# Shadow Simulated Annealing algorithm: a new tool for global optimisation and statistical inference

## TL;DR

This paper introduces a novel global optimisation method called Shadow Simulated Annealing, which efficiently handles complex criteria including intractable posteriors, and demonstrates its effectiveness through simulations and cosmological data analysis.

## Contribution

The paper presents a new global optimisation algorithm that bypasses re-sampling and provides convergence guarantees for complex, partially known criteria, including intractable posteriors.

## Key findings

- Validated on simulated data showing effective optimisation.
- Applied to cosmological data confirming galaxy distribution hypotheses.
- Demonstrated improved inference without re-sampling in complex models.

## Abstract

This paper develops a new global optimisation method that applies to a family of criteria that are not entirely known. This family includes the criteria obtained from the class of posteriors that have nor-malising constants that are analytically not tractable. The procedure applies to posterior probability densities that are continuously differen-tiable with respect to their parameters. The proposed approach avoids the re-sampling needed for the classical Monte Carlo maximum likelihood inference, while providing the missing convergence properties of the ABC based methods. Results on simulated data and real data are presented. The real data application fits an inhomogeneous area interaction point process to cosmological data. The obtained results validate two important aspects of the galaxies distribution in our Universe : proximity of the galaxies from the cosmic filament network together with territorial clustering at given range of interactions. Finally, conclusions and perspectives are depicted.