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
