DerivKit: stable numerical derivatives bridging Fisher forecasts and MCMC

TL;DR

DerivKit is a Python package that provides stable numerical derivatives for statistical inference, enabling efficient Fisher forecasts and non-Gaussian likelihood approximations, bridging fast forecasts and MCMC methods.

Contribution

It introduces a versatile Python toolkit for stable numerical derivatives supporting complex models, enhancing Fisher forecasts and likelihood expansions beyond Gaussian assumptions.

Findings

Supports scalar and vector models, including black-box functions

Enables accurate Fisher bias and non-Gaussian likelihood estimates

Bridges fast Fisher forecasts with MCMC sampling methods

Abstract

DerivKit is a Python package for derivative-based statistical inference. It implements stable numerical differentiation and derivative assembly utilities for Fisher-matrix forecasting and higher-order likelihood approximations in scientific applications, supporting scalar- and vector-valued models including black-box or tabulated functions where automatic differentiation is impractical or unavailable. These derivatives are used to construct Fisher forecasts, Fisher bias estimates, and non-Gaussian likelihood expansions based on the Derivative Approximation for Likelihoods (DALI). By extending derivative-based inference beyond the Gaussian approximation, DerivKit forms a practical bridge between fast Fisher forecasts and more computationally intensive sampling-based methods such as Markov chain Monte Carlo (MCMC).