Richard A Lockhart
Priors in which a large number of parameters are specified to be independent are dangerous; they make it hard to learn from data. I present a couple of examples from the literature and work through a bit of large sample theory to show what happens.
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We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of non-informative priors for selection models. These priors may be employed to produce a posterior distribution in the absence of prior information as well as to provide well-calibrated frequentist inference for the selected parameter. We test the proposed priors empirically in several scenarios.
Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated with the response variable of interest. Model inference performed on the observed sample taken from the population will be biased for the population generative model under informative sampling since the balance of information in the sample data is different from that for the population. Typical approaches to account for an informative sampling design under B…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to be correlated with the response variable of interest. Sampling weights constructed from marginal inclusion probabilities are typically used to form an exponentiated pseudo likelihood that adjusts the population likelihood for estimation on the sample due to ease-of-estimation. We propose an alternative adjustment based on a Bayes rule construction that simult…
In problems with large amounts of missing data one must model two distinct data generating processes: the outcome process which generates the response and the missing data mechanism which determines the data we observe. Under the ignorability condition of Rubin (1976), however, likelihood-based inference for the outcome process does not depend on the missing data mechanism so that only the former needs to be estimated; partially because of this simplification, ignorability is often used as a baseline assumption. We study the implications of Bayesian ignorability in the presence of high-dimensi…
The normal-normal hierarchical model (NNHM) constitutes a simple and widely used framework for meta-analysis. In the common case of only few studies contributing to the meta-analysis, standard approaches to inference tend to perform poorly, and Bayesian meta-analysis has been suggested as a potential solution. The Bayesian approach, however, requires the sensible specification of prior distributions. While non-informative priors are commonly used for the overall mean effect, the use of weakly informative priors has been suggested for the heterogeneity parameter, in particular in the setting of…
We study the accuracy of Bayesian supervised method used to cluster individuals into genetically homogeneous groups on the basis of dominant or codominant molecular markers. We provide a formula relating an error criterion the number of loci used and the number of clusters. This formula is exact and holds for arbitrary number of clusters and markers. Our work suggests that dominant markers studies can achieve an accuracy similar to that of codominant markers studies if the number of markers used in the former is about 1.7 times larger than in the latter.
Motivated by the analysis of the distribution of university grades, which is usually asymmetric, we discuss two informative priors for the shape parameter of the skew-normal distribution, showing that they lead to closed-form full-conditional posterior distributions, particularly useful in MCMC computation. Gibbs sampling algorithms are discussed for the joint vector of parameters, given independent prior distributions for the location and scale parameters. Simulation studies are performed to assess the performance of Gibbs samplers and to compare the choice of informative priors against a non…
Using a collection of simulated an real benchmarks, we compare Bayesian and frequentist regularization approaches under a low informative constraint when the number of variables is almost equal to the number of observations on simulated and real datasets. This comparison includes new global noninformative approaches for Bayesian variable selection built on Zellner's g-priors that are similar to Liang et al. (2008). The interest of those calibration-free proposals is discussed. The numerical experiments we present highlight the appeal of Bayesian regularization methods, when compared with non-B…
The aim of this work is to study the problem of prior elicitation for the Mallows model with Spearman's distance, a popular distance-based model for rankings or permutation data. Previous Bayesian inference for such model has been limited to the use of the uniform prior over the space of permutations. We present a novel strategy to elicit subjective prior beliefs on the location parameter of the model, discussing the interpretation of hyper-parameters and the implication of prior choices for the posterior analysis.
Unit-level models for survey data offer many advantages over their area-level counterparts, such as potential for more precise estimates and a natural benchmarking property. However two main challenges occur in this context: accounting for an informative survey design and handling non-Gaussian data types. The pseudo-likelihood approach is one solution to the former, and conjugate multivariate distribution theory offers a solution to the latter. By combining these approaches, we attain a unit-level model for count data that accounts for informative sampling designs and includes fully Bayesian m…
The United States Bureau of Labor Statistics collects data using survey instruments under informative sampling designs that assign probabilities of inclusion to be correlated with the response. The bureau extensively uses Bayesian hierarchical models and posterior sampling to impute missing items in respondent-level data and to infer population parameters. Posterior sampling for survey data collected based on informative designs are computationally expensive and do not support production schedules of the bureau. Motivated by this problem, we propose a new method to scale Bayesian computations …
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…
Pseudo-Bayesian unit level modeling for small area estimation under informative sampling
本文提出一种伪贝叶斯单元级小区域估计方法，通过纳入抽样权重处理信息性抽样，并引入后处理重缩放步骤校准可信集，从而在真实与模拟数据上获得接近名义覆盖率的估计结果。
Computational convenience has led to widespread use of Bayesian inference with vague or flat priors to analyze state-space models in ecology. Vague priors are claimed to be objective and to let the data speak. Neither of these claims is valid. Statisticians have criticized the use of vague priors from philosophical to computational to pragmatic reasons. Ecologists, however, dismiss such criticisms as empty philosophical wonderings with no practical implications. We illustrate that use of vague priors in population viability analysis and occupancy models can have significant impact on the analy…
Statistical estimates from survey samples have traditionally been obtained via design-based estimators. In many cases, these estimators tend to work well for quantities such as population totals or means, but can fall short as sample sizes become small. In today's "information age," there is a strong demand for more granular estimates. To meet this demand, using a Bayesian pseudo-likelihood, we propose a computationally efficient unit-level modeling approach for non-Gaussian data collected under informative sampling designs. Specifically, we focus on binary and multinomial data. Our approach i…
Beyond the classical type I error: Bayesian metrics for Bayesian designs using informative priors
本文针对使用信息先验的贝叶斯临床试验设计，提出平均I型错误等贝叶斯度量以评估假阳性风险，并证明在借用对照数据时其渐近可控性，助力监管讨论。
In this paper, the panel count data analysis for recurrent events is considered. Such analysis is useful for studying tumor or infection recurrences in both clinical trial and observational studies. A bivariate Gaussian Cox process model is proposed to jointly model the observation process and the recurrent event process. Bayesian nonparametric inference is proposed for simultaneously estimating regression parameters, bivariate frailty effects and baseline intensity functions. Inference is done through Markov chain Monte Carlo, with fully developed computational techniques. Predictive inferenc…
In recent years, Bayesian statistics methods in neuroscience have been showing important advances. In particular, detection of brain signals for studying the complexity of the brain is an active area of research. Functional magnetic resonance imagining (fMRI) is an important tool to determine which parts of the brain are activated by different types of physical behavior. According to recent results there is evidence that the values of the connectivity brain signal parameters are close to zero and due to the nature of time series fMRI data with high frequency behavior, Bayesian dynamic models f…
When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no longer produces asymptotically unbiased inference. We construct a weight-exponentiated formulation for the random effects distribution that achieves unbiased inference for generating hyperparameters of the random effects. We contrast our approach with frequentist methods that rely on numerical integration to reveal that only the Bayesian method achieves both…
Functional data are often extremely high-dimensional and exhibit strong dependence structures but can often prove valuable for both prediction and inference. The literature on functional data analysis is well developed; however, there has been very little work involving functional data in complex survey settings. Motivated by physical activity monitor data from the National Health and Nutrition Examination Survey (NHANES), we develop a Bayesian model for functional covariates that can properly account for the survey design. Our approach is intended for non-Gaussian data and can be applied in m…
Survey data are often collected under multistage sampling designs where units are binned to clusters that are sampled in a first stage. The unit-indexed population variables of interest are typically dependent within cluster. We propose a Fully Bayesian method that constructs an exact likelihood for the observed sample to incorporate unit-level marginal sampling weights for performing unbiased inference for population parameters while simultaneously accounting for the dependence induced by sampling clusters of units to produce correct uncertainty quantification. Our approach parameterizes clus…
There are many practical difficulties in the calibration of computer models to experimental data. One such complication is the fact that certain combinations of the calibration inputs can cause the code to output data lacking fundamental properties, or even to produce no output at all. In many cases the researchers want or need to exclude the possibility of these "failures" within their analyses. We propose a Bayesian (meta-)model in which the posterior distribution for the calibration parameters naturally excludes regions of the input space corresponding to failed runs. That is, we define a s…
In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this research I investigate the problem of informative sampling from the Bayesian perspective. Application of the Bayesian approach permits solving the problems, which arise due to complexity of the models, being used for handling informative sampling. The main objective of the re- search is to combine the elements of the classical sampling theory and Bayesian a…
Bayesian Optimization with Informative Covariance
针对高维贝叶斯优化中平稳协方差模型无法表达输入相关信息及信息均值函数表现不佳的问题，提出利用非平稳性编码区域偏好并自适应促进局部探索的新型信息协方差函数，有效提升了高维场景下的样本效率。
Identifying Informative Environments for Cognition Parameter Inference via Bayesian Experimental Design
该研究针对认知参数推断的环境选择问题，将认知规划实验建模为贝叶斯实验设计问题，提出摊销贝叶斯实验设计框架，经Mouselab-MDP实验验证其高效性，揭示了环境选择的权衡关系。
Uncertainty-Aware Bayes' Rule and Its Applications
本文提出不确定性感知的贝叶斯法则，用于应对模型不确定性，应用于分类和估计中的多种滤波器和分类器。
Additive Bayesian networks are types of graphical models that extend the usual Bayesian generalized linear model to multiple dependent variables through the factorisation of the joint probability distribution of the underlying variables. When fitting an ABN model, the choice of the prior of the parameters is of crucial importance. If an inadequate prior - like a too weakly informative one - is used, data separation and data sparsity lead to issues in the model selection process. In this work a simulation study between two weakly and a strongly informative priors is presented. As weakly informa…
A Bayesian Model for Co-clustering Ordinal Data with Informative Missing Entries
本文提出一种贝叶斯非参数模型，用于共聚类多变量有序数据，通过将缺失值视为信息而非缺失，提升对数据潜在结构的理解。
Evaluating the effect of different non-informative prior specifications on the Bayesian proportional odds model in randomised controlled trials: a simulation study
本研究通过模拟试验对比不同无信息先验对贝叶斯比例优势模型的影响，发现先验选择会影响治疗效应估计与早期停止决策，建议结合对照组概率分布选先验并做敏感性分析。
Using Large Language Models to Suggest Informative Prior Distributions in Bayesian Statistics
本研究探讨了利用大型语言模型建议贝叶斯统计中的信息先验分布，通过设计详尽提示词让模型建议并反思先验，在两个真实数据集上评估发现LLM能正确识别关联方向，但中等先验常过于自信，Claude和Gemini表现优于ChatGPT，主要挑战在于校准先验宽度。
In nonlinear regression models the Fisher information depends on the parameters of the model. Consequently, optimal designs maximizing some functional of the information matrix cannot be implemented directly but require some preliminary knowledge about the unknown parameters. Bayesian optimality criteria provide an attractive solution to this problem. These criteria depend sensitively on a reasonable specification of a prior distribution for the model parameters which might not be available in all applications. In this paper we investigate Bayesian optimality criteria with non-informative prio…
Mode-Matched Inverse Gamma Priors for Variance Components in Bayesian Multilevel Models
本文提出通过卡方—Gamma—逆 Gamma 变换构造众数匹配的信息性 IG 方差先验，并经模拟与 TIMSS 数据验证其可显著改善小样本多层模型估计。
We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we demonstrate the horseshoe priors, originally designed to handle sparsity, also possess regular variation and thus are appropriate for default Bayesian analysis. To illustrate our methodology, we solve a problem of non-informative priors due to Efron (1973), who showed standard flat non-informative priors in high-dimensional normal means model can be highly informative for nonlinear parameters of interest. We…
Bayesian likelihood-free inference, which is used to perform Bayesian inference when the likelihood is intractable, enjoys an increasing number of important scientific applications. However, many aspects of a Bayesian analysis become more challenging in the likelihood-free setting. One example of this is prior-data conflict checking, where the goal is to assess whether the information in the data and the prior are inconsistent. Conflicts of this kind are important to detect, since they may reveal problems in an investigator's understanding of what are relevant values of the parameters, and can…
This paper is an early version. We propose to generalise the notion of "ignoring" a random process as well as the notions of informative and ignorable random processes in a very general setup and for different types of inference (Bayesian or frequentist), and for different purposes (estimation, prediction or testing). We then confront the definitions we propose to mentions or definitions of informative and ignorable processes found in the litterature. To that purpose, we provide a very general statistical framework for survey sampling in order to define precisely the notions of design and sele…
The discovery of rare genetic variants through Next Generation Sequencing is a very challenging issue in the field of human genetics. We propose a novel region-based statistical approach based on a Bayes Factor (BF) to assess evidence of association between a set of rare variants (RVs) located on the same genomic region and a disease outcome in the context of case-control design. Marginal likelihoods are computed under the null and alternative hypotheses assuming a binomial distribution for the RV count in the region and a beta or mixture of Dirac and beta prior distribution for the probabilit…
Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecification
本文提出R-IDeA新准则，通过代表性、信息性和去放大三方面缓解模型不规范导致的泛化误差，实验显示其优于仅关注信息性或代表性的方法。
Coherent and robust Bayesian inference under informative sampling via sample-level weight models
本文提出两种贝叶斯方法处理信息性抽样下的分析推断：一种通过样本级权重模型构建相干似然，另一种采用Neyman正交化得分与损失似然自助法，实现稳健且高效的可信区间估计。
An informative sampling design leads to unit inclusion probabilities that are correlated with the response variable of interest. However, multistage sampling designs may also induce higher order dependencies, which are typically ignored in the literature when establishing consistency of estimators for survey data under a condition requiring asymptotic independence among the unit inclusion probabilities. We refine and relax this condition of asymptotic independence or asymptotic factorization and demonstrate that consistency is still achieved in the presence of residual sampling dependence. A p…
We explore the Cauchy and a new heavy tailed (Fuquene, Perez and Pericchi (2011)) priors to estimate proportions on small areas. Hierarchical models and the Binomial likelihood in the exponential family form are used. We believe that the heavy tailed priors in survey sampling settings could be more effective than the choice of noninformative priors to eliminate antipathy towards methods that involve subjective elements or assumptions. To illustrate the robust Bayesian approach, we apply this methodology in a popular example: "the clement problem". Finally, we recommend to use the Cauchy prior …
Early Prediction of Student Performance Using Bayesian Updating with Informative Priors Across Cohorts
本文通过利用前一届学生数据的贝叶斯更新方法，提升跨班级学生表现预测的鲁棒性，结果显示在早期周数内，信息先验能显著降低误判率和假阴性率。
Bayesian Joint Modeling for Longitudinal Magnitude Data with Informative Dropout: an Application to Critical Care Data
本文提出了一种包含随机效应的贝叶斯回归方法来分析幅度数据，并扩展为联合建模策略以应对信息性退出问题，有效减轻缺失数据偏差，最后应用于ICU患者膈肌厚度变化研究。
An informative sampling design leads to the selection of units whose inclusion probabilities are correlated with the response variable of interest. Model inference performed on the resulting observed sample will be biased for the population generative model. One approach that produces asymptotically unbiased inference employs marginal inclusion probabilities to form sampling weights used to exponentiate each likelihood contribution of a pseudo likelihood used to form a pseudo posterior distribution. Conditions for posterior consistency restrict applicable sampling designs to those under which …
Sensor Informativeness, Identifiability, and Uncertainty in Bayesian Inverse Problems for Structural Health Monitoring
本文提出了一种贝叶斯反演框架，用于量化结构健康监测中传感器信息量、可识别性和不确定性，通过分析弯曲刚度分布来提升传感器布置的优化与诊断可信度。
Ultrasonic guided waves offer a convenient and practical approach to structural health monitoring and non-destructive evaluation, thanks to some distinct advantages. Guided waves, in particular Lamb waves, can be used to localise damage by utilising prior knowledge of propagation and reflection characteristics. Typical localisation methods make use of the time of arrival of waves emitted or reflected from the damage, the simplest of which involves triangulation. It is useful to decompose the measured signal into the expected waves propagating directly from the actuation source in the absence o…
Bayesian inference provides a flexible way of combining data with prior information. However, quantile regression is not equipped with a parametric likelihood, and therefore, Bayesian inference for quantile regression demands careful investigation. This paper considers the Bayesian empirical likelihood approach to quantile regression. Taking the empirical likelihood into a Bayesian framework, we show that the resultant posterior from any fixed prior is asymptotically normal; its mean shrinks toward the true parameter values, and its variance approaches that of the maximum empirical likelihood …
This article focuses on the performance of Bayes estimators, in comparison with the MLE, in multinomial models with a relatively large number of cells. The prior for the Bayes estimator is taken to be the conjugate Dirichlet, i.e., the multivariate Beta, with exchangeable distributions over the coordinates, including the non-informative uniform distribution. The choice of the multinomial is motivated by its many applications in business and industry, but also by its use in providing a simple nonparametric estimator of an unknown distribution. It is striking that the Bayes procedure outperforms…
While mixtures of Gaussian distributions have been studied for more than a century (Pearson, 1894), the construction of a reference Bayesian analysis of those models still remains unsolved, with a general prohibition of the usage of improper priors (Fruwirth-Schnatter, 2006) due to the ill-posed nature of such statistical objects. This difficulty is usually bypassed by an empirical Bayes resolution (Richardson and Green, 1997). By creating a new parameterisation cantered on the mean and possibly the variance of the mixture distribution itself, we manage to develop here a weakly informative pri…
Bayesian Semiparametric Model for Sequential Treatment Decisions with Informative Timing
针对儿童AML序贯ACT治疗中时变混杂、信息性治疗时间及中途死亡或退出问题，提出基于Gamma Process先验的贝叶斯半参数生成模型，并用g-computation推断动态心功能指导规则的生存疗效。
Translating predictive distributions into informative priors
本文提出将可观测量或模型导出的边际量的先验分布转化为有信息的联合先验，通过参数化先验分布和优化超参数来减少预测分布与给定分布的差异。
Bayesian Prognostic Covariate Adjustment With Additive Mixture Priors
本文提出 Bayesian PROCOVA，用 DTG 生成的预后评分调整协变量，并以可预指定的加性混合先验融合历史对照信息，从而在控制偏倚的同时降低方差、缩小试验规模。
For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one for which the two expectations are equal and one for which they are different. The choice between the two models is performed through a Bayesian analysis, based on a robust choice of combined objective and subjective priors, set on the parameters space and on the models space. Three steps are necessary to evaluate the posterior probability of each model using …
There has been an increasing interest in using interval-based Bayesian designs for dose finding, one of which is the modified toxicity probability interval (mTPI) method. We show that the decision rules in mTPI correspond to an optimal rule under a formal Bayesian decision theoretic framework. However, the probability models in mTPI are overly sharpened by the Ockham's razor, which, while in general helps with parsimonious statistical inference, leads to suboptimal decisions in small-sample inference such as dose finding. We propose a new framework that blunts the Ockham's razor, and demonstra…
We are interested in the estimation and prediction of a parametric model on a short dataset upon which it is expected to overfit and perform badly. To overcome the lack of data (relatively to the dimension of the model) we propose the construction of an informative hierarchical Bayesian prior based upon another longer dataset which is assumed to share some similarities with the original, short dataset. We illustrate the performance of our prior on simulated dataset from three standard models. Then we apply the methodology to a working model for the electricity load forecasting on real datasets…
Leveraging population information in brain connectivity via Bayesian ICA with a novel informative prior for correlation matrices
本研究提出一种带群体先验和新型相关矩阵信息先验的贝叶斯ICA方法，通过模拟和Human Connectome Project数据验证，其能更准确估计脑功能连接，适用于单受试者分析，具临床潜力。
Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions about all aspects of such a parameter, but may have real information about functionals of the parameter, such the population mean or variance. This article proposes a new framework for nonparametric Bayes inference in which the prior distribution for a possibly infinite-dimensional parameter is decomposed into two parts: an informative prior on a finite set of…
In this paper we propose to make Bayesian inferences for the parameters of the Lomax distribution using non-informative priors, namely the Jeffreys prior and the reference prior. We assess Bayesian estimation through a Monte Carlo study with 500 simulated data sets. To evaluate the possible impact of prior specification on estimation, two criteria were considered: the bias and square root of the mean square error. The developed procedures are illustrated on a real data set.
Encoding domain knowledge into the prior over the high-dimensional weight space of a neural network is challenging but essential in applications with limited data and weak signals. Two types of domain knowledge are commonly available in scientific applications: 1. feature sparsity (fraction of features deemed relevant); 2. signal-to-noise ratio, quantified, for instance, as the proportion of variance explained (PVE). We show how to encode both types of domain knowledge into the widely used Gaussian scale mixture priors with Automatic Relevance Determination. Specifically, we propose a new join…
Dangers of Bayesian analyses and how to address them
本文针对FDA支持贝叶斯方法背景下，指出贝叶斯分析对先验偏倚敏感的危险性，提出基于实证文献论证先验、参考分析及将先验转化为数据等安全措施，并主张其作为传统分析的补充而非替代。
Changepoint analysis (also known as segmentation analysis) aims at analyzing an ordered, one-dimensional vector, in order to find locations where some characteristic of the data changes. Many models and algorithms have been studied under this theme, including models for changes in mean and / or variance, changes in linear regression parameters, etc. In this work, we are interested in an algorithm for the segmentation of long duration acoustic signals; the segmentation is based on the change of the RMS power of the signal. We investigate a Bayesian model with two possible parameterizations, and…
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