arXiv subjects

Nicholas Heard

Publications and source records attributed to Nicholas Heard.

2 recordsLinked to original sources

arXiv2017

Choosing Between Methods of Combining p-values

Combining p-values from independent statistical tests is a popular approach to meta-analysis, particularly when the data underlying the tests are either no longer available or are difficult to combine. A diverse range of p-value combination methods appear in the literature, each with different statistical properties. Yet all too often the final choice used in a meta-analysis can appear arbitrary, as if all effort has been expended building the models that gave rise to the p-values. Birnbaum (1954) showed that any reasonable p-value combiner must be optimal against some alternative hypothesis. Starting from this perspective and recasting each method of combining p-values as a likelihood ratio test, we present theoretical results for some of the standard combiners which provide guidance about how a powerful combiner might be chosen in practice.

stat.ME↗

arXiv2015

Monte Carlo convergence of rival samplers

It is often necessary to make sampling-based statistical inference about many probability distributions in parallel. Given a finite computational resource, this article addresses how to optimally divide sampling effort between the samplers of the different distributions. Formally approaching this decision problem requires both the specification of an error criterion to assess how well each group of samples represent their underlying distribution, and a loss function to combine the errors into an overall performance score. For the first part, a new Monte Carlo divergence error criterion based on Jensen-Shannon divergence is proposed. Using results from information theory, approximations are derived for estimating this criterion for each target based on a single run, enabling adaptive sample size choices to be made during sampling.

stat.ME↗