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 be analytically challenging and computationally costly especially for multivariate data sets; it also runs the risk of generating misleading BEP if the model is mis-specified. We propose an approach based on the Bayesian bootstrap technique (BBS) to simulate future trials in the presence of individual-level pilot data, based on which the empirical BEP can be calculated. The BBS approach is model-free with no assumptions about the distribution of the prior data and circumvents the analytical and computational complexity associated with obtaining the posterior distribution of the parameters. Information from multiple pilot studies is also straightforward to combine. We also propose the double bootstrap (BS2), a frequentist counterpart to the BBS, that shares similar properties and achieves the same goal as the BBS for BEP assessment. Simulation studies and case studies are presented to demonstrate the implementation of the BBS and BS2 techniques and to compare the BEP results with model-based approaches.
A major focus of causal inference is the estimation of heterogeneous average treatment effects (HTE) - average treatment effects within strata of another variable of interest such as levels of a biomarker, education, or age strata. Inference involves estimating a stratum-specific regression and integrating it over the distribution of confounders in that stratum - which itself must be estimated. Standard practice involves estimating these stratum-specific confounder distributions independently (e.g. via the empirical distribution or Rubin's Bayesian bootstrap), which becomes problematic for spa…
在这篇文章中，我们提出了数据子集算法，允许近似和可扩展的实现贝叶斯引导。它们类似于频率论文献中的两个现有算法：小引导包（Kleiner et al.，2014）和二次抽样双自举（SDB; Sengupta et al.，2016）。我们的算法有吸引力的理论和计算性能，是他们的频率论同行。此外，我们提供了一种策略，用于执行无损推理的一类泛函的贝叶斯引导，并简要介绍了扩展的狄利克雷过程。
For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a loss function. We survey existing work on both Bayesian parametric inference with Gibbs posteriors as well as Bayesian non-parametric inference. We then highlight recent bootstrap computational approaches to approximating loss-driven posteriors. In particular, we focus on implicit bootstrap distributions defined through an underlying push-forward mapping. We…
University of Warwick（华威大学）；University College London（伦敦大学学院）
Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth the…
We propose Posterior Bootstrap, a set of algorithms extending Weighted Likelihood Bootstrap, to properly incorporate prior information and address the problem of model misspecification in Bayesian inference. We consider two approaches to incorporating prior knowledge: the first is based on penalization of the Weighted Likelihood Bootstrap objective function, and the second uses pseudo-samples from the prior predictive distribution. We also propose methodology for hierarchical models, which was not previously known for methods based on Weighted Likelihood Bootstrap. Edgeworth expansions guide t…
In this paper, we employ variational arguments to establish a connection between ensemble methods for Neural Networks and Bayesian inference. We consider an ensemble-based scheme where each model/particle corresponds to a perturbation of the data by means of parametric bootstrap and a perturbation of the prior. We derive conditions under which any optimization steps of the particles makes the associated distribution reduce its divergence to the posterior over model parameters. Such conditions do not require any particular form for the approximation and they are purely geometrical, giving insig…
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…
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 use of longitudinal finite mixture models such as group-based trajectory modeling has seen a sharp increase during the last decades in the medical literature. However, these methods have been criticized especially because of the data-driven modelling process which involves statistical decision-making. In this paper, we propose an approach that uses bootstrap to sample observations with replacement from the original data to validate the number of groups identified and to quantify the uncertainty in the number of groups. The method allows investigating the statistical validity and the uncert…
University of Trieste（的里雅斯特大学）；University of Milan-Bicocca（米兰比可卡大学）
Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. Within the context of Bayesian Networks, a practical and surprisingly successful solution to this learning problem is achieved by adopting score-functions optimisation schema, augmented with multiple restarts to avoid local optima. Yet, the conditions under which such strategies work well are poorly understood, and there are also some intrinsic limitations to learning the directionality of the interaction among the variables. Following an early intuition of Fr…
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…
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…
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…
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…
