PC priors for residual correlation parameters in one-factor mixed models

@article{Ventrucci2019PCPF,
  title={PC priors for residual correlation parameters in one-factor mixed models},
  author={Massimo Ventrucci and Daniela Cocchi and Gemma Burgazzi and Alex Laini},
  journal={Statistical Methods \& Applications},
  year={2019}
}
Lack of independence in the residuals from linear regression motivates the use of random effect models in many applied fields. We start from the one-way anova model and extend it to a general class of one-factor Bayesian mixed models, discussing several correlation structures for the within group residuals. All the considered group models are parametrized in terms of a single correlation (hyper-)parameter, controlling the shrinkage towards the case of independent residuals (iid). We derive a… 
Predictive Complexity Priors
TLDR
P predictive complexity priors are proposed: a functional prior that is defined by comparing the model's predictions to those of a reference function via a change of variables, which is originally defined on the model outputs.
Prior specification in one-factor mixed models applied to community ecology data
In community ecology studies the goal is to evaluate the effect of environmental covariates on a response variable while investigating the nature unobserved heterogeneity. We focus on onefactor mixed
Variance partitioning in spatio-temporal disease mapping models.
TLDR
A reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that is named the variance partitioning model, which includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability.

References

SHOWING 1-10 OF 25 REFERENCES
Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression
. The selection of appropriate hyperpriors for variance parameters is an important and sensible topic in all kinds of Bayesian regression models involving the specification of (conditionally) Gaussian
Testing Random Effects in the Linear Mixed Model Using Approximate Bayes Factors
TLDR
A simple approach for testing random effects in the linear mixed model using Bayes factors using a default prior distribution on the parameter controlling the contribution of each random effect and conduct simulations to show that the method has good properties for model selection problems.
Fractional Gaussian noise: Prior specification and model comparison
Fractional Gaussian noise (fGn) is a stationary stochastic process used to model antipersistent or persistent dependency structures in observed time series. Properties of the autocovariance function
Penalised Complexity Priors for Stationary Autoregressive Processes
TLDR
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.
Constructing Priors that Penalize the Complexity of Gaussian Random Fields
TLDR
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.
Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper)
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
Bayesian Variable Selection for Random Intercept Modeling of Gaussian and non-Gaussian Data
where yit are repeated responses observed for N units (e.g. subjects) i = 1, . . . , N on Ti occasions t = 1, . . . , Ti. xit is the (1×d) design matrix for an unknown regression coefficient α = (α1,
Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors
TLDR
A new concept for constructing prior distributions that is invariant to reparameterisations, have a natural connection to Jeffreys’ priors, seem to have excellent robustness properties, and allow this approach to define default prior distributions.
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations
TLDR
This work considers approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non‐Gaussian response variables and can directly compute very accurate approximations to the posterior marginals.
The Use of Score Tests for Inference on Variance Components
Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance
...
...