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LikelihoodProfiler.jl: Unified Interface to Profile Likelihood Methods

LikelihoodProfiler.jl is a Julia package for practical identifiability analysis and confidence intervals estimation using the profile likelihood approach. The package provides a unified interface for various profile likelihood methods, including optimization-based OptimizationProfiler and integration-based profiles IntegrationProfiler, CI endpoints search CICOProfiler, and more.

Who is this package for?

LikelihoodProfiler.jl is intended for researchers and practitioners working with maximum-likelihood estimation (MLE) problems in any scientific or engineering domain. The package does not assume a specific model type and can be applied to statistical models, mechanistic models, models defined through simulations, optimization problems, or arbitrary likelihood functions. Applicable to a broad class of MLE problems, profile likelihood is especially valuable for complex nonlinear models — such as high-dimensional mechanistic models — where standard asymptotic confidence intervals can be unreliable.

Typical application areas include (but are not limited to):

  • Systems biology & Quantitative Systems Pharmacology,
  • Engineering and control,
  • Scientific Machine Learning and any field requiring identifiability and uncertainty analysis of MLE parameters.

What problems does this package solve?

Profile likelihood methods provide insight into practical identifiability - how precisely model parameters (or predictions derived from them) are determined by the available data. LikelihoodProfiler.jl offers a unified interface for:

  • Parameter profile likelihoods. Profile the likelihood function to explore how well parameters are constrained by the data.
  • Confidence intervals for parameters. Estimate confidence intervals for parameter values based on likelihood threshold to quantify the level of certainty in the parameter estimates.
  • Functional profile likelihoods. Profile arbitrary functions of the parameters (e.g., predictions, reparameterizations, etc).

These capabilities apply to any setting where an MLE objective (e.g., negative log-likelihood) can be evaluated.

Installation

In Julia terminal run the following command:

import Pkg; Pkg.add("LikelihoodProfiler")

Other implementations of the profile likelihood approach in Julia include:

  • ProfileLikelihood.jl implements fixed-step optimization-based profiles and supports bivariate profile likelihoods.
  • InformationalGeometry.jl implements various methods to study likelihood functions (including profile likelihood) using the tools of differential geometry.

There are also well-known profile likelihood implementations in other languages, namely: Data2Dynamics, dMod, pyPESTO, sbioparametersci

Citation

Borisov I., Metelkin E. An Algorithm for Practical Identifiability Analysis and Confidence Intervals Evaluation Based on Constrained Optimization. 2018. October. ICSB2018. https://doi.org/10.13140/RG.2.2.18935.06563