arXiv subjects

Finn Lindgren

Publications and source records attributed to Finn Lindgren.

43 records · Page 3Linked to original sources

arXiv2013

Bayesian computing with INLA: new features

The INLA approach for approximate Bayesian inference for latent Gaussian models has been shown to give fast and accurate estimates of posterior marginals and also to be a valuable tool in practice via the R-package R-INLA. In this paper we formalize new developments in the R-INLA package and show how these features greatly extend the scope of models that can be analyzed by this interface. We also discuss the current default method in R-INLA to approximate posterior marginals of the hyperparameters using only a modest number of evaluations of the joint posterior distribution of the hyperparameters, without any need for numerical integration.

stat.CO↗

arXiv2012

Excursion and contour uncertainty regions for latent Gaussian models

An interesting statistical problem is to find regions where some studied process exceeds a certain level. Estimating such regions so that the probability for exceeding the level in the entire set is equal to some predefined value is a difficult problem that occurs in several areas of applications ranging from brain imaging to astrophysics. In this work, a method for solving this problem, as well as the related problem of finding uncertainty regions for contour curves, for latent Gaussian models is proposed. The method is based on using a parametric family for the excursion sets in combination with a sequential importance sampling method for estimating joint probabilities. The accuracy of the method is investigated using simulated data and two environmental applications are presented. In the first application, areas where the air pollution in the Piemonte region in northern Italy exceeds the daily limit value, set by the European Union for human health protection, are estimated. In the second application, regions in the African Sahel that experienced an increase in vegetation after the drought period in the early 1980s are estimated.

stat.ME↗

arXiv2012

Bayesian Adaptive Smoothing Spline using Stochastic Differential Equations

The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that restrict the use of smoothing spline in practical statistical work. Firstly, it becomes computationally prohibitive for large data sets because the number of basis functions roughly equals the sample size. Secondly, its global smoothing parameter can only provide constant amount of smoothing, which often results in poor performances when estimating inhomogeneous functions. In this work, we introduce a class of adaptive smoothing spline models that is derived by solving certain stochastic differential equations with finite element methods. The solution extends the smoothing parameter to a continuous data-driven function, which is able to capture the change of the smoothness of underlying process. The new model is Markovian, which makes Bayesian computation fast. A simulation study and real data example are presented to demonstrate the effectiveness of our method.

math.ST↗

arXiv2011

How do Markov approximations compare with other methods for large spatial data sets?

The Matérn covariance function is a popular choice for modeling dependence in spatial environmental data. Standard Matérn covariance models are, however, often computationally infeasible for large data sets. In this work, recent results for Markov approximations of Gaussian Matérn fields based on Hilbert space approximations are extended using wavelet basis functions. These Markov approximations are compared with two of the most popular methods for efficient covariance approximations; covariance tapering and the process convolution method. The results show that, for a given computational cost, the Markov methods have a substantial gain in accuracy compared with the other methods.

stat.CO↗

arXiv2011

Think continuous: Markovian Gaussian models in spatial statistics

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as the Markov property is difficult to deploy in continuous space. Following the pioneering work of Lindgren et al. (2011), we expound on the link between Markovian Gaussian random fields and GMRFs. In particular, we discuss the theoretical and practical aspects of fast computation with continuously specified Markovian Gaussian random fields, as well as the clear advantages they offer in terms of clear, parsimonious and interpretable models of anisotropy and non-stationarity.

math.ST↗

arXiv2011

Fast approximate inference with INLA: the past, the present and the future

Latent Gaussian models are an extremely popular, flexible class of models. Bayesian inference for these models is, however, tricky and time consuming. Recently, Rue, Martino and Chopin introduced the Integrated Nested Laplace Approximation (INLA) method for deterministic fast approximate inference. In this paper, we outline the INLA approximation and its related R package. We will discuss the newer components of the r-INLA program as well as some possible extensions.

stat.CO↗

arXiv2011

Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Matérn fields and a wide family of fields with oscillating covariance functions. Nonstationary covariance models are obtained by spatially varying the parameters in the SPDEs, and the model parameters are estimated using direct numerical optimization, which is more efficient than standard Markov Chain Monte Carlo procedures. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.

stat.AP↗