API references

chi2_quantile(α, df=1)

Computes α quantile for Chi2 distribution with df degrees of freedom

profile(plprob::PLProblem, method::AbstractProfilerMethod; 
        idxs::AbstractVector{<:Int} = eachindex(get_optpars(plprob)),
        parallel_type::Symbol=:none, kwargs...)

Profiles the likelihood function for the given problem plprob using the specified profiling method.

Arguments

• plprob::PLProblem{ParameterProfile}: The profiling problem instance containing the parameters and likelihood function to be profiled.
• method::AbstractProfilerMethod: The method to be used for profiling.
• idxs::AbstractVector{<:Int}: Indices of the parameters to be profiled. Defaults to all parameters. (note!) Ensure that each parameter index in idxs has a finite (lower, upper) range in the PLProblem’s profile_range – the profile procedure will validate this.
• parallel_type::Symbol: Specifies the type of parallelism to be used. Supported values: :none, :threads, :distributed. Defaults to :none.
• maxiters::Int: Maximum number of iterations for one branch (left and right) of the profiling process. Defaults to 1e4.
• verbose::Bool: Indicates whether to display the progress of the profiling process. Defaults to false.

Returns

• Returns the profiling results PLSolution.

Example

plprob = PLProblem(optprob, optpars, [(-10.,10.), (-5.,5.)])
method = OptimizationProfiler(optimizer = Optimization.LBFGS(), stepper = FixedStep())
sol = profile(plprob, method; idxs=[1])

CICOProfiler

Confidence Intervals by Constrained Optimization (CICO) method to find the intersections of the likelihood function with the threshold. See CICOBase docs for more details. Requires using CICOBase.

Fields

• optimizer::Symbol: The optimizer used for the optimization process. Defaults to NLopt :LN_NELDERMEAD.
• scan_tol::Float64: The tolerance for the endpoints scan. Defaults to 1e-3.

Example

profiler = CICOProfiler(optimizer = :LN_NELDERMEAD, scan_tol = 1e-3)

IntegrationProfiler{opType, optsType, DEAlg, DEOpts}

A profiler method that uses integration of differential equations system to profile the likelihood function.

Fields

• reoptimize::Bool: Indicates whether to re-optimization after each step of the integrator. Defaults to false.
• optimizer::opType: The optimizer used for the optimization process. Defaults to nothing.
• optimizer_opts::optsType: Options for the optimizer. Defaults to NamedTuple().
• integrator::DEAlg: The differential equation algorithm used for integration.
• integrator_opts::DEOpts: Options for the differential equation solver. Defaults to NamedTuple().
• matrix_type::Symbol: The type of matrix to be used for the Hessian approximation. Possible options are: :hessian, :identity. Defaults to :hessian.
• gamma::Float64: Correction factor used in integration if full hessian is not computed (e.g. matrix_type = :identity). Defaults to 1.0.

Example

using OrdinaryDiffEq
profiler = IntegrationProfiler(integrator = Tsit5(), integrator_opts = (dtmax=0.3,), matrix_type = :hessian)

OptimizationProfiler{S, opType, optsType}

A profiler method that uses stepwise re-optimization to profile the likelihood function.

Fields

• stepper::S: The algorithm used to compute the next profile point.
• optimizer::opType: The optimizer used for the optimization process.
• optimizer_opts::optsType: Options for the optimizer. Defaults to NamedTuple().

Example

using Optimization
profiler = OptimizationProfiler(; optimizer = Optimization.LBFGS(), optimizer_opts = (reltol=1e-4,), stepper = FixedStep())

PLProblem{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

PLProblem(optprob, optpars, profile_range = tuple.(optprob.lb, optprob.ub); 
  conf_level = 0.95, df = 1, threshold = chi2_quantile(conf_level, df))

Arguments

• optprob: The OptimizationProblem to be solved.
• optpars: Initial (optimal) values of the parameters.
• profile_range: 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: The confidence level for the profile likelihood. Defaults to 0.95.
• df: The degrees of freedom for the profile likelihood. Defaults to 1.
• threshold: 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).

PLSolution{probType,P}

Contains the results of a profile likelihood analysis.

Fields

• prob::probType: The profile likelihood problem PLProblem.
• profiles::P: The computed profiles.
• elapsed_time::Float64: The time elapsed during the computation.

Selectors

A number of selectors are available to extract information from the sol::PLSolution object. These can be applied to each computed profile sol[i]:

• get_endpoints(sol[i]): Returns the confidence interval (CI) endpoints, marking the intersection of the profile with the threshold.
• get_retcodes(sol[i]): Returns the retcodes of the CI endpoints estimation.
• get_stats(sol[i]): Returns the statistics of the profile computation.