INTEGRATE - a Python package for fast localized probabilistic inversion using informed priors, applied to EM data

We present INTEGRATE, a Python package for fast localized probabilistic inversion of geophysical data. The framework provides a general approach for Bayesian inference in localized inverse problems, where the same prior information applies to many independent datasets. INTEGRATE implements an extended rejection sampling algorithm with temperature annealing for efficient posterior sampling. The package is modular and open, supporting both continuous and discrete model parameters, arbitrarily complex prior information, flexible noise models (including multivariate Gaussian and multinomial distributions), and parallel processing with shared-memory optimization. All data exchange is handled through \texttt{HDF5}, allowing seamless integration with external forward modeling codes and easy adaptation to a wide range of geophysical or non-geophysical applications. We demonstrate the framework for electromagnetic (EM) inversion, integrating time-domain EM using informed geological priors, achieving over 200× speedups relative to traditional MCMC approaches. INTEGRATE efficiently computes Bayesian evidence for hypothesis testing and model comparison. A case study from Daugaard, Denmark (11,693 soundings) illustrates the method’s performance, including automatic annealing temperature selection and the influence of lookup-table size on computational efficiency. The open-source package provides command-line tools and visualization utilities, facilitating integration into existing geophysical workflows.