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

Get_Fdev_PE_loglik.Rd

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,
  UseCatch,
  UseCatch_pop,
  missing_catch
)

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.

UseCatch, UseCatch_pop

Same binary catch-usage indicators as elsewhere; a cell is penalized if aggregated catch or any population-specific catch is used.

missing_catch

Logical array [n_regions x n_years x n_seas x n_fish_fleets], TRUE where the aggregate catch observation (ObsCatch) is missing (NA) rather than a true recorded zero. A cell with UseCatch == 0 (and no population-specific catch used) is still penalized as an ordinary active year when missing_catch is TRUE there (fishing presumably continued, we simply lack a value to fit), as opposed to a true recorded zero, which is treated as a real closure and excluded from the gap count.

Value

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

Details

Note: Unlike Get_sel_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 \(d = 1\).