# Intuitive principle-based priors for attributing variance in additive model structures

@article{Fuglstad2019IntuitivePP, title={Intuitive principle-based priors for attributing variance in additive model structures}, author={Geir-Arne Fuglstad and Ingeborg Gullikstad Hem and Alexander Knight and H. Rue and Andrea Riebler}, journal={arXiv: Methodology}, year={2019} }

Variance parameters in additive models are often assigned independent priors that are selected haphazardly from simple parametric families. We present a new framework for constructing joint priors for the variance parameters that treats the model structure as a whole. The focus is latent Gaussian models where penalised complexity priors can be computed exactly and generalised to a principled-based joint prior. The prior distributes the total variance of the model components to the individual… Expand

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#### References

SHOWING 1-10 OF 33 REFERENCES

Constructing Priors that Penalize the Complexity of Gaussian Random Fields

- Computer Science, Mathematics
- 2015

A principled joint prior is developed for the range and the marginal variance of one-dimensional, two- dimensional, and three-dimensional Matérn GRFs with fixed smoothness and is applied to a dataset of annual precipitation in southern Norway, leading to conservative estimates of nonstationarity and improved predictive performance over the stationary model. Expand

Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors

- Mathematics
- 2014

In this paper, we introduce a new concept for constructing prior
distributions. We exploit the natural nested structure inherent to many model
components, which defines the model component to be a… Expand

Careful prior specification avoids incautious inference for log‐Gaussian Cox point processes

- Mathematics, Geography
- Journal of the Royal Statistical Society: Series C (Applied Statistics)
- 2018

Prior specifications for hyperparameters of random fields in Bayesian spatial point process modelling can have a major impact on the statistical inference and the conclusions made. We consider… Expand

Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)

- Mathematics
- 2004

Various noninformative prior distributions have been suggested for scale parameters in hierarchical models. We construct a new folded-noncentral-t family of conditionally conjugate priors for… Expand

An intuitive Bayesian spatial model for disease mapping that accounts for scaling

- Computer Science, Mathematics
- Statistical methods in medical research
- 2016

A recently proposed parameterisation of the BYM model is discussed that leads to improved parameter control as the hyperparameters can be seen independently from each other, and the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors. Expand

Scaling intrinsic Gaussian Markov random field priors in spatial modelling

- Mathematics
- 2014

Abstract In Bayesian hierarchical regression models, intrinsic Gaussian Markov random fields (IGMRFs) are commonly applied to model underlying spatial or temporal dependency structures. IGMRFs have a… Expand

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

- Mathematics
- 2009

Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive… Expand

Penalised Complexity Priors for Stationary Autoregressive Processes

- Computer Science, Mathematics
- 2016

This paper proposes a sequential approach, where the base model for AR ($p$) is the corresponding AR($p-1$) model expressed using the partial autocorrelations, and discusses two natural base model choices, corresponding to either independence in time or no change in time. Expand

The Prior Can Often Only Be Understood in the Context of the Likelihood

- Mathematics, Computer Science
- Entropy
- 2017

This paper resolves an apparent paradox in prior modeling: a model encoding true prior information should be chosen without reference to the model of the measurement process, but almost all common prior modeling techniques are implicitly motivated by a reference likelihood. Expand

Bayesian Computing with INLA: A Review

- Mathematics, Computer Science
- 2016

The reasons for the success of the INLA approach, the R-INLA package, why it is so accurate, why the approximations are very quick to compute, and why LGMs make such a useful concept for Bayesian computing are discussed. Expand