find_invgamma_parms: Find parameters for Inverse gamma prior based on prior mean...

In bayesics: Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Find parameters for Inverse gamma prior based on prior mean and one quantile

Description

Find parameters for Inverse gamma prior based on prior mean and one quantile

Usage

find_invgamma_parms(
  lower_quantile,
  upper_quantile,
  response_variance,
  lower_R2,
  upper_R2,
  probability,
  plot_results = TRUE
)

Arguments

lower_quantile	lower quantile desired
upper_quantile	upper quantile desired
response_variance	variance of the response variable of the regression model
lower_R2, upper_R2	We are a priori probability sure that the coefficient of determination (R^2) falls within these lower and upper bounds.
probability	prior probability to be contained within the lower and upper quantiles
plot_results	logical. Should the resulting inverse gamma distribution be plotted?

Details

Either provide the lower and upper quantiles that contain probability of the inverse gamma distribution, or if this is for linear regression, you can specify that you are a priori probability sure that the coefficient of determination (R^2) falls within the two bounds provided, assuming that the residual variance is 1-R^2 times the total variance.

Value

twice the shape and rate of the inverse gamma distribution.

Examples

# When aimed at linear regression via coefficient of determination...
hypothetical_s2_y = 2.0
lower_R2 = 0.05
upper_R2 = 0.85
find_invgamma_parms(response_variance = hypothetical_s2_y,
                    lower_R2 = lower_R2,
                    upper_R2 = upper_R2,
                    probability = 0.8)

# More arbitrary task...
find_invgamma_parms(0.3, # hypothetical_s2_y * (1.0 - upper_R2)
                    1.9, #hypothetical_s2_y * (1.0 - lower_R2)
                    probability = 0.8)

bayesics documentation built on March 11, 2026, 5:07 p.m.