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09: Priors

RSTr-priors.Rmd

Overview

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.

Prior specifications

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.

Priors for the MSTCAR model

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.

Priors for the MCAR model

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.

Priors for the CAR/RCAR model

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.