To make decisions based on a model fit with auto-encoding variational Bayes (AEVB), practitioners often let the variational distribution serve as a surrogate for the posterior distribution. This approach yields biased estimates of the expected risk, and therefore leads to poor decisions for two reasons. First, the model fit with AEVB may not equal the underlying data distribution. Second, the variational distribution may not equal the posterior distribution under the fitted model. We explore how fitting the variational distribution based on several objective functions other than the ELBO, while continuing to fit the generative model based on the ELBO, affects the quality of downstream decisions. For the probabilistic principal component analysis model, we investigate how importance sampling error, as well as the bias of the model parameter estimates, varies across several approximate posteriors when used as proposal distributions. Our theoretical results suggest that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model and combining them using multiple importance sampling for decision-making. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing. In this challenging instance of multiple hypothesis testing, our proposed approach surpasses the current state of the art.

pdf/decision-making-with-auto-encoding-variational-bayes-4qad28o2bp.pdf

Decision-Making with Auto-Encoding Variational Bayes

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges

Being able to replicate scientific findings is crucial for scientific progress. We replicate 21 systematically selected experimental studies in the social sciences published in Nature and Science between 2010 and 2015. The replications follow analysis plans reviewed by the original authors and pre-registered prior to the replications. The replications are high powered, with sample sizes on average about five times higher than in the original studies. We find a significant effect in the same direction as the original study for 13 (62%) studies, and the effect size of the replications is on average about 50% of the original effect size. Replicability varies between 12 (57%) and 14 (67%) studies for complementary replicability indicators. Consistent with these results, the estimated true-positive rate is 67% in a Bayesian analysis. The relative effect size of true positives is estimated to be 71%, suggesting that both false positives and inflated effect sizes of true positives contribute to imperfect reproducibility. Furthermore, we find that peer beliefs of replicability are strongly related to replicability, suggesting that the research community could predict which results would replicate and that failures to replicate were not the result of chance alone.

/pdf/evaluating-the-replicability-of-social-science-experiments-5c0dkci5cq.pdf

Evaluating the replicability of social science experiments in Nature and Science between 2010 and 2015

In psychology, attempts to replicate published findings are less successful than expected. For properly powered studies replication rate should be around 80%, whereas in practice less than 40% of the studies selected from different areas of psychology can be replicated. Researchers in cognitive psychology are hindered in estimating the power of their studies, because the designs they use present a sample of stimulus materials to a sample of participants, a situation not covered by most power formulas. To remedy the situation, we review the literature related to the topic and introduce recent software packages, which we apply to the data of two masked priming studies with high power. We checked how we could estimate the power of each study and how much they could be reduced to remain powerful enough. On the basis of this analysis, we recommend that a properly powered reaction time experiment with repeated measures has at least 1,600 word observations per condition (e.g., 40 participants, 40 stimuli). This is considerably more than current practice. We also show that researchers must include the number of observations in meta-analyses because the effect sizes currently reported depend on the number of stimuli presented to the participants. Our analyses can easily be applied to new datasets gathered.

/pdf/power-analysis-and-effect-size-in-mixed-effects-models-a-1ox1118bc1.pdf

Power Analysis and Effect Size in Mixed Effects Models: A Tutorial

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Mathematical Methods Of Statistics

Main article included invited and contributed discussions: https://dx.doi.org/10.1214/17-BA1091 (Bayesian Analysis 13:3 (2018), pages 917-1007).

/pdf/discussion-of-using-stacking-to-average-bayesian-predictive-3kibf4qst2.pdf

Discussion of "Using Stacking to Average Bayesian Predictive Distributions" by Yao et. al

The widely recommended procedure of Bayesian model averaging is flawed in the M-open setting in which the true data-generating process is not one of the candidate models being fit. We take the idea of stacking from the point estimation literature and generalize to the combination of predictive distributions, extending the utility function to any proper scoring rule, using Pareto smoothed importance sampling to efficiently compute the required leave-one-out posterior distributions and regularization to get more stability. We compare stacking of predictive distributions to several alternatives: stacking of means, Bayesian model averaging (BMA), pseudo-BMA using AIC-type weighting, and a variant of pseudo-BMA that is stabilized using the Bayesian bootstrap. Based on simulations and real-data applications, we recommend stacking of predictive distributions, with BB-pseudo-BMA as an approximate alternative when computation cost is an issue.

Using stacking to average Bayesian predictive distributions

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit Bayesian models, but this still leaves us with many options regarding constructing, evaluating, and using these models, along with many remaining challenges in computation. Using Bayesian inference to solve real-world problems requires not only statistical skills, subject matter knowledge, and programming, but also awareness of the decisions made in the process of data analysis. All of these aspects can be understood as part of a tangled workflow of applied Bayesian statistics. Beyond inference, the workflow also includes iterative model building, model checking, validation and troubleshooting of computational problems, model understanding, and model comparison. We review all these aspects of workflow in the context of several examples, keeping in mind that in practice we will be fitting many models for any given problem, even if only a subset of them will ultimately be relevant for our conclusions.

Bayesian Workflow.

Efficient Leave-One-Out Cross-Validation and WAIC for Bayesian Models [R package loo version 2.4.1]

This article is an invited discussion of the article by Gronau and Wagenmakers (2018) that can be found at this https URL.

Limitations of "Limitations of Bayesian leave-one-out cross-validation for model selection"

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