Corpus ID: 214775135

Duality between Approximate Bayesian Methods and Prior Robustness

@article{Joshi2020DualityBA,
  title={Duality between Approximate Bayesian Methods and Prior Robustness},
  author={Chaitanya Joshi and F. Ruggeri},
  journal={arXiv: Methodology},
  year={2020}
}
In this paper we show that there is a link between approximate Bayesian methods and prior robustness. We show that what is typically recognized as an approximation to the likelihood, either due to the simulated data as in the Approximate Bayesian Computation (ABC) methods or due to the functional approximation to the likelihood, can instead also be viewed upon as an implicit exercise in prior robustness. We first define two new classes of priors for the cases where the sufficient statistics is… Expand

Figures from this paper

References

SHOWING 1-10 OF 30 REFERENCES
Calibration Procedures for Approximate Bayesian Credible Sets
TLDR
Two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods are developed and applied. Expand
Extending conventional priors for testing general hypotheses in linear models
We consider that observations come from a general normal linear model and that it is desirable to test a simplifying null hypothesis about the parameters. We approach this problem from an objectiveExpand
Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation (with Discussion)
TLDR
This work shows how to construct appropriate summary statistics for ABC in a semi-automatic manner, and shows that optimal summary statistics are the posterior means of the parameters. Expand
Diagnostic tools for approximate Bayesian computation using the coverage property
Summary Approximate Bayesian computation (ABC) is an approach to sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A commonExpand
Prior Distributions for Objective Bayesian Analysis
TLDR
This paper discusses principles for objective Bayesian model comparison, and singles out some major concepts for building priors, which are subsequently illustrated in some detail for the classic problem of variable selection in normal linear models. Expand
Prior Robustness for Bayesian Implementation of the Fault Tree Analysis
TLDR
It is shown that minor misspecification of priors for elementary events can result in a significant prior misspecify for the top event of the fault tree analysis. Expand
Robust Bayesian analysis of selection models
Selection models arise when the data are selected to enter the sample only if they occur in a certain region of the sample space. When this selection occurs according to some probabilityExpand
An Introduction to Variational Methods for Graphical Models
TLDR
This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields), and describes a general framework for generating variational transformations based on convex duality. Expand
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additiveExpand
Expectation Propagation for approximate Bayesian inference
  • T. Minka
  • Computer Science, Mathematics
  • UAI
  • 2001
TLDR
Expectation Propagation approximates the belief states by only retaining expectations, such as mean and varitmce, and iterates until these expectations are consistent throughout the network, which makes it applicable to hybrid networks with discrete and continuous nodes. Expand
...
1
2
3
...