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Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
Null hypothesis significance tests and p values are widely used despite very strong arguments against their use in many contexts. Confidence intervals are often recommended as an alternative, but these do not achieve the objective of…
Nonresponse weighting adjustment using propensity score is a popular method for handling unit nonresponse. However, including all available auxiliary variables into the propensity model can lead to inefficient and inconsistent estimation,…
I proposed (8, 1, 3) that p values should be supplemented by an estimate of the false positive risk (FPR). FPR was defined as the probability that, if you claim that there is a real effect on the basis of p value from a single unbiased…
We study Bayesian discriminative inference given a model family $p(c,\x, \theta)$ that is assumed to contain all our prior information but still known to be incorrect. This falls in between "standard" Bayesian generative modeling and…
Substantial advances in Bayesian methods for causal inference have been developed in recent years. We provide an introduction to Bayesian inference for causal effects for practicing statisticians who have some familiarity with Bayesian…
By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior…
Practitioners are interested in not only the average causal effect of the treatment on the outcome but also the underlying causal mechanism in the presence of an intermediate variable between the treatment and outcome. However, in many…
The Posterior distribution of the Likelihood Ratio (PLR) is proposed by Dempster in 1974 for significance testing in the simple vs composite hypotheses case. In this hypotheses test case, classical frequentist and Bayesian hypotheses tests…
Determination of posterior probability for go-no-go decision and predictive power are becoming increasingly common for resource optimization in clinical investigation. There are vast published literature on these topics; however, the…
Observational healthcare data offer the potential to estimate causal effects of medical products on a large scale. However, the confidence intervals and p-values produced by observational studies only account for random error and fail to…
One of the most fundamental problems in causal inference is the estimation of a causal effect when variables are confounded. This is difficult in an observational study, because one has no direct evidence that all confounders have been…
We study the problem of conditional predictive inference on multiple outcomes missing at random (MAR) -- or equivalently, under covariate shift. While the weighted conformal prediction offers a tool for inference under covariate shift with…
When performing Bayesian inference, we frequently need to work with conditional probability densities. For example, the posterior function is the conditional density of the parameters given the data. Some might worry that conditional…
Methods for causal inference are well developed for binary and continuous exposures, but in many settings, the exposure has a substantial mass at zero-such exposures are called semi-continuous. We propose a general causal framework for such…
Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…
When examining a contrast between two interventions, longitudinal causal inference studies frequently encounter positivity violations when one or both regimes are impossible to observe for some subjects. Existing weighting methods either…
In many fields of research null hypothesis significance tests and p values are the accepted way of assessing the degree of certainty with which research results can be extrapolated beyond the sample studied. However, there are very serious…
Causal inference analyses often use existing observational data, which in many cases has some clustering of individuals. In this paper we discuss propensity score weighting methods in a multilevel setting where within clusters individuals…
When a strict subset of covariates are given, we propose conditional quantile treatment effect to capture the heterogeneity of treatment effects via the quantile sheet that is the function of the given covariates and quantile. We focus on…