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Profile likelihood methods

LikelihoodProfiler provides a range of methods to profile likelihood functions and explore practical identifiability. The method should be provided as the second argument to the profile function.

Optimization-based profiles

The method computes profiles for each parameter by iteratively changing the value of the parameter and re-optimizing the likelihood function with respect to all other parameters.

LikelihoodProfiler.OptimizationProfiler — Type
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())
source

Integration-based profiles

The method computes profiles for each parameter by integrating the differential equations system.

LikelihoodProfiler.IntegrationProfiler — Type
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)
source

References:

  1. Chen, J.-S. & Jennrich, R. I. Simple Accurate Approximation of Likelihood Profiles. Journal of Computational and Graphical Statistics 11, 714–732 (2002).
  2. Chen, J.-S. & Jennrich, R. I. The Signed Root Deviance Profile and Confidence Intervals in Maximum Likelihood Analysis. Journal of the American Statistical Association 91, 993–998 (1996).

Confidence Intervals by Constrained Optimization (CICO)

The method computes intersections (endpoints of the confidence interval (CI)) of the profile with the predefined confidence level (threshold) without restoring the exact trajectory of the profile. Requires using CICOBase package.

LikelihoodProfiler.CICOProfiler — Type
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)
source

References:

  1. Borisov, I. & Metelkin, E. Confidence intervals by constrained optimization—An algorithm and software package for practical identifiability analysis in systems biology. PLoS Comput Biol 16, e1008495 (2020).
  2. Venzon, D. J. & Moolgavkar, S. H. A Method for Computing Profile-Likelihood-Based Confidence Intervals. Applied Statistics 37, 87 (1988).