mu.mblalc: Bayesian sample size determination for estimating a single...

In SampleSizeMeans: Sample Size Calculations for Normal Means

Bayesian sample size determination for estimating a single normal mean using the Mixed Bayesian/Likelihood Average Length Criterion

Description

The function mu.mblalc returns the required sample size to reach a given posterior credible interval length on average - using a mixed Bayesian/likelihood approach - for a fixed coverage probability for a normal mean.

Usage

mu.mblalc(len, alpha, beta, level = 0.95)

Arguments

len	The desired average length of the posterior credible interval for the mean
alpha	First prior parameter of the Gamma density for the precision (reciprocal of the variance)
beta	Second prior parameter of the Gamma density for the precision (reciprocal of the variance)
level	The desired fixed coverage probability of the posterior credible interval (e.g., 0.95)

Details

Assume that a sample will be collected in order to estimate the mean of a normally distributed random variable. Assume that the precision (reciprocal of the variance) of this random variable is unknown, but has prior information in the form of a Gamma(alpha, beta) density. The function mu.mblalc returns the required sample size to attain the desired average length len for the posterior credible interval of fixed coverage probability level for the unknown mean.

This function uses a Mixed Bayesian/Likelihood (MBL) approach. MBL approaches use the prior information to derive the predictive distribution of the data, but use only the likelihood function for final inferences. This approach is intended to satisfy investigators who recognize that prior information is important for planning purposes but prefer to base final inferences only on the data.

Value

The required sample size given the inputs to the function.

Note

The sample size returned by this function is exact.

Author(s)

Lawrence Joseph [e-mail] and Patrick Bélisle

References

Joseph L, Bélisle P.
Bayesian sample size determination for Normal means and differences between Normal means
The Statistician 1997;46(2):209-226.

See Also

mu.mblacc, mu.mblmodwoc, mu.mbl.varknown, mu.acc, mu.alc, mu.modwoc, mu.varknown, mu.freq, mudiff.mblacc, mudiff.mblalc, mudiff.mblmodwoc, mudiff.mblacc.equalvar, mudiff.mblalc.equalvar, mudiff.mblmodwoc.equalvar, mudiff.mbl.varknown, mudiff.acc, mudiff.alc, mudiff.modwoc, mudiff.acc.equalvar, mudiff.alc.equalvar, mudiff.modwoc.equalvar, mudiff.varknown, mudiff.freq

Examples

mu.mblalc(len=0.2, alpha=2, beta=2)

SampleSizeMeans documentation built on Aug. 23, 2023, 1:09 a.m.