On implementing Jeffreys' substitution likelihood for Bayesian inference concerning the medians of unknown distributions. (13th December 2022)

• Record Type: Journal Article
• Authors: Grieve, Andrew P.
• Is Part Of: Pharmaceutical statistics. Volume 22:Number 2(2023)
• Page Start: 365
• Page End: 377
• Publication Date: 2022-12-13
• Subjects: approximate likelihood -- Bayesian inference -- bioequivalence -- comparative bioavailability -- non‐parametric -- sampling/re‐sampling -- von Neumann's accept/ reject algorithm; Pharmacy -- Statistical methods -- Periodicals; Pharmacy -- Statistics -- Periodicals; 615.10727
• DOI: 10.1002/pst.2277
• Languages: English
• ISSNs: 1539-1604

Abstract

Abstract: When statisticians are uncertain as to which parametric statistical model to use to analyse experimental data, they will often resort to a non‐parametric approach. The purpose of this paper is to provide insight into a simple approach to take when it is unclear as to the appropriate parametric model and plan to conduct a Bayesian analysis. I introduce an approximate, or substitution likelihood, first proposed by Harold Jeffreys in 1939 and show how to implement the approach combined with both a non‐informative and an informative prior to provide a random sample from the posterior distribution of the median of the unknown distribution. The first example I use to demonstrate the approach is a within‐patient bioequivalence design and then show how to extend the approach to a parallel group design.