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Compute Process Error Log-Likelihood for a Deviation Surface (Positive Scale)

Get_PE_loglik.Rd

Calculates the positive log-likelihood contribution for a surface of deviations indexed by year and by some second dimension, under a variety of temporal and spatiotemporal structures. Selectivity deviations use it over years and bins, growth's semi-parametric deviations over years and ages, and a time-varying growth parameter over years alone (a surface one column wide). The argument names still read bin for that second dimension.

Usage

Get_PE_loglik(
  PE_model,
  PE_pars,
  ln_devs,
  map_sel_devs,
  map_sel_devs_full,
  min_sel_devs_shared_bins,
  rw_init_sigma = 5
)

Arguments

PE_model

Integer specifying the process error structure:

  • 1 = IID: deviations drawn independently as \(N(0, \sigma^2)\).

  • 2 = Random walk: deviations follow a first-order random walk initialized with a diffuse prior (\(\sigma = 5\)) at y = 1.

  • 3 = 3D GMRF with marginal variance parameterization.

  • 4 = 3D GMRF with conditional variance parameterization.

  • 5 = Separable 2D AR(1) across bins and years.

PE_pars

Array of process error parameters dimensioned [1, par_index, sex, 1]. The par_index slot meaning depends on PE_model:

  • Models 1-2: [1,1,s,1] = log standard deviation (\(\log \sigma\)) for sex s, indexed by bin/age.

  • Models 3-4: [1,1,s,1] = unconstrained partial correlation by age/bin; [1,2,s,1] = unconstrained partial correlation by year; [1,3,s,1] = unconstrained partial correlation by cohort; [1,4,s,1] = log variance.

  • Model 5: [1,1,s,1] = unconstrained bin correlation (transformed via \(2/(1+e^{-2x})-1\)); [1,2,s,1] = unconstrained year correlation; [1,4,s,1] = log standard deviation.

ln_devs

Array of log-scale selectivity deviations dimensioned [1, year, bin, sex, 1].

map_sel_devs

Integer array dimensioned [fleet, year, bin, sex] mapping deviations to unique estimated parameters. Shared deviations hold the same integer value; NA entries are treated as fixed and excluded from likelihood evaluation.

map_sel_devs_full

The same map across every unit this penalty is evaluated over, that unit being the first dim: regions for selectivity, populations by region for growth. A deviation shared over those units is one parameter appearing in each of their slices, and this function runs one unit at a time, so its contribution is divided by the number holding it. Without the split, a series shared over n units is penalized n times, an implicit \(\sigma / \sqrt{n}\). A deviation that is not shared appears once, divides by one, and is unaffected.

min_sel_devs_shared_bins

Integer vector. Indices of the reference (minimum) bin within each shared deviation group, used to subset the bin dimension when evaluating GMRF or 2D AR(1) likelihoods (PE models 3-5). When no bin sharing is specified, defaults to 1:n_bins (i.e., all bins are included).

rw_init_sigma

Standard deviation given to the first year of a random walk. A number (5 by default) leaves that year effectively unconstrained; NA starts the walk at zero under its own sigma instead.

Value

Numeric scalar: the positive log-likelihood contribution from selectivity process error. Negated externally to form the negative log-likelihood.

Details

The function supports:

  • IID process error

  • Random walk process error

  • 3D Gaussian Markov Random Field (GMRF) models (marginal or conditional variance)

  • Separable 2D AR(1) models

Note: The returned value is on the positive log-likelihood scale. It must be negated to obtain a negative log-likelihood contribution, which is handled outside this function.