Coverage probability

About: Coverage probability is a research topic. Over the lifetime, 2479 publications have been published within this topic receiving 53259 citations.

Improving the coverage of credible sets in Bayesian genetic fine-mapping.

Abstract: Genome Wide Association Studies (GWAS) have successfully identified thousands of loci associated with human diseases. Bayesian genetic fine-mapping studies aim to identify the specific causal variants within GWAS loci responsible for each association, reporting credible sets of plausible causal variants, which are interpreted as containing the causal variant with some "coverage probability". Here, we use simulations to demonstrate that the coverage probabilities are over-conservative in most fine-mapping situations. We show that this is because fine-mapping data sets are not randomly selected from amongst all causal variants, but from amongst causal variants with larger effect sizes. We present a method to re-estimate the coverage of credible sets using rapid simulations based on the observed, or estimated, SNP correlation structure, we call this the "adjusted coverage estimate". This is extended to find "adjusted credible sets", which are the smallest set of variants such that their adjusted coverage estimate meets the target coverage. We use our method to improve the resolution of a fine-mapping study of type 1 diabetes. We found that in 27 out of 39 associated genomic regions our method could reduce the number of potentially causal variants to consider for follow-up, and found that none of the 95% or 99% credible sets required the inclusion of more variants-a pattern matched in simulations of well powered GWAS. Crucially, our method requires only GWAS summary statistics and remains accurate when SNP correlations are estimated from a large reference panel. Using our method to improve the resolution of fine-mapping studies will enable more efficient expenditure of resources in the follow-up process of annotating the variants in the credible set to determine the implicated genes and pathways in human diseases.

Model‐Averaged Confidence Intervals

Abstract: We develop an approach to evaluating frequentist model averaging procedures by considering them in a simple situation in which there are two-nested linear regression models over which we average. We introduce a general class of model averaged confidence intervals, obtain exact expressions for the coverage and the scaled expected length of the intervals, and use these to compute these quantities for the model averaged profile likelihood (MPI) and model-averaged tail area confidence intervals proposed by D. Fletcher and D. Turek. We show that the MPI confidence intervals can perform more poorly than the standard confidence interval used after model selection but ignoring the model selection process. The model-averaged tail area confidence intervals perform better than the MPI and postmodel-selection confidence intervals but, for the examples that we consider, offer little over simply using the standard confidence interval for θ under the full model, with the same nominal coverage.

The Behrens-Fisher problem revisited: a Bayes-frequentist synthesis

Abstract: The Behrens-Fisher problem concerns the inference for the difference between the means of two normal populations whose ratio of variances is unknown. In this situation, Fisher's fiducial interval differs markedly from the Neyman-Pearson confidence interval. A prior proposed by Jeffreys leads to a credible interval that is equivalent to Fisher's solution but it carries a different interpretation. The authors propose an alternative prior leading to a credible interval whose asymptotic coverage probability matches the fre- quentist coverage probability more accurately than the interval of Jeffreys. Their simulation results indicate excellent matching even in small samples.

Output analysis: ASAP2: an improved batch means procedure for simulation output analysis

Abstract: We introduce ASAP2, an improved variant of the batchmeans algorithm ASAP for steady-state simulation output analysis. ASAP2 operates as follows: the batch size is progressively increased until the batch means pass the Shapiro-Wilk test for multivariate normality; and then ASAP2 delivers a correlation-adjusted confidence interval. The latter adjustment is based on an inverted Cornish-Fisher expansion for the classical batch means t-ratio, where the terms of the expansion are estimated via a first-order autoregressive time series model of the batch means. ASAP2 is a sequential procedure designed to deliver a confidence interval that satisfies a prespecified absolute or relative precision requirement. When used in this way, ASAP2 compares favorably to ASAP and the well-known procedures ABATCH and LBATCH with respect to close conformance to the precision requirement as well as coverage probability and mean and variance of the half-length of the final confidence interval.