle reliability of a structural system, (b) to the optimization of a decision on performing measurements in that structural system, and (c) to the risk assessment of an infrastructure system subject to natural hazards and deterioration of constituent structures. In all applications, observations of system performances …
Robust Survival Estimation under Interval Censoring: Expectation-Maximization and Bayesian Accelerated Failure Time Assessment via Simulation and Application
The aim of the present study is to detect abrupt trend changes in the mean of a multidimensional sequential signal. Directly inspired by papers of Fernhead and Liu ([4] and [5]), this work describes the signal in a hierarchical manner : the change dates of a time segmentation process trigger the renewal of a piece-wise constant emission law. Bayesian posterior information on the change dates and emission parameters is obtained. These estimations can be revised online, i.e. as new data arrive. This paper proposes explicit formulations corresponding to various emission laws, as well as a general…
Previous likelihood-based linear modeling of nutritional data has been limited by the availability of software that allows flexible error structures in the data. We demonstrate the use of a Bayesian modeling approach to the analysis of such data. Our goal is to model the relationship between the energy intake derived from Food Frequency Questionnaires (FFQs) and the energy expenditure estimated from the doubly labeled water method. We consider models with different distributions for the FFQ energy intake. The models include previously identified covariates describing social desirability, educa…
We consider Markov chain Monte Carlo (MCMC) algorithms for Bayesian high-dimensional regression with continuous shrinkage priors. A common challenge with these algorithms is the choice of the number of iterations to perform. This is critical when each iteration is expensive, as is the case when dealing with modern data sets, such as genome-wide association studies with thousands of rows and up to hundred of thousands of columns. We develop coupling techniques tailored to the setting of high-dimensional regression with shrinkage priors, which enable practical, non-asymptotic diagnostics of conv…
Addressing complex structures of measurement error arising in the exposure assessment in occupational epidemiology using a Bayesian hierarchical approach
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse Bayesian learning model from our previous work, we propose two Gibbs sampling algorithms. The algorithms differ in their strategies to deal with the posterior uncertainty of the equation-error precision parameter, but both sample from the conditional posterior probability density functions (PDFs) for the structural stiffness parameters and system modal parameter…
Universitá degli Studi di Milano-Bicocca（米兰比可卡大学）；NOVA Information Management School (NOVA IMS), Universidade Nova de Lisboa（里斯本大学学院NOVA信息管理学院）；INESC Coimbra（科英布拉系统与计算机工程研究所）；University of Coimbra（科英布拉大学）；Stanford University（斯坦福大学）
One of the most challenging tasks when adopting Bayesian Networks (BNs) is the one of learning their structure from data. This task is complicated by the huge search space of possible solutions, and by the fact that the problem is NP-hard. Hence, full enumeration of all the possible solutions is not always feasible and approximations are often required. However, to the best of our knowledge, a quantitative analysis of the performance and characteristics of the different heuristics to solve this problem has never been done before. For this reason, in this work, we provide a detailed comparison …
Pair Hidden Markov Models (PHMMs) are probabilistic models used for pairwise sequence alignment, a quintessential problem in bioinformatics. PHMMs include three types of hidden states: match, insertion and deletion. Most previous studies have used one or two hidden states for each PHMM state type. However, few studies have examined the number of states suitable for representing sequence data or improving alignment accuracy.We developed a novel method to select superior models (including the number of hidden states) for PHMM. Our method selects models with the highest posterior probability usin…
Benedict College（本尼迪克特学院）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Clemson University（克莱姆森大学）
This study presents a methodology to quantify vulnerability of cyber attacks and their impacts based on probabilistic graphical models for intelligent transportation systems under connected and autonomous vehicles framework. Cyber attack vulnerabilities from various types and their impacts are calculated for intelligent signals and cooperative adaptive cruise control (CACC) applications based on the selected performance measures. Numerical examples are given that show impact of vulnerabilities in terms of average intersection queue lengths, number of stops, average speed, and delays. At a sign…
Many wild species affected by human activities require multiple surveys with differing designs to capture behavioural response to wide ranging habitat conditions and map and quantify them. While data from for example intersecting but disparate fish surveys using different gear, are widely available, differences in design and methodology often limit their integration. Novel statistical approaches which can draw on observations from diverse sources could enhance our understanding of multiple species distributions simultaneously and thus provide vital evidence needed to conserve their populations…
In cargo logistics, a key performance measure is transport risk, defined as the deviation of the actual arrival time from the planned arrival time. Neither earliness nor tardiness is desirable for customer and freight forwarders. In this paper, we investigate ways to assess and forecast transport risks using a half-year of air cargo data, provided by a leading forwarder on 1336 routes served by 20 airlines. Interestingly, our preliminary data analysis shows a strong multimodal feature in the transport risks, driven by unobserved events, such as cargo missing flights. To accommodate this featur…
Attack graphs are a powerful tool for security risk assessment by analysing network vulnerabilities and the paths attackers can use to compromise network resources. The uncertainty about the attacker's behaviour makes Bayesian networks suitable to model attack graphs to perform static and dynamic analysis. Previous approaches have focused on the formalization of attack graphs into a Bayesian model rather than proposing mechanisms for their analysis. In this paper we propose to use efficient algorithms to make exact inference in Bayesian attack graphs, enabling the static and dynamic network ri…
Phase I dose-finding trials in oncology seek to find the maximum tolerated dose (MTD) of a drug under a specific schedule. Evaluating drug-schedules aims at improving treatment safety while maintaining efficacy. However, while we can reasonably assume that toxicity increases with the dose for cytotoxic drugs, the relationship between toxicity and multiple schedules remains elusive. We proposed a Bayesian dose-regimen assessment method (DRtox) using pharmacokinetics/pharmacodynamics (PK/PD) information to estimate the maximum tolerated dose-regimen (MTD-regimen), at the end of the dose-escalati…
We consider the problem of assessing goodness of fit of a single Bayesian model to the observed data in the inverse problem context. A novel procedure of goodness of fit test is proposed, based on construction of reference distributions using the `inverse' part of the given model. This is motivated by an example from palaeoclimatology in which it is of interest to reconstruct past climates using information obtained from fossils deposited in lake sediment. Technically, given a model $f(Y\mid X,θ)$, where $Y$ is the observed data and $X$ is a set of (non-random) covariates, we obtain reference …
In the classical literature on infinite series there are various tests to determine if a given infinite series converges, diverges, or oscillates. But unfortunately, for very many infinite series all the existing tests can fail to provide definitive answers. In this article we propose a novel Bayesian theory for assessment of convergence properties of any given infinite series. Remarkably, this theory attempts to provide conclusive answers to the question of convergence even where all the existing tests of convergence fail. We apply our ideas to seven different examples, obtaining very encoura…
Doubly-intractable posterior distributions arise in many applications of statistics concerned with discrete and dependent data, including physics, spatial statistics, machine learning, the social sciences, and other fields. A specific example is psychometrics, which has adapted high-dimensional Ising models from machine learning, with a view to studying the interactions among binary item responses in educational assessments. To estimate high-dimensional Ising models from educational assessment data, $\ell_1$-penalized nodewise logistic regressions have been used. Theoretical results in high-di…
The National Health and Nutrition Examination Survey (NHANES) is a major program of the National Center for Health Statistics, designed to assess the health and nutritional status of adults and children in the United States. The analysis of NHANES dental caries data faces several challenges, including (1) the data were collected using a complex, multistage, stratified, unequal-probability sampling design; (2) the sample size of some primary sampling units (PSU), e.g., counties, is very small; (3) the measures of dental caries have complicated structure and correlation, and (4) there is a subst…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating characteristics of classical nonparametric methods, as well as coherent uncertainty assessments provided by Bayesian procedures. However, as the authors say in the conclusion to their article, nonparametric Bayesian methods may be more aptly described as "massively parametric." Furthermore, I argue that many of the default nonparametric Bayes procedures are only Bayesia…
