Compute Fishing Mortality Deviation Process Error Log-Likelihood (Negative Scale)

Calculates the negative log-likelihood contribution for fishing mortality deviations (ln_F_devs) under an iid, random walk, or AR1 process error structure.

Usage

Get_Fdev_PE_loglik(
  PE_model,
  ln_sigmaF,
  Fdev_rho,
  ln_F_devs,
  map_ln_F_devs,
  Fdev_pen_center = 0
)

Arguments

PE_model: Integer specifying the process error structure: 1 = IID (deviations drawn independently as $N(0, \sigma^2)$); 2 = random walk (first active year initialized with a diffuse $N(0, 5)$ prior); 3 = AR1 (first active year drawn from its stationary marginal distribution $N(0, \sigma^2 / (1 - \rho^2))$).
ln_sigmaF: Array [n_regions x n_seas x n_fish_fleets] of log-scale process error SD.
Fdev_rho: Array [n_regions x n_seas x n_fish_fleets] of unconstrained AR1 partial correlation (only used when PE_model == 3); transformed to $(-1, 1)$ via $2 / (1 + e^{-2x}) - 1$.
ln_F_devs: Array [n_regions x n_years x n_seas x n_fish_fleets] of log-scale fishing mortality deviations.
map_ln_F_devs: Array [n_regions x n_years x n_seas x n_fish_fleets] mirroring $map$ln_F_devs: an estimation index where a deviation is estimated, NA where it is fixed. Only estimated deviations are penalized, and they alone form the active sequence, so a fixed cell is skipped and widens the gap $d$ between the deviations either side of it. do_Fmort_mapping builds this from the catch-usage indicators, estimating a deviation wherever aggregated or any population-specific catch is used, or where the aggregate catch observation (ObsCatch) is missing (NA) rather than a true recorded zero (fishing presumably continued, we simply lack a value to fit), while a true recorded zero is a real closure and is excluded.

Value

Array with the same dimensions as ln_F_devs: the negative log-likelihood contribution per cell.

Details

Note: Unlike Get_PE_loglik and Get_move_PE_loglik, which return a single positive log-likelihood scalar to be negated by the caller, this function returns an already-negated array with the same dimensions as ln_F_devs (one value per region/year/season/fleet cell, 0 where catch is not used), matching the existing Fmort_nLL reporting convention.

Random walk and AR1 do not require catch-active years to be contiguous. Instead, the transition between two active years is taken over the elapsed gap $d$ between them, exactly the marginal transition you would get from estimating deviations for the closed years in between and integrating them out, without actually estimating them:

Random walk: $\delta_t \mid \delta_s \sim N(\delta_s, d\sigma^2)$
AR1: $\delta_t \mid \delta_s \sim N(\rho^d \delta_s, \sigma^2 \sum_{i=0}^{d-1} \rho^{2i})$, where the sum has closed form $(1 - \rho^{2d}) / (1 - \rho^2)$

Both reduce exactly to the standard single-step transition when $d = 1$.