Estimating cross‐validatory predictive p‐values with integrated importance sampling for disease mapping models

@article{Li2016EstimatingCP,
  title={Estimating cross‐validatory predictive p‐values with integrated importance sampling for disease mapping models},
  author={Longhai Li and Cindy Xin Feng and Shi Qiu},
  journal={Statistics in Medicine},
  year={2016},
  volume={36},
  pages={2220 - 2236}
}
An important statistical task in disease mapping problems is to identify divergent regions with unusually high or low risk of disease. Leave‐one‐out cross‐validatory (LOOCV) model assessment is the gold standard for estimating predictive p‐values that can flag such divergent regions. However, actual LOOCV is time‐consuming because one needs to rerun a Markov chain Monte Carlo analysis for each posterior distribution in which an observation is held out as a test case. This paper introduces a new… 
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References

SHOWING 1-10 OF 46 REFERENCES

Approximate cross‐validatory predictive checks in disease mapping models

An importance sampling approximation is considered that can be improved upon through replication of both random effects and data and may aid the criticism of any Bayesian hierarchical model.

Approximating cross-validatory predictive evaluation in Bayesian latent variable models with integrated IS and WAIC

iIS and iWAIC aim at improving the approximations given by importance sampling and WAIC in Bayesian models with possibly correlated latent variables by integrating the predictive density over the distribution of the latent variables associated with the held-out without reference to its observation.

Posterior predictive model checks for disease mapping models.

This work proposes the use of the cross-validation posterior predictive distribution, obtained by reanalyzing the data without a suspect small area, as a method for assessing whether the observed count in the area is consistent with the model.

Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC

An efficient computation of LOO is introduced using Pareto-smoothed importance sampling (PSIS), a new procedure for regularizing importance weights, and it is demonstrated that PSIS-LOO is more robust in the finite case with weak priors or influential observations.

Towards joint disease mapping

A review of methods for separate analyses of diseases, then a move to ecological regression approaches, where the rates from one of the diseases enter as surrogate covariates for exposure, and a general framework for jointly modelling the variation of two or more diseases.

Bayesian Model Assessment and Comparison Using Cross-Validation Predictive Densities

This work proposes an approach using cross-validation predictive densities to obtain expected utility estimates and Bayesian bootstrap to obtain samples from their distributions, and discusses the probabilistic assumptions made and properties of two practical cross- validate methods, importance sampling and k-fold cross- validation.

Model Determination Using Predictive Distributions with Implementation via Sampling-Based Methods

Model determination is divided into the issues of model adequacy and model selection and it is proposed to validate conditional predictive distributions arising from single point deletion against observed responses.

Disease mapping models: an empirical evaluation

The main general results presented here show that the gamma-Poisson exchangeable model and the Besag, York and Mollie (BYM) model are most robust across a range of diverse models.

A comparison of Bayesian spatial models for disease mapping

A comprehensive review of the main classes of such models that have been used for disease mapping within a Bayesian estimation paradigm, and a performance comparison between representative models in these classes are reported, using a set of simulated data to help illustrate their respective properties.

Case-deletion importance sampling estimators: Central limit theorems and related results

Case-deleted analysis is a popular method for evaluating the influence of a subset of cases on inference. The use of Monte Carlo estima- tion strategies in complicated Bayesian settings leads…