Bayesian influence diagnostics using normalizing functional Bregman divergence

04/07/2019
by   Ian M Danilevicz, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/10/2019

Efficient Bayesian estimation for GARCH-type models via Sequential Monte Carlo

This paper exploits the advantages of sequential Monte Carlo (SMC) to de...
research
06/08/2023

Monte Carlo inference for semiparametric Bayesian regression

Data transformations are essential for broad applicability of parametric...
research
06/16/2022

Generalised Bayesian Inference for Discrete Intractable Likelihood

Discrete state spaces represent a major computational challenge to stati...
research
09/21/2022

Single chain differential evolution Monte-Carlo for self-tuning Bayesian inference

1. Bayesian inference is difficult because it often requires time consum...
research
04/13/2022

Investigating the efficiency of marginalising over discrete parameters in Bayesian computations

Bayesian analysis methods often use some form of iterative simulation su...
research
02/06/2013

Support and Plausibility Degrees in Generalized Functional Models

By discussing several examples, the theory of generalized functional mod...
research
11/14/2022

Bayesian Reconstruction and Differential Testing of Excised mRNA

Characterizing the differential excision of mRNA is critical for underst...

Please sign up or login with your details

Forgot password? Click here to reset