Statistical Modelling and Regression Structures: Festschrift in Honour of Ludwig Fahrmeir
Abstract
Model criticism and comparison of Bayesian hierarchical models is often based on posterior or leave-one-out cross-validatory predictive checks. Crossvalidatory checks are usually preferred because posterior predictive checks are difficult to assess and tend to be too conservative. However, techniques for statistical inference in such models often try to avoid full (manual) leave-one-out crossvalidation, since it is very time-consuming. In this paper we will compare two approaches for estimating Bayesian hierarchical models: Markov chain Monte Carlo (MCMC) and integrated nested Laplace approximations (INLA). We review how both approaches allow for the computation of leave-one-out cross-validatory checks without re-running the model for each observation in turn.We then empirically compare the two approaches in an extensive case study analysing the spatial distribution of bovine viral diarrhoe (BVD) among cows in Switzerland.
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Vague zero-mean Gaussian priors with a variance of 100 were assigned to the fixed effects; these priors approximate non-informative priors designed to have little influence on the posterior distribution.
“Vague zero-mean Gaussian prior distributions with a variance of 100 were assigned for the fixed effects, as recommended by Held et al. (2010) [25]. These priors are approximations of non-informative priors designed to have little influence on posterior distribution.”
From Shift in Tuna Catches Due to Ocean Warming (2017) · cites this paper as Held et al. (2010)
Applying a bootstrap technique with the percentile method to each time series yields a 95% confidence interval for the original lowess fit.
“In addition, we applied a bootstrap technique to each time series with the percentile method, in order to account for the variability in the original lowess fit. With this methodology, each series would have a 95% confidence interval for the original lowess [28, 29].”
From Shift in Tuna Catches Due to Ocean Warming (2017) · cites this paper as [28]
Vague zero-mean Gaussian priors with a variance of 100 were assigned to the fixed effects; these priors approximate non-informative priors designed to have little influence on the posterior distribution.
“Vague zero-mean Gaussian prior distributions with a variance of 100 were assigned for the fixed effects, as recommended by Held et al. (2010) [25]. These priors are approximations of non-informative priors designed to have little influence on posterior distribution.”
From Shift in Tuna Catches Due to Ocean Warming (2017) · cites this paper as [25]
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Shift in Tuna Catches Due to Ocean Warming
Monllor-Hurtado, A., Pennino, M. G., & Sanchez-Lizaso, J. L. (2017) · PLoS ONE · doi:10.1371/journal.pone.0178196 · Cited by 54 · see citing works
- Authors
- Held, L., Schrödle, B., & Rue, H.
- Affiliations
- Carl von Ossietzky Universität Oldenburg (DE)
- Ludwig-Maximilians-Universität München (DE)
- Venue
- Physica-Verlag eBooks
- Publisher
- Physica-Verlag HD
- Published
- 2010
- OpenAlex
- W2482914338
- Cited by
- 80
- References
- 0
- Citations by year
- 2025: 1 · 2024: 7 · 2023: 7 · 2022: 6 · 2021: 9 · 2020: 5 · 2019: 6 · 2018: 7 · 2017: 4 · 2016: 4 · 2015: 4 · 2014: 9 · 2013: 6
- FWCI
- 1.01
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- Locations
- Physica-Verlag eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Zurich Open Repository and Archive (University of Zurich) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Markov Chains and Monte Carlo Methods
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- Bayesian hierarchical model, leave-one-out cross-validation, posterior predictive checks, model criticism, model comparison, integrated nested Laplace approximation, Markov chain Monte Carlo, computational efficiency, bovine viral diarrhea, spatial distribution of disease
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