2018/09/22 by Erik W. van Zwet, van Zwet, Erik
Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.1809.08449
openalex publication_date 2018/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When the sample size is not too small, M-estimators of regression coefficients are approximately normal and unbiased. This leads to the familiar frequentist inference in terms of normality-based confidence intervals and p-values. From a Bayesian perspective, use of the (improper) uniform prior yields matching results in the sense that posterior quantiles agree with one-sided confidence bounds. For this, and various other reasons, the uniform prior is often considered objective or non-informative. In spite of this, we argue that the uniform prior is not suitable as a default prior for inference about a regression coefficient in the context of the bio-medical and social sciences. We propose that a more suitable default choice is the normal distribution with mean zero and standard deviation equal to the standard error of the M-estimator. We base this recommendation on two arguments. First, we show that this prior is non-informative for inference about the sign of the regression coefficient. Secondly, we show that this prior agrees well with a meta-analysis of 50 articles from the MEDLINE database.