arXiv subjects

Haavard Rue

Publications and source records attributed to Haavard Rue.

25 records · Page 2Linked to original sources

arXiv2020

A principled distance-based prior for the shape of the Weibull model

The use of flat or weakly informative priors is popular due to the objective a priori belief in the absence of strong prior information. In the case of the Weibull model the improper uniform, equal parameter gamma and joint Jeffrey's priors for the shape parameter are popular choices. The effects and behaviors of these priors have yet to be established from a modeling viewpoint, especially their ability to reduce to the simpler exponential model. In this work we propose a new principled prior for the shape parameter of the Weibull model, originating from a prior on the distance function, and advocate this new prior as a principled choice in the absence of strong prior information. This new prior can then be used in models with a Weibull modeling component, like competing risks, joint and spatial models, to mention a few. This prior is available in the R-INLA for use, and is applied in a joint longitudinal-survival model framework using the INLA method.

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arXiv2019

A Novel Method of Marginalisation using Low Discrepancy Sequences for Integrated Nested Laplace Approximations

Recently, it has been shown that approximations to marginal posterior distributions obtained using a low discrepancy sequence (LDS) can outperform standard grid-based methods with respect to both accuracy and computational efficiency. This recent method, which we will refer to as LDS-StM, can also produce good approximations to multimodal posteriors. However, implementation of LDS-StM into integrated nested Laplace approximations (INLA), a methodology in which grid-based methods are used, is challenging. Motivated by this problem, we propose modifications to LDS-StM that improves the approximations and make it compatible with INLA, without sacrificing computational speed. We also present two examples to demonstrate that LDS-StM with modifications can outperform INLA's own grid approximation with respect to speed and accuracy. We also demonstrate the flexibility of the new approach for the approximation of multimodal marginals.

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arXiv2019

Competing risks joint models using R-INLA

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models have largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this paper, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, time dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model, as specific examples.

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arXiv2019

New frontiers in Bayesian modeling using the INLA package in R

The INLA package provides a tool for computationally efficient Bayesian modeling and inference for various widely used models, more formally the class of latent Gaussian models. It is a non-sampling based framework which provides approximate results for Bayesian inference, using sparse matrices. The swift uptake of this framework for Bayesian modeling is rooted in the computational efficiency of the approach and catalyzed by the demand presented by the big data era. In this paper, we present new developments within the INLA package with the aim to provide a computationally efficient mechanism for the Bayesian inference of relevant challenging situations.

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arXiv2019

Model-aware Quantile Regression for Discrete Data

Quantile regression relates the quantile of the response to a linear predictor. For a discrete response distributions, like the Poission, Binomial and the negative Binomial, this approach is not feasible as the quantile function is not bijective. We argue to use a continuous model-aware interpolation of the quantile function, allowing for proper quantile inference while retaining model interpretation. This approach allows for proper uncertainty quantification and mitigates the issue of quantile crossing. Our reanalysis of hospitalisation data considered in Congdon (2017) shows the advantages of our proposal as well as introducing a novel method to exploit quantile regression in the context of disease mapping.

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arXiv2019

Joint models as latent Gaussian models - not reinventing the wheel

Joint models have received increasing attention during recent years with extensions into various directions; numerous hazard functions, different association structures, linear and non-linear longitudinal trajectories amongst others. Many of these resulted in new R packages and new formulations of the joint model. However, a joint model with a linear bivariate Gaussian association structure is still a latent Gaussian model (LGM) and thus can be implemented using most existing packages for LGM's. In this paper, we will show that these joint models can be implemented from a LGM viewpoint using the R-INLA package. As a particular example, we will focus on the joint model with a non-linear longitudinal trajectory, recently developed and termed the partially linear joint model. Instead of the usual spline approach, we argue for using a Bayesian smoothing spline framework for the joint model that is stable with respect to knot selection and hence less cumbersome for practitioners.

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arXiv2017

Unemployment estimation: Spatial point referenced methods and models

Portuguese Labor force survey, from 4th quarter of 2014 onwards, started geo-referencing the sampling units, namely the dwellings in which the surveys are carried. This opens new possibilities in analysing and estimating unemployment and its spatial distribution across any region. The labor force survey choose, according to an preestablished sampling criteria, a certain number of dwellings across the nation and survey the number of unemployed in these dwellings. Based on this survey, the National Statistical Institute of Portugal presently uses direct estimation methods to estimate the national unemployment figures. Recently, there has been increased interest in estimating these figures in smaller areas. Direct estimation methods, due to reduced sampling sizes in small areas, tend to produce fairly large sampling variations therefore model based methods, which tend to "borrow strength" from area to area by making use of the areal dependence, should be favored. These model based methods tend use areal counting processes as models and typically introduce spatial dependence through the model parameters by a latent random effect. In this paper, we suggest modeling the spatial distribution of residential buildings across Portugal by a Log Gaussian Cox process and the number of unemployed per residential unit as a mark attached to these random points. Thus the main focus of the study is to model the spatial intensity function of this marked point process. Number of unemployed in any region can then be estimated using a proper functional of this marked point process. The principal objective of this point referenced method for unemployment estimation is to get reliable estimates at higher spatial resolutions and at the same time incorporate in the model the auxiliary information available at residential units such as average income or education level of individuals surveyed in these units.

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