Sigrunn Holbek Sørbye

Penalising model component complexity:A principled, practical approach to constructing priors

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 flexible extension of a base model. Proper priors are defined to penalise the complexity induced by deviating from the simpler base model and are formulated after the input of a user-defined scaling parameter for that model component, both in the univariate and the multivariate case. These priors are invariant to reparameterisations, have a natural connection to Jeffreys’ priors, are designed to support Occam’s razor and seem to have excellent robustness properties, all which are highly desirable and allow us to use this approach to define default prior distributions. Through examples and theoretical results, we demonstrate the appropriateness of this approach and how it can be applied in various situations.

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

In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level have been proposed but all come with inherent issues. In the classical BYM (Besag, York and Mollié) model, the spatially structured component cannot be seen independently from the unstructured component. This makes prior definitions for the hyperparameters of the two random effects challenging. There are alternative model formulations that address this confounding; however, the issue on how to choose interpretable hyperpriors is still unsolved. Here, we discuss a recently proposed parameterisation of the BYM model that leads to improved parameter control as the hyperparameters can be seen independently from each other. Furthermore, the need for a scaled spatial component is addressed, which facilitates assignment of interpretable hyperpriors and make these transferable between spatial applications with different graph structures. The hyperparameters themselves are used to define flexible extensions of simple base models. Consequently, penalised complexity priors for these parameters can be derived based on the information-theoretic distance from the flexible model to the base model, giving priors with clear interpretation. We provide implementation details for the new model formulation which preserve sparsity properties, and we investigate systematically the model performance and compare it to existing parameterisations. Through a simulation study, we show that the new model performs well, both showing good learning abilities and good shrinkage behaviour. In terms of model choice criteria, the proposed model performs at least equally well as existing parameterisations, but only the new formulation offers parameters that are interpretable and hyperpriors that have a clear meaning.

Bayesian multiscale feature detection of log-spectral densities

A fully-automatic Bayesian visualization tool to identify periodic components of evenly sampled stationary time series, is presented. The given method applies the multiscale ideas of the SiZer-methodology to the log-spectral density of a given series. The idea is to detect significant peaks in the true underlying curve viewed at different resolutions or scales. The results are displayed in significance maps, illustrating for which scales and for which frequencies, peaks in the log-spectral density are detected as significant. The inference involved in producing the significance maps is performed using the recently developed simplified Laplace approximation. This is a Bayesian deterministic approach used to get accurate estimates of posterior marginals for latent Gaussian Markov random fields at a low computational cost, avoiding the use of Markov chain Monte Carlo techniques. Application of the given exploratory tool is illustrated analyzing both synthetic and real time series.

Penalised Complexity Priors for Stationary Autoregressive Processes

The autoregressive process of order

Ocean migration of pop-up satellite archival tagged Atlantic salmon from the Miramichi River in Canada

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Finite sample properties of an adaptive density estimator

(AR(

You Just Keep on Pushing My Love over the Borderline: A Rejoinder

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A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)

)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR(

Going off grid: computationally efficient inference for log-Gaussian Cox processes

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Bayesian computing with INLA:a review

) model. Although it is easy to write down some prior, it is not at all obvious how to understand and interpret the prior, to ensure that it behaves according to the users prior knowledge. In this paper, we approach this problem using the recently developed ideas of penalised complexity (PC) priors. These priors have important properties like robustness and invariance to reparameterisations, as well as a clear interpretation. A PC prior is computed based on specific principles, where model component complexity is penalised in terms of deviation from simple base model formulations. In the AR(1) case, we discuss two natural base model choices, corresponding to either independence in time or no change in time. The latter case is illustrated in a survival model with possible time-dependent frailty. For higher-order processes, we propose a sequential approach, where the base model for AR(