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Negative Log-Likelihood for Compound Poisson-Normal Regression

cpn_neg_log_likelihood.Rd

Computes the negative log-likelihood for a regression model where the response is assumed to follow a Compound Poisson-Normal distribution.

Usage

cpn_neg_log_likelihood(beta_mu_sigma, X, y, k_max = 10)

Arguments

beta_mu_sigma

Numeric vector. Contains the regression coefficients for the log-link Poisson mean (lambda), followed by the mean (mu) and standard deviation (sigma) of the Normal components.

X

Numeric matrix. The design matrix for the regression model (rows = observations, columns = covariates).

y

Numeric vector. The observed responses.

k_max

Integer. Maximum number of Poisson events to consider for truncation in likelihood approximation (default is 10).

Value

A numeric value giving the negative log-likelihood. Returns Inf if invalid parameters are provided or numerical issues occur.

Details

The function computes the likelihood for each observation as a weighted sum over a finite number of Poisson-Normal mixtures, truncating at k_max. If any resulting likelihood is zero, the function returns Inf to penalize the parameter set.

Examples

X <- matrix(c(1, 2, 3, 4), ncol = 2)
y <- c(0.5, 1.5)
beta_mu_sigma <- c(0.1, 0.2, 1, 0.5)
cpn_neg_log_likelihood(beta_mu_sigma, X, y, k_max = 10)
#> [1] 3.42991