Prior distributions
priors.RdThese functions are used to specify priors on selected (hyper)parameters in salmonIPM models.
The default priors used in the various models are intended to be weakly
informative, in that they provide moderate regularization and help
stabilize sampling. Priors on scaling parameters, e.g. Rmax or mu_Rmax,
are automatically adjusted to be weakly informative but consistent with the
observed marginal distribution of population density. For many applications
these defaults will perform well, but if external information not included
in fish_data is available, it can be incorporated via user-specified
priors on key parameters. See Details for a table of available prior
options.
Usage
normal(mean = 0, sd = 1)
gnormal(mean = 0, scale = 1, shape = 1)
lognormal(meanlog = 0, sdlog = 1)
beta(a = 1, b = 1)
dirichlet(concentration = 1)
uniform(lb = 0, ub = 1)
lkj_corr(eta = 1)Arguments
- mean
Prior mean for normal or generalized normal distribution.
- sd
Prior standard deviation for normal distribution.
- scale
Prior scale for generalized normal distribution. Equivalent to
alphain gnorm, but renamed to avoid confusion with the spawner-recruit intrinsic productivity parameter.- shape
Prior shape for generalized normal distribution. Equivalent to
betain gnorm but renamed to avoid confusion with covariate slopes.- meanlog, sdlog
Prior log-scale mean and standard deviation, respectively, for lognormal distribution. See Lognormal.
- a, b
Prior shape parameters for the beta distribution. Equivalent to
shape1andshape2, respectively, in Beta.- concentration
Vector of shape parameters for the Dirichlet distribution. Equivalent to
alphain gtools::dirichlet, but renamed to avoid confusion with the spawner-recruit intrinsic productivity parameter.- lb, ub
Lower and upper bounds for the uniform distribution.
- eta
Prior shape parameter for the LKJ distribution over correlation matrices.
Details
The table below shows the parameters in each model that can be given user-specified priors and the corresponding distributions. Note that users can modify the prior parameters but not the distribution families; attempting to do the latter will result in an error.
Priors for parameters that are bounded on the positive real line (e.g.
tau, tau_S and tau_M) are automatically left-truncated at zero.
For parameters that are modeled as functions of covariates using the
par_models argument to salmonIPM(), the specified prior applies when
all predictors are at their sample means.
If RRS != "none", the global spawner-recruit parameters must be replaced
with their W and H counterparts; e.g. if RRS == "alpha" then instead
of a prior on alpha one would specify priors on alpha_W and alpha_H.
If the former is provided, it will have no effect. See salmonIPM() for
details of the RRS argument.
The generalized normal density with shape >> 1 is useful as a platykurtic
"soft-uniform" prior to regularize the posterior away from regions of
parameter space that may cause computational or sampling problems. In the
case of spawner and smolt observation error log-SDs, the default prior
bounds them ≳ 0.1.
The uniform distribution and the LKJ distribution are included for internal use; currently no correlation matrices have user-specified priors.
| Parameter (PDF) | ||||||||||||
| Model | alpha | lognormal | mu_alpha | normal | mu_psi | beta | Rmax | lognormal | mu_Rmax | normal | Mmax | lognormal |
mu_Mmax | normal | mu_MS | beta | mu_p | dirichlet | mu_SS | beta | tau | gnormal | tau_S | tau_M | gnormal |
IPM_SS_np | ☑ | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☐ | ☑ | ☐ | ☑ | ☐ |
IPM_SSiter_np | ☑ | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☐ | ☑ | ☑ | ☑ | ☐ |
IPM_SS_pp | ☐ | ☑ | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☑ | ☐ | ☑ | ☐ |
IPM_SSiter_pp | ☐ | ☑ | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☑ | ☑ | ☑ | ☐ |
IPM_SMS_np | ☑ | ☐ | ☐ | ☐ | ☐ | ☑ | ☐ | ☑ | ☑ | ☐ | ☐ | ☑ |
IPM_SMS_pp | ☐ | ☑ | ☐ | ☐ | ☐ | ☐ | ☑ | ☑ | ☑ | ☐ | ☐ | ☑ |
IPM_SMaS_np | ☑ | ☐ | ☐ | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☐ | ☐ | ☑ |
IPM_LCRchum_pp | ☐ | ☐ | ☑ | ☐ | ☐ | ☐ | ☑ | ☑ | ☑ | ☐ | ☐ | ☐ |