# Importance sampling with transformed weights

## TL;DR

This paper investigates the use of transformed importance weights in standard importance sampling, demonstrating that it improves robustness to weight degeneracy through a bias-variance trade-off.

## Contribution

It provides a numerical assessment of transformed importance weights in standard IS, showing their effectiveness in reducing weight degeneracy.

## Key findings

- Transformed importance weights improve robustness in importance sampling.
- The method achieves a bias-variance trade-off that mitigates weight degeneracy.
- Numerical results confirm the effectiveness of TIWs in standard IS.

## Abstract

The importance sampling (IS) method lies at the core of many Monte Carlo-based techniques. IS allows the approximation of a target probability distribution by drawing samples from a proposal (or importance) distribution, different from the target, and computing importance weights (IWs) that account for the discrepancy between these two distributions. The main drawback of IS schemes is the degeneracy of the IWs, which significantly reduces the efficiency of the method. It has been recently proposed to use transformed IWs (TIWs) to alleviate the degeneracy problem in the context of Population Monte Carlo, which is an iterative version of IS. However, the effectiveness of this technique for standard IS is yet to be investigated. In this letter we numerically assess the performance of IS when using TIWs, and show that the method can attain robustness to weight degeneracy thanks to a bias/variance trade-off.