infer_SLik_joint {Infusion}

Infer a (summary) likelihood surface from a simulation table

Description

This infers the likelihood surface from a simulation table where each simulated data set is drawn for a distinct (vector-valued) parameter, as is usual for reference tables in ABC. A parameter density is inferred, as well as a joint density of parameters and summary statistics, and the likelihood surface is inferred from these two densities.

Usage

infer_SLik_joint(data, stat.obs, logLname = Infusion.getOption("logLname"), 
                Simulate = attr(data, "Simulate"), 
                nbCluster= seq_nbCluster(nr=nrow(data)),
                using = Infusion.getOption("mixturing"), 
                verbose = list(most=interactive(),pedantic=FALSE,final=FALSE),
                marginalize = TRUE)

Arguments

data

A data frame, whose each row contains a vector of parameters and one realization of the summary statistics for these parameters.

stat.obs

Named numeric vector of observed values of summary statistics.

logLname

The name to be given to the log Likelihood in the return object, or the root of the latter name in case of conflict with other names in this object.

Simulate

Either NULL or the name of the simulation function if it can be called from the R session.

nbCluster

controls the nbCluster argument of Rmixmod::mixmodCluster ; a vector of integers, or "max" which is interpreted as the maximum of the default nbCluster value.

using

Either "Rmixmod" or "mclust" to select the clustering methods used.

marginalize

Boolean; whether to derive the clustering of fitted parameters by marginalization of the joint clustering (default, and introduced in version 1.3.5); or by a distinct call to a clustering function.

verbose

A list as shown by the default, or simply a vector of booleans, indicating respectively whether to display (1) some information about progress; (2) more information whose importance is not clear to me; (3) a final summary of the results after all elements of simuls have been processed.

Value

An object of class SLik_j, which is a list including an Rmixmod::mixmodCluster object (or equivalent objects produced by non-default methods), and additional members not documented here. If projection was used, the list includes a data.frame raw_data of cumulated unprojected simulations.

Examples

if (Infusion.getOption("example_maxtime")>50) {
  myrnorm <- function(mu,s2,sample.size) {
    s <- rnorm(n=sample.size,mean=mu,sd=sqrt(s2))
    return(c(mean=mean(s),var=var(s)))
  } # simulate means and variances of normal samples of size 'sample.size'
  set.seed(123)
  # pseudo-sample with stands for the actual data to be analyzed:  
  ssize <- 40
  Sobs <- myrnorm(mu=4,s2=1,sample.size=ssize) 
  # Uniform sampling in parameter space:
  npoints <- 600
  parsp <- data.frame(mu=runif(npoints,min=2.8,max=5.2),
                      s2=runif(npoints,min=0.4,max=2.4),sample.size=ssize)
  # Build simulation table:
  simuls <- add_reftable(Simulate="myrnorm",par.grid=parsp)
  # Infer surface:
  densv <- infer_SLik_joint(simuls,stat.obs=Sobs)
  # Usual workflow using inferred surface:
  slik_j <- MSL(densv) ## find the maximum of the log-likelihood surface
  slik_j <- refine(slik_j,maxit=5)
  plot(slik_j)
  # etc:
  profile(slik_j,c(mu=4)) ## profile summary logL for given parameter value
  confint(slik_j,"mu") ## compute 1D confidence interval for given parameter
  plot1Dprof(slik_j,pars="s2",gridSteps=40) ## 1D profile
}