gamma_pred: gamma_pred

In kDGLM: Bayesian Analysis of Dynamic Generalized Linear Models

gamma_pred

Description

Calculate the values for the predictive distribution given the values of the parameter of the conjugated distribution of the linear predictor. The data is assumed to have Gamma distribution with known shape parameter phi and its mean having distribution Inverse-Gamma with shape parameter a e rate parameter b. In this scenario, the marginal distribution of the data is Beta prime with parameters phi, alpha, beta / phi.

Usage

gamma_pred(conj.param, outcome = NULL, parms = list(), pred.cred = 0.95)

Arguments

conj.param	list or data.frame: The parameters of the conjugated distributions of the linear predictor.
outcome	numeric or matrix (optional): The observed values at the current time. Not used in this function.
parms	list: A list of extra parameters for the model. For this function, it must contain the shape parameter phi of the observational model.
pred.cred	numeric: the desired credibility for the credibility interval.

Value

A list containing the following values:

• pred numeric/matrix: the mean of the predictive distribution of a next observation. Same type and shape as the parameter in model.

• var.pred numeric/matrix: the variance of the predictive distribution of a next observation. Same type and shape as the parameter in model.

• icl.pred numeric/matrix: the percentile of 100*((1-pred.cred)/2)

• icu.pred numeric/matrix: the percentile of 100*(1-(1-pred.cred)/2)

• log.like numeric: the The log likelihood for the outcome given the conjugated parameters.

See Also

Other auxiliary functions for a Gamma outcome with known shape: convert_Gamma_Normal(), convert_Normal_Gamma(), update_Gamma()

kDGLM documentation built on April 4, 2025, 4:44 a.m.