R/get_model_iid_gaussian.R

In pierrejacob/bayeshscore: Bayesian Model Comparison using the Hyvarinen Score

#'@rdname get_model_iid_gaussian
#'@title get_model_iid_gaussian
#'@description Univariate iid normal observations with unknown mean and variance
#'@export
get_model_iid_gaussian <- function(mu0,kappa0,nu0,sigma02){
  model = list()
  # Type of observations (string): "continuous" or "discrete"
  model$observation_type = "continuous"
  # Dimension of parameter, observations, and possibly latent states (int)
  model$dimtheta = 2
  model$dimY = 1
  # Sampler from the prior distribution on parameters
  # inputs: Ntheta (int)
  # outputs: matrix (dimtheta by Ntheta) of prior draws
  model$rprior = function(Ntheta){
    return (rnorminvchisq(Ntheta,mu0,kappa0,nu0,sigma02))
  }
  # prior density on parameters
  # inputs: theta (single vector), log (TRUE by default)
  # outputs: prior (log)-density theta (double)
  model$dprior = function(theta, log = TRUE){
    return (dnorminvchisq(theta,mu0,kappa0,nu0,sigma02,log))
  }
  #----------------------------------------------------------------------------------------------------
  #----------------------------------------------------------------------------------------------------
  # Note: to use SMC, one may specify either the likelihood OR the one-step ahead predictive
  # (one is automatically filled given the other, via set_default_model in util_default.R)
  #----------------------------------------------------------------------------------------------------
  #----------------------------------------------------------------------------------------------------
  # OPTIONAL: one-step predicitve density of the observation at t given the past from 1 to (t-1) and theta
  # inputs: observations (dimY by T matrix, with T >= t), time index t (int), theta (single vector),
  #         byproduct (OPTIONAL: auxiliary object needed to compute likelihood, e.g. Kalman filter),
  #         log (TRUE by default)
  # outputs: log-likelihood of the observations from time 1 to t given theta (double)
  # WARNING: must be an explicit function of the observation at time t to allow the
  # computation of the derivative of the log-predictive density
  model$dpredictive = function(observations,t,theta,log = TRUE){
    return (dnorm(observations[,t],mean = theta[1],sd = sqrt(theta[2]), log))
  }
  # OPTIONAL: derivatives of the predicitve density with respect to the observation at time t
  # inputs: observations (dimY by T matrix, with T >= t), time index t (int), theta (single vector),
  #         byproduct (OPTIONAL: auxiliary object needed to compute likelihood, e.g. Kalman filter)
  # outputs: list with the following fields
  # jacobian >> the transpose of the gradient (1 by dimY)
  # hessiandiag >> the Hessian diagonal coefficients (1 by dimY)
  # NB: if missing, this field is automatically filled with numerical derivatives
  # via set_default_model in util_default.R)
  model$derivativelogdpredictive = function(observations,t,theta,byproduct) {
    deriv1 <- -(observations[,t]-theta[1])/theta[2]
    deriv2 <- -1/theta[2]
    return (list(jacobian = matrix(deriv1, 1, 1), hessiandiag = matrix(deriv2, 1, 1)))
  }


  # OPTIONAL: simulate Ny draws of y_t given theta and the past y_1 to y_(t-1)
  # (with the convention y_0 = NULL)
  # outputs: matrix of Ny draws of Yt given theta and past (dimY by Ny matrix)
  model$rpredictive = function(Ny,t,theta,y_past){
    return (matrix(rnorm(Ny, mean = 0, sd = sqrt(theta)),ncol = Ny))
  }

  return(model)
}