# Bayesian influence diagnostics using normalizing functional Bregman divergence

## TL;DR

This paper develops a Bayesian influence diagnostic method using normalized Bregman divergence for complex models like time series and spatial data, leveraging Hamiltonian Monte Carlo for efficient computation.

## Contribution

It extends Bregman divergence-based influence diagnostics to dependent data models and introduces a rescaling strategy for better interpretability.

## Key findings

- Effective in complex models such as time series and spatial data
- Maintains theoretical properties with minimal computational effort
- Validated through simulated and empirical studies

## Abstract

Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods. Kullback-Leiber and Bregman divergences were already applied in Bayesian inference to measure the isolated impact of each observation in a model. We extend these ideas to models for dependent data and with non-normal probability distributions such as time series, spatial models and generalized linear models. We also propose a strategy to rescale the functional Bregman divergence to lie in the (0,1) interval thus facilitating interpretation and comparison. This is accomplished with a minimal computational effort and maintaining all theoretical properties. For computational efficiency, we take advantage of Hamiltonian Monte Carlo methods to draw samples from the posterior distribution of model parameters. The resulting Markov chains are then directly connected with Bregman calculus, which results in fast computation. We check the propositions in both simulated and empirical studies.