# Kernel Recursive ABC: Point Estimation with Intractable Likelihood

## TL;DR

This paper introduces Kernel Recursive ABC, a new method for parameter estimation in models with intractable likelihoods, combining kernel ABC and herding to improve accuracy and convergence.

## Contribution

The paper presents a novel recursive approach that combines kernel ABC and herding, with theoretical guarantees and superior empirical performance.

## Key findings

- Method converges to true parameters under certain assumptions
- Outperforms existing approaches in numerical experiments
- Effective in real-world pedestrian flow simulation

## Abstract

We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We provide a theoretical explanation regarding why the approach works, showing (for the population setting) that, under a certain assumption, point estimates obtained with this method converge to the true parameter, as recursion proceeds. We have conducted a variety of numerical experiments, including parameter estimation for a real-world pedestrian flow simulator, and show that in most cases our method outperforms existing approaches.