ProfileLikelihoodProblem{T,probType,P,PF,PR}

Defines a profile likelihood problem.

Mathematical Specification of a Profile Likelihood Problem:

A profile likelihood problem is defined by

• an objective function (usually negative log-likelihood function) wrapped within an optprob::OptimizationProblem. Consult Optimization.jl docs for details.
• a set of optimal values of the parameters optpars that minimize the objective function.

Constructors

ProfileLikelihoodProblem(optprob::OptimizationProblem, optpars::AbstractVector{<:Real},
  profile_range::Union{AbstractVector, Tuple} = tuple.(optprob.lb, optprob.ub); 
  conf_level::Float64 = 0.95, df::Int = 1, threshold::Real = chi2_quantile(conf_level, df))

Arguments

• optprob::OptimizationProblem: The OptimizationProblem to be solved.
• optpars::AbstractVector{<:Real}: Initial (optimal) values of the parameters.
• profile_range::Union{AbstractVector, Tuple}: The range over which the profile likelihood is computed. A tuple (lower, upper) specifying a common profiling interval for all parameters, or an array of such tuples (one per parameter). By default, it uses the OptimizationProblem bounds for each parameter (i.e., tuple.(optprob.lb, optprob.ub)). (note!) If a parameter is not meant to be profiled, you may use nothing or infinite bounds.

Keyword arguments

• conf_level::Float64: The confidence level for the profile likelihood. Defaults to 0.95.
• df::Int: The degrees of freedom for the profile likelihood. Defaults to 1.
• threshold::Real: The threshold for the profile likelihood. Can be set to Inf if confidence interval endpoint estimation is not required. Defaults to chi2_quantile(conf_level, df).