There are two main opposing schools of statistical reasoning, Frequentist and Bayesian approaches. Until recent days, the frequentist or classical approach has dominated the scientific research, but Bayesianism has reappeared with a strong impulse that is starting to change the situation. Recently the controversy about the primacy of one of the two approaches seems to be unfinished at a philosophical level, but scientific practices are giving an increasingly important position to the Bayesian approach. This paper eludes philosophical debate to focus on the pragmatic point of view of scientists' day-to-day practices, in which Bayesian methodology is very useful. Several facts and operational values are described as the core-set for understanding the change.
This paper explores the intrinsic connections between the Bayesian false discovery rate (FDR) control procedures and their counterpart of frequentist procedures. We attempt to offer a unified view of FDR control within and beyond the setting of testing exchangeable hypotheses. Under the standard two-groups model and the Oracle condition, we show that the Bayesian and the frequentist methods can achieve asymptotically equivalent FDR control at arbitrary levels. Built on this result, we further illustrate that rigorous post-fitting model diagnosis is necessary and effective to ensure robust FDR …
Prevalence estimation in infectious diseases with imperfect tests: A comparison of Frequentist and Bayesian Logistic Regression methods with misclassification correction
In many application domains, such as computational biology, the goal of graphical model structure learning is to uncover discrete relationships between entities. For example, in our problem of interest concerning HIV vaccine design, we want to infer which HIV peptides interact with which immune system molecules (HLA molecules). For problems of this nature, we are interested in determining the number of nonspurious arcs in a learned graphical model. We describe both a Bayesian and frequentist approach to this problem. In the Bayesian approach, we use the posterior distribution over model struct…
Consider a testing problem for the null hypothesis $H_0:θ\inΘ_0$. The standard frequentist practice is to reject the null hypothesis when the p-value is smaller than a threshold value $α$, usually 0.05. We ask the question how many of the null hypotheses a frequentist rejects are actually true. Precisely, we look at the Bayesian false discovery rate $δ_n=P_g(θ\inΘ_0|p-value<α)$ under a proper prior density $g(θ)$. This depends on the prior $g$, the sample size $n$, the threshold value $α$ as well as the choice of the test statistic. We show that the Benjamini--Hochberg FDR in fact converges to…
A recent paper presents the "false confidence theorem" (FCT) which has potentially broad implications for statistical inference using Bayesian posterior uncertainty. This theorem says that with arbitrarily large (sampling/frequentist) probability, there exists a set which does \textit{not} contain the true parameter value, but which has arbitrarily large posterior probability. Since the use of Bayesian methods has become increasingly popular in applications of science, engineering, and business, it is critically important to understand when Bayesian procedures lead to problematic statistical i…
When searching over a large parameter space for anomalies such as events, peaks, objects, or particles, there is a large probability that spurious signals with seemingly high significance will be found. This is known as the look-elsewhere effect and is prevalent throughout cosmology, (astro)particle physics, and beyond. To avoid making false claims of detection, one must account for this effect when assigning the statistical significance of an anomaly. This is typically accomplished by considering the trials factor, which is generally computed numerically via potentially expensive simulations.…
In many scientific fields, researchers are interested in discovering features with substantial effect on the response from a large number of features while controlling the proportion of false discoveries. By incorporating the knockoff procedure in the Bayesian framework, we develop the Bayesian knockoff filter (BKF) for selecting features that have important effect on the response. In contrast to the fixed knockoff variables in a frequentist procedure, we allow the knockoff variables to be continuously updated using the Markov chain Monte Carlo. Based on the posterior samples and the elaborate…
Progressive Bayesian Confidence Architectures for Cold-Start Personal Health Analytics: Formalizing Early Insight Through Posterior Contraction and Risk-Aware Interpretation
Next generation sequencing allows the identification of genes consisting of differentially expressed transcripts, a term which usually refers to changes in the overall expression level. A specific type of differential expression is differential transcript usage (DTU) and targets changes in the relative within gene expression of a transcript. The contribution of this paper is to: (a) extend the use of cjBitSeq to the DTU context, a previously introduced Bayesian model which is originally designed for identifying changes in overall expression levels and (b) propose a Bayesian version of DRIMSeq,…
Designing efficient exploration is central to Reinforcement Learning due to the fundamental problem posed by the exploration-exploitation dilemma. Bayesian exploration strategies like Thompson Sampling resolve this trade-off in a principled way by modeling and updating the distribution of the parameters of the action-value function, the outcome model of the environment. However, this technique becomes infeasible for complex environments due to the computational intractability of maintaining probability distributions over parameters of outcome models of corresponding complexity. Moreover, the a…
Basket trials are increasingly used for the simultaneous evaluation of a new treatment in various patient subgroups under one overarching protocol. We propose a Bayesian approach to sample size determination in basket trials that permit borrowing of information between commensurate subsets. Specifically, we consider a randomised basket trial design where patients are randomly assigned to the new treatment or a control within each trial subset (`subtrial' for short). Closed-form sample size formulae are derived to ensure each subtrial has a specified chance of correctly deciding whether the new…
Flexible Empirical Bayesian Approaches to Pharmacovigilance for Simultaneous Signal Detection and Signal Strength Estimation in Spontaneous Reporting Systems Data
A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks
University of Hong Kong（香港大学）；University of Maryland（马里兰大学）
