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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.

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