postshrink: Estimate posterior shrink

In cbrown5/BayeSens: Prior sensitivity analysis for Bayesian MCMC models

Description

Estimate posterior shrink

Usage

postshrink(thetaprior, thetapost, thetaMLE)

Arguments

thetaprior	A numeric giving the estimate of a parameter from the prior
thetapost	A numeric giving the estimate of a parameter from the posterior
thetaMLE	A numeric giving the maximum likelihood estimate of a parameter

Details

Posterior shrinkage measures the degree to which the posterior estimate has shrunk towards the maximum likelihood estimate and away from the prior.

Values close to 1 indicate the prior has little influence on the posterior, whereas values close to 0 indicate the prior has a large influence on the posterior.

Some care must be taken in selecting parameter estimates to use in the shrink equation and also in estimating the MLE (which is not always straightfoward). For complex models the MLE may be estiamted using data cloning, see dataclone.

Shrink values can occaisionally be >1 or <0. Values <0 occur when the posterior parameter estimate has moved in the opposite direction from the prior than the MLE. Values >1 occur when the MLE is closer to the prior estimate than the posterior. Values not in 0-1 can occur if (1) your MLE estimate is inaccurate, (2) your posterior is multi-model, or (3) your posterior estimate is constrained by other parameters. If (1) then try other methods for obtaining an MLE or increase replication if using data cloning. If (2) or (3) posterior shrink may be inappropriate for your model, because the posterior shrink cannot be characterised by a simple univariate measure.

See: Berger JO (1985) Statistical Decision Theory and Bayesian Analysis, Second Edition, Springer, New York.

Thanks to Ed Boone for suggesting this one.

Value

An estimate of posterior shrinkage.

Author(s)

Christopher J. Brown [e-mail]

cbrown5/BayeSens documentation built on April 26, 2020, 12:40 a.m.