priors is a list specifying the priors for
various hyperparameters and auxiliary values in the model. By default,
all of these values are specified according to the literature, but RSTr
allows the capability of specifying your own priors. If you wish to
provide priors, note that you don’t have to specify priors
for all parameters if you only want to specify some of them -
any undefined priors will be defined by the default values.
For example, you can specify only the priors for lambda_sd
and all other values will be generated on their own. However, if one
value is specified for a certain parameter in priors, all
values must be specified for that parameter in priors: you
cannot, for example, define priors for just one year of
lambda_sd. Finally, any values included in your
priors list that aren’t aligned with the above names will
be ignored.
The models in RSTr share many priors, but a couple of
models have inits that are unique to them. All potential
priors are presented here.
The following are all priors used in the MSTCAR model:
Ag_scale and Ag_df: These are the scale
and degrees of freedom priors used with Wishart-distributed
random variable Ag. Ag_scale is a
positive-definite symmetric matrix and Ag_df is a
double of at least size n_group;
G_scale and G_df: These are the scale
and degrees of freedom priors used with Inverse-Wishart
distributed matrix slices of random variable G.
G_scale is a positive-definite symmetric matrix and
G_df is a double of at least size
n_group;
tau_a and tau_b: These are the rate and
scale priors used with Inverse-Gamma
distributed random variable tau2. tau_a
and tau_b must both be positive real numbers;
rho_a and rho_b: These are the shape
priors used with Beta-distributed
random variable rho. rho_a and
rho_b must both be positive real numbers;
lambda_sd: An array of positive real numbers
describing the candidate standard deviation in the Metropolis update for
the estimated rates lambda. These values will be adaptively
updated at the start of each batch; and
rho_sd: A vector of positive real numbers describing
the candidate standard deviation in the Metropolis update for the
temporal correlation rho. These values will be adaptively
updated at the start of each batch. Note that this is only used if
update_rho = TRUE.
The MCAR model shares all of the priors as the MSTCAR model, but does
not include the following: Ag_scale, Ag_df,
rho_a, rho_b, rho_sd.
The CAR models include only the following from above:
lambda_sd, tau_a, and tau_b. CAR
models also take priors sig_a and sig_b, which
hold similar shape and restriction to tau_a and
tau_b.