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. Supported steppers include:
  • FixedStep: Proposes a constant step size in the profiling direction (Default).
  • LineSearchStep: Uses a line search to adaptively determine the step size in the direction which is chosen by the direction keyword argument.
• optimizer::opType: The optimizer used for the optimization process.
• optimizer_opts::optsType: Options for the optimizer. Defaults to NamedTuple().

Stepping Options

The stepper argument controls how the next profile point is chosen. For example:

• stepper = FixedStep(initial_step=0.1): Use a constant step size of 0.1.
• stepper = LineSearchStep(direction=:Secant, linesearch=InterpolationLineSearch()): Use a line search with secant direction.

See the documentation for each stepper type (e.g., ?FixedStep, ?LineSearchStep) for more details and customization options.

Example

using OptimizationLBFGSB
profiler = OptimizationProfiler(; optimizer = LBFGSB(), optimizer_opts = (reltol=1e-4,))

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)

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)

QuadraticApproxProfiler

Quadratic-approximation confidence intervals (Wald approximation) based on local curvature at the optimum. The curvature is approximated by the Fisher Information Matrix/Hessian, so the resulting confidence intervals reflect the local quadratic approximation of the likelihood around optpars. By default this method reuses Hessian logic from OptimizationProblem (user-supplied Hessian or AD backend). The confidence interval is computed as θ̂ ± z * sqrt(Σ[idx, idx]), where - θ̂ is the optpars[idx], - z is the quantile of the chi-squared distribution corresponding to the conf_level and df parameters of the ProfileLikelihoodProblem, - Σ is the covariance matrix obtained by inverting the FIM.

cov_factor controls Hessian/objective scaling conventions. Common choices are:

• 1.0 when Hessian is for -logL.
• 2.0 when Hessian is for -2logL and you want covariance on the -logL scale.

Any strictly positive value is allowed (not only 1 or 2), which can be useful for calibrated or robust variance scaling.

Fields

• inversion::Symbol: Matrix inversion strategy (:cholesky, :pinv).
• clamp_to_bounds::Bool: Clip estimated interval endpoints to profile bounds.
• cov_factor::Real: Multiplicative factor applied to inv(H) to obtain covariance (Σ = cov_factor * inv(H)).
• resolution::Int: Number of points per branch (left/right) used to sample the quadratic approximation.