convert_gamma_to_chisq {RARtrials}

Convert parameters from a Normal-Inverse-Gamma Distribution to a Normal-Inverse-Chi-Squared Distribution

Description

Convert parameters from a Normal-Inverse-Gamma distribution to a Normal-Inverse-Chi-Squared distribution.

Usage

convert_gamma_to_chisq(gpar)

Arguments

gpar

a list of parameters including m, V, a, b from a Normal-Inverse-Gamma distribution.

Details

This function convert parameters from a Normal-Inverse-Gamma ((\mu,\sigma^2) \sim NIG(mean=m,variance=V \times \sigma^2,shape=a,rate=b)) distribution to a Normal-Inverse-Chi-Squared ((\mu,\sigma^2) \sim NIX(mean=\mu,effective sample size=\kappa,degrees of freedom=\nu,variance=\sigma^2/\kappa)) distribution.

Value

a list of parameters including mu, kappa, nu, sigsq from a Normal-Inverse-Chi-Squared distribution.

References

Murphy K (2007). “Conjugate Bayesian analysis of the Gaussian distribution.” University of British Columbia. https://www.cs.ubc.ca/~murphyk/Papers/bayesGauss.pdf.

Examples

convert_gamma_to_chisq(list(V=1/2,a=0.5,m=9.1/100,b=0.00002))