Infusion (version 2.2.0)

infer_SLik_joint: 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 other forms of simulation-based inference such as Approximate Bayesian Computation. 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,
                constr_crits=NULL,
                projectors=NULL,
                is_trainset)

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 reftable_raw of cumulated unprojected simulations.

Arguments

data

A data frame, whose each row contains a vector of parameters and one realization of the summary statistics for these parameters. Typically this holds the projected reference table (but see projectors argument for an experimental alternative).

stat.obs

Named numeric vector of observed values of summary statistics. Typically this holds the projected values (but see projectors argument for an experimental alternative).

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 (see add_reftable for more information on this function).

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; if not, a distinct call to a clustering function is performed. It is strongly advised not to change the default. This argument might be deprecated in future versions.

constr_crits

NULL, or quoted expression specifying a constraints on parameters, beyond the ones defined by the ranges over each parameter: see constr_crits for details. This will control the parameter space both for maximization of the summary-likelihood, and for generation of new parameter points when refine() is called on the return object. See Examples section for a nice artificial toy example.

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.

projectors

if not NULL, this argument may be passed to project in the case the data or stat.obs do not yet contain the projected statistics. This experimental feature aims to remove the two user-level calls to project in the inference workflow.

is_trainset

Passed to project in the case the projectors argument is used.

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)
  # simulated data 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", parsTable=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
  
  # With constraints:
  heart <- quote({ x <- 3*(mu-4.25);  y <- 3*(s2-0.75); x^2+(y-(x^2)^(1/3))^2-1})
  c_densv <- infer_SLik_joint(simuls,stat.obs=Sobs, constr_crits = heart)
  c_slik_j <- MSL(c_densv, CIs=FALSE) 
  refine(c_slik_j, target_LR=10, ntot=3000) 

}