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Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics have traditionally dominated empirical data analysis, and certainly remain prevalent in empirical software…
We develop scalable methods for producing conformal Bayesian predictive intervals with finite sample calibration guarantees. Bayesian posterior predictive distributions, $p(y \mid x)$, characterize subjective beliefs on outcomes of…
An aggregate data meta-analysis is a statistical method that pools the summary statistics of several selected studies to estimate the outcome of interest. When considering a continuous outcome, typically each study must report the same…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
Baseline covariates in randomized experiments are often used in the estimation of treatment effects, for example, when estimating treatment effects within covariate-defined subgroups. In practice, however, covariate values may be missing…
Meta-analysis aims to combine effect measures from several studies. For continuous outcomes, the most popular effect measures use simple or standardized differences in sample means. However, a number of applications focus on the absolute…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
We consider the problem of meta-analyzing two-group studies that report the median of the outcome. Often, these studies are excluded from meta-analysis because there are no well-established statistical methods to pool the difference of…
Non-compliance is common in real world experiments. We focus on inference about the sample complier average causal effect, that is, the average treatment effect for experimental units who are compliers. We present three types of inference…
We present a method of constructing statistical intervals that obtain a natural middle ground between Bayesian and frequentist statistical intervals, previously unexplored in literature: To a p% Bayesian credible interval we should assign a…
Meta-analysis is commonly used to combine results from multiple clinical trials, but traditional meta-analysis methods do not refer explicitly to a population of individuals to whom the results apply and it is not clear how to use their…
Meta-analysis combines pertinent information from existing studies to provide an overall estimate of population parameters/effect sizes, as well as to quantify and explain the differences between studies. However, testing the between-study…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…
In meta-analysis, the random-effects models are standard tools to address between-study heterogeneity in evidence synthesis analyses. For the random-effects distribution models, the normal distribution model has been adopted in most…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
We distinguish two questions (i) how much information does the prior contain? and (ii) what is the effect of the prior? Several measures have been proposed for quantifying effective prior sample size, for example Clarke [1996] and Morita et…
While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…