# Monte Carlo Fusion

## TL;DR

This paper introduces Monte Carlo Fusion, a novel theoretical framework and methodology for unifying distributed analyses on shared parameters without approximation errors, applicable to various complex data settings.

## Contribution

It provides the first general, approximation-error-free approach for combining distributed inferences, with a focus on theoretical foundations and Monte Carlo interpretations.

## Key findings

- First general approach avoiding approximation errors in inference fusion
- Theoretical underpinnings of Monte Carlo Fusion methodology
- Potential for tailored, efficient parallel implementations

## Abstract

This paper proposes a new theory and methodology to tackle the problem of unifying distributed analyses and inferences on shared parameters from multiple sources, into a single coherent inference. This surprisingly challenging problem arises in many settings (for instance, expert elicitation, multi-view learning, distributed 'big data' problems etc.), but to-date the framework and methodology proposed in this paper (Monte Carlo Fusion) is the first general approach which avoids any form of approximation error in obtaining the unified inference. In this paper we focus on the key theoretical underpinnings of this new methodology, and simple (direct) Monte Carlo interpretations of the theory. There is considerable scope to tailor the theory introduced in this paper to particular application settings (such as the big data setting), construct efficient parallelised schemes, understand the approximation and computational efficiencies of other such unification paradigms, and explore new theoretical and methodological directions.