Compute the Bayesian posterior mean given a normal prior and experimental result

Applies the precision-weighted updating formula from FEDAI Equations 11.2–11.4. The posterior mean is a weighted average of the prior mean g and the bias-corrected experimental estimate x_e, where the weights depend on prior variance, sampling-bias variance, and sampling variance.

Usage

posterior_mean_fn(x_e, g, sigma_g, sigma_B, sigma_x)

Arguments

x_e

Numeric. Experimental estimate(s).

g

Numeric. Prior mean on the PATE.

sigma_g

Numeric. Prior standard deviation on the PATE.

sigma_B

Numeric. Standard deviation of the sampling-bias distribution.

sigma_x

Numeric. Standard error of the experimental estimate.

Value

Numeric vector of posterior means, same length as x_e.