Calculate log-likelihood for Poisson-distributed count data

Computes the total log-likelihood for integer count data under the Poisson distribution. Each observation can be weighted via weights, defaulting to equal weights.

Usage

calc_log_likelihood_poisson(
  observed,
  estimated,
  weights = NULL,
  zero_buffer = TRUE,
  eps_rel = 0.02,
  verbose = TRUE
)

Arguments

observed

Integer vector of observed non-negative counts (e.g., cases, deaths).

estimated

Numeric vector of expected values from the model (same length as observed).

weights

Optional numeric vector of non-negative weights, same length as observed. Default is NULL, which sets all weights to 1.

zero_buffer

Logical; if TRUE (default), rounds observed values to integers and adds small buffer to avoid zero estimates. If FALSE, enforces strict integer requirements.

eps_rel

Positive scalar; the predicted mean of every cell is floored at max(1e-4, eps_rel * mean(observed)) before the density is evaluated. Default 0.02. See calc_log_likelihood_negbin.

verbose

Logical; if TRUE, prints diagnostics and total log-likelihood.

Value

A scalar representing the total log-likelihood (numeric).

Details

The Poisson distribution assumes that the variance equals the mean, \(\mathrm{Var}(Y) = \mu\). Weighted log-likelihood is summed across observations. If the variance/mean ratio is > 1.5, a warning about possible overdispersion is issued.

Examples

calc_log_likelihood_poisson(c(2, 3, 4), c(2.2, 2.9, 4.1))
#> Poisson log-likelihood: -4.45
#> [1] -4.447966