prior_spec: prior specification

In pomp: Statistical Inference for Partially Observed Markov Processes

prior specification

Description

Specification of prior distributions via the rprior and dprior components.

Details

A prior distribution on parameters is specified by means of the rprior and/or dprior arguments to pomp. As with the other basic model components, it is preferable to specify these using C snippets. In writing a C snippet for the prior sampler (rprior), keep in mind that:

1. Within the context in which the snippet will be evaluated, only the parameters will be defined.

2. The goal of such a snippet is the replacement of parameters with values drawn from the prior distribution.

3. Hyperparameters can be included in the ordinary parameter list. Obviously, hyperparameters should not be replaced with random draws.

In writing a C snippet for the prior density function (dprior), observe that:

1. Within the context in which the snippet will be evaluated, only the parameters and give_log will be defined.

2. The goal of such a snippet is computation of the prior probability density, or the log of same, at a given point in parameter space. This scalar value should be returned in the variable lik. When give_log == 1, lik should contain the log of the prior probability density.

3. Hyperparameters can be included in the ordinary parameter list.

General rules for writing C snippets can be found here.

Alternatively, one can furnish R functions for one or both of these arguments. In this case, rprior must be a function that makes a draw from the prior distribution of the parameters and returns a named vector containing all the parameters. The only required argument of this function is ....

Similarly, the dprior function must evaluate the prior probability density (or log density if log == TRUE) and return that single scalar value. The only required arguments of this function are ... and log.

Default behavior

By default, the prior is assumed flat and improper. In particular, dprior returns 1 (0 if log = TRUE) for every parameter set. Since it is impossible to simulate from a flat improper prior, rprocess returns missing values (NAs).

Note for Windows users

Some Windows users report problems when using C snippets in parallel computations. These appear to arise when the temporary files created during the C snippet compilation process are not handled properly by the operating system. To circumvent this problem, use the cdir and cfile options to cause the C snippets to be written to a file of your choice, thus avoiding the use of temporary files altogether.

See Also

dprior rprior

More on implementing POMP models: Csnippet, accumvars, basic_components, betabinomial, covariates, dinit_spec, dmeasure_spec, dprocess_spec, emeasure_spec, eulermultinom, parameter_trans(), pomp-package, pomp_constructor, rinit_spec, rmeasure_spec, rprocess_spec, skeleton_spec, transformations, userdata, vmeasure_spec

More on Bayesian methods: abc(), bsmc2(), dprior(), pmcmc(), rprior()

Examples

 # takes too long for R CMD check
  ## Starting with an existing pomp object:
  verhulst() |> window(end=30) -> po
  
  ## We add or change prior distributions using the two
  ## arguments 'rprior' and 'dprior'. Here, we introduce
  ## a Gamma prior on the 'r' parameter.
  ## We construct 'rprior' and 'dprior' using R functions.

  po |>
    bsmc2(
      rprior=function (n_0, K0, K1, sigma, tau, r0, r1, ...) {
        c(
          n_0 = n_0,
          K = rgamma(n=1,shape=K0,scale=K1),
          r = rgamma(n=1,shape=r0,scale=r1),
          sigma = sigma,
          tau = tau
        )
      },
      dprior=function(K, K0, K1, r, r0, r1, ..., log) {
        p <- dgamma(x=c(K,r),shape=c(K0,r0),scale=c(K1,r1),log=log)
        if (log) sum(p) else prod(p)
      },
      params=c(n_0=10000,K=10000,K0=10,K1=1000,
        r=0.9,r0=0.9,r1=1,sigma=0.5,tau=0.3),
      Np=1000
    ) -> B

  ## We can also pass them as C snippets:

  po |>
    bsmc2(
      rprior=Csnippet("
         K = rgamma(K0,K1);
         r = rgamma(r0,r1);"
      ),
      dprior=Csnippet("
         double lik1 = dgamma(K,K0,K1,give_log);
         double lik2 = dgamma(r,r0,r1,give_log);
         lik = (give_log) ? lik1+lik2 : lik1*lik2;"
      ),
      paramnames=c("K","K0","K1","r","r0","r1"),
      params=c(n_0=10000,K=10000,K0=10,K1=1000,
        r=0.9,r0=0.9,r1=1,sigma=0.5,tau=0.3),
      Np=10000
    ) -> B

  ## The prior is plotted in grey; the posterior, in blue.
  plot(B)

  B |>
    pmcmc(Nmcmc=100,Np=1000,proposal=mvn_diag_rw(c(r=0.01,K=10))) -> Bb

  plot(Bb,pars=c("loglik","log.prior","r","K"))

pomp documentation built on Aug. 8, 2023, 1:08 a.m.