Bayesian credible interval for a normal prior distribution

Source: R/statpsych1.R

Computes an approximate Bayesian credible interval for a normal prior distribution. This function can be used with any parameter estimator (e.g., mean, mean difference, linear contrast of means, slope coefficient, standardized mean difference, standardized linear contrast of means, median, median difference, linear contrast of medians, etc.) that has an approximate normal sampling distribution. The mean and standard deviation of the posterior normal distribution are also reported.

ci.bayes.normal(alpha, prior.mean, prior.sd, est, se)

Arguments

alpha

alpha level for 1-alpha credibility interval

prior.mean

mean of prior Normal distribution

prior.sd

standard deviation of prior Normal distribution

est

sample estimate

se

standard error of sample estimate

Value

Returns a 1-row matrix. The columns are:

  • Posterior mean - posterior mean of Normal distribution

  • Posterior SD - posterior standard deviation of Normal distribution

  • LL - lower limit of the credible interval

  • UL - upper limit of the credible interval

References

Gelman A, B. CJ, Stern HS, Rubin DB (2004). Bayesian Data Analysis, 2nd edition. Chapman & Hall.

Examples

ci.bayes.normal(.05, 30, 2, 24.5, 0.577)
#>  Posterior mean Posterior SD       LL       UL
#>         24.9226    0.5543895 23.83602 26.00919

# Should return:
# Posterior mean Posterior SD       LL       UL
#        24.9226    0.5543895 23.83602 26.00919