We combine Bayesian networks (BNs) and structural reliability methods (SRMs) to create a new computational framework, termed enhanced Bayesian network (eBN), for reliability and risk analysis of engineering structures and infrastructure. BNs are efficient in representing and evaluating complex probabilistic dependence structures, as present in infrastructure and structural systems, and they facilitate Bayesian updating of the model when new information becomes available. On the other hand, SRMs enable accurate assessment of probabilities of rare events represented by computationally demanding, physically-based models. By combining the two methods, the eBN framework provides a unified and powerful tool for efficiently computing probabilities of rare events in complex structural and infrastructure systems in which information evolves in time. Strategies for modeling and efficiently analyzing the eBN are described by way of several conceptual examples. The companion paper applies the eBN methodology to example structural and infrastructure systems.
A Bayesian changepoint methodology for high dimensional multivariate time series and space-time data: A study of structural change using remotely sensed data
In employing spatial regression models for counts, we usually meet two issues. First, ignoring the inherent collinearity between covariates and the spatial effect would lead to causal inferences. Second, real count data usually reveal over or under-dispersion where the classical Poisson model is not appropriate to use. We propose a flexible Bayesian hierarchical modeling approach by joining non-confounding spatial methodology and a newly reconsidered dispersed count modeling from the renewal theory to control the issues. Specifically, we extend the methodology for analyzing spatial count data …
The uptake of behind-the-meter distributed energy resources in low-voltage distribution networks has reached a level where network issues have started to emerge, which requires new tools for operation and planning. In this paper, we propose a methodology for synthesizing stochastic demand and generation profiles for unobserved customers with rooftop PV, called prosumers. The proposed model bridges the gap between the limited available empirical data, and the large amount of high-quality, stochastic demand and generation data required for probabilistic analysis. The approach employs clustering …
Bayesian Nonparametric Conditional Copula Estimation of Twin Data
一些关于双胞胎遗传力的研究旨在了解环境和遗传因素对特定性状的不同贡献。结合全国优秀双胞胎研究，我们的目的是正确分析社会经济地位对双胞胎认知能力关系的影响。我们的方法是基于条件Copula，这使我们能够模拟协变量驱动的主要变量之间的依赖强度的影响。我们提出了一个灵活的贝叶斯非参数方法估计的条件copula，它可以模拟任何条件copula密度。我们的方法扩展了Wu et al（2015）的工作，通过在无限混合模型中引入协变量的依赖性。我们的研究结果表明，环境因素在社会经济地位较低的家庭中更有影响力。
We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks, such as description, testing, estimation, and prediction. This work is not meant to be either a reference text or a survey in Bayesian statistical inference. Our goal is simply to provide several examples that use Bayesian methodology to solve data-driven problems. The topics we cover here, include problems in Bayesian nonparametrics, Bayesian analysis of t…
Harvard University（哈佛大学）；Institute for Quantitative Social Science（定量社会科学研究所）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；Harvard Data Science Initiative（哈佛大学数据科学计划）；L2, Inc.（L2公司）
Prediction of individual's race and ethnicity plays an important role in social science and public health research. Examples include studies of racial disparity in health and voting. Recently, Bayesian Improved Surname Geocoding (BISG), which uses Bayes' rule to combine information from Census surname files with the geocoding of an individual's residence, has emerged as a leading methodology for this prediction task. Unfortunately, BISG suffers from two Census data problems that contribute to unsatisfactory predictive performance for minorities. First, the decennial Census often contains zero …
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous responses. In this paper, we present methodology which allows for information to be shared nonparametrically across various model components using Bayesian sum-of-tree models. Our simulation results demonstrate that sharing of information across related model components is often very beneficial, particularly in sparse high-dimensional problems in which variabl…
This paper develops Bayesian sample size formulae for experiments comparing two groups. We assume the experimental data will be analysed in the Bayesian framework, where pre-experimental information from multiple sources can be represented into robust priors. In particular, such robust priors account for preliminary belief about the pairwise commensurability between parameters that underpin the historical and new experiments, to permit flexible borrowing of information. Averaged over the probability space of the new experimental data, appropriate sample sizes are found according to criteria th…
This paper aims to propose a novel deep learning-integrated framework for deriving reliable simulation input models through incorporating multi-source information. The framework sources and extracts multisource data generated from construction operations, which provides rich information for input modeling. The framework implements Bayesian deep neural networks to facilitate the purpose of incorporating richer information in input modeling. A case study on road paving operation is performed to test the feasibility and applicability of the proposed framework. Overall, this research enhances inpu…
Measurement of operator quality performance has been challenging in the construction fabrication industry. Among various causes, the learning effect is a significant factor, which needs to be incorporated in achieving a reliable operator quality performance analysis. This research aims to enhance a previously developed operator quality performance measurement approach by incorporating the learning effect (i.e., work experience). To achieve this goal, the Plateau learning model is selected to quantitatively represent the relationship between quality performance and work experience through a bet…
We investigate Bayesian predictive inference for finite population quantities when there are unequal probabilities of selection. Only limited information about the sample design is available; i.e., only the first-order selection probabilities corresponding to the sample units are known. Our methodology, unlike that of Chambers, Dorfman and Wang (1998), can be used to make inference for finite population quantities and provides measures of precision and intervals. Moreover, our methodology, using Markov chain Monte Carlo methods, avoids the necessity of using asymptotic closed form approximatio…
This work proposes a new methodology to fit zero inflated Bernoulli data from a Bayesian approach, able to distinguish between two potential sources of zeros (structurals and non-structurals). Its usage is illustrated by means of a real example from the field of occupational health as the phenomenon of sickness presenteeism, in which it is reasonable to think that some individuals will never be at risk of suffering it because they have not been sick in the period of study (structural zeros). Without separating structural and non-structural zeros one would one would be studying jointly the gene…
The Alan Turing Institute（艾伦图灵研究所）；Imperial College London（伦敦帝国理工学院）
We introduce a novel rule-based approach for handling regression problems. The new methodology carries elements from two frameworks: (i) it provides information about the uncertainty of the parameters of interest using Bayesian inference, and (ii) it allows the incorporation of expert knowledge through rule-based systems. The blending of those two different frameworks can be particularly beneficial for various domains (e.g. engineering), where, even though the significance of uncertainty quantification motivates a Bayesian approach, there is no simple way to incorporate researcher intuition in…
In this paper, we propose a non-parametric Bayesian network method to generate synthetic scenarios of hourly generation for variable renewable energy(VRE) plants. The methodology consists of a non-parametric estimation of the probability distribution of VRE generation, followed by an inverse probability integral transform, in order to obtain normally distributed variables of VRE generation. Then, we build a Bayesian network based on the evaluation of the spatial correlation between variables (VRE generation and hydro inflows, but load forecast, temperature, and other types of random variables …
Tracer-kinetic analysis of dynamic contrast-enhanced magnetic resonance imaging data is commonly performed with the well-known Tofts model and nonlinear least squares (NLLS) regression. This approach yields point estimates of model parameters, uncertainty of these estimates can be assessed e.g. by an additional bootstrapping analysis. Here, we present a Bayesian probabilistic modeling approach for tracer-kinetic analysis with a Tofts model, which yields posterior probability distributions of perfusion parameters and therefore promises a robust and information-enriched alternative based on a fr…
Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age…
We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, Extreme value models, to name but a few. All of those models include a gamma function which does not admit a natural conjugate prior distribution providing a significant challenge to inference and prediction. To provide a data augmentation strategy, we construct and develop the t…
The Alan Turing Institute（艾伦·图灵研究所）；Imperial College London（帝国理工学院）；Newcastle University（纽卡斯尔大学）
In our previous work, we introduced the rule-based Bayesian Regression, a methodology that leverages two concepts: (i) Bayesian inference, for the general framework and uncertainty quantification and (ii) rule-based systems for the incorporation of expert knowledge and intuition. The resulting method creates a penalty equivalent to a common Bayesian prior, but it also includes information that typically would not be available within a standard Bayesian context. In this work, we extend the aforementioned methodology with grammatical evolution, a symbolic genetic programming technique that we ut…
U-DESPE: a Bayesian Utility-based methodology for dosing regimen optimization in early-phase oncology trials based on Dose-Exposure, Safety, Pharmacodynamics, Efficacy
Cluster analysis aims at partitioning data into groups or clusters. In applications, it is common to deal with problems where the number of clusters is unknown. Bayesian mixture models employed in such applications usually specify a flexible prior that takes into account the uncertainty with respect to the number of clusters. However, a major empirical challenge involving the use of these models is in the characterisation of the induced prior on the partitions. This work introduces an approach to compute descriptive statistics of the prior on the partitions for three selected Bayesian mixture …
Finite element model updating is challenging because 1) the problem is oftentimes underdetermined while the measurements are limited and/or incomplete; 2) many combinations of parameters may yield responses that are similar with respect to actual measurements; and 3) uncertainties inevitably exist. The aim of this research is to leverage upon computational intelligence through statistical inference to facilitate an enhanced, probabilistic finite element model updating using incomplete modal response measurement. This new framework is built upon efficient inverse identification through optimiza…
It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such hierarchical structure feature have considerable limitations in terms of modelling and/or inference. Motivated by those limitations and the importance of the theme, this paper aims at proposing an improved methodology in terms of both modelling and inference to deal with hierarchically structured latent traits in an item response theory context. From a modell…
The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried…
On integral priors for multiple comparison in Bayesian model selection
University of Murcia（穆尔西亚大学）；CIBER de Epidemiología y Salud Pública (CIBERESP)（公共卫生与流行病学网络中心（CIBERESP））；Biomedical Research Institute of Murcia Pascual Parrilla–IMIB（穆尔西亚生物医学研究所帕斯夸尔·帕里利亚-IMIB）；Université Paris Dauphine PSL（巴黎第九大学PSL）；University of Warwick（华威大学）
Beijing University of Posts and Telecommunications（北京邮电大学）；Tianjin University（天津大学）；University of Technology Sydney（悉尼科技大学）；University College London（伦敦大学学院）；Aalborg University（奥尔堡大学）
Due to lack of data, overfitting ubiquitously exists in real-world applications of deep neural networks (DNNs). We propose advanced dropout, a model-free methodology, to mitigate overfitting and improve the performance of DNNs. The advanced dropout technique applies a model-free and easily implemented distribution with parametric prior, and adaptively adjusts dropout rate. Specifically, the distribution parameters are optimized by stochastic gradient variational Bayes in order to carry out an end-to-end training. We evaluate the effectiveness of the advanced dropout against nine dropout techni…
London School of Economics and Political Science（伦敦政治经济学院）；J.P. Morgan（摩根大通）；Bayes Business School, City, University of London（伦敦大学城市学院贝叶斯商学院）；University of Oxford（牛津大学）
Training deep graph neural networks (GNNs) poses a challenging task, as the performance of GNNs may suffer from the number of hidden message-passing layers. The literature has focused on the proposals of {over-smoothing} and {under-reaching} to explain the performance deterioration of deep GNNs. In this paper, we propose a new explanation for such deteriorated performance phenomenon, {mis-simplification}, that is, mistakenly simplifying graphs by preventing self-loops and forcing edges to be unweighted. We show that such simplifying can reduce the potential of message-passing layers to capture…
