| 1. |
- Lindgren, Finn, et al.
(författare)
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An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
- 2011
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Ingår i: Journal of the Royal Statistical Society. Series B: Statistical Methodology. - : Oxford University Press (OUP). - 1369-7412 .- 1467-9868. ; 73:4, s. 423-498
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Tidskriftsartikel (refereegranskat)abstract
- Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive interpretation of the field properties. On the computational side, GFs are hampered with the big n problem, since the cost of factorizing dense matrices is cubic in the dimension. Although computational power today is at an all time high, this fact seems still to be a computational bottleneck in many applications. Along with GFs, there is the class of Gaussian Markov random fields (GMRFs) which are discretely indexed. The Markov property makes the precision matrix involved sparse, which enables the use of numerical algorithms for sparse matrices, that for fields in R-2 only use the square root of the time required by general algorithms. The specification of a GMRF is through its full conditional distributions but its marginal properties are not transparent in such a parameterization. We show that, using an approximate stochastic weak solution to (linear) stochastic partial differential equations, we can, for some GFs in the Matern class, provide an explicit link, for any triangulation of R-d, between GFs and GMRFs, formulated as a basis function representation. The consequence is that we can take the best from the two worlds and do the modelling by using GFs but do the computations by using GMRFs. Perhaps more importantly, our approach generalizes to other covariance functions generated by SPDEs, including oscillating and non-stationary GFs, as well as GFs on manifolds. We illustrate our approach by analysing global temperature data with a non-stationary model defined on a sphere.
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| 2. |
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| 3. |
- Hall, P, et al.
(författare)
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On the adequacy of variational lower bound functions for likelihood-based inference in Markovian models with missing values
- 2002
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Ingår i: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY. - : Oxford University Press (OUP). - 1369-7412 .- 1467-9868. ; 64, s. 549-564
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Variational methods have been proposed for obtaining deterministic lower bounds for log-likelihoods within missing data problems, but with little formal justification or investigation of the worth of the lower bound surfaces as tools for inference. We provide, within a general Markovian context, sufficient conditions under which estimators from the variational approximations are asymptotically equivalent to maximum likelihood estimators, and we show empirically, for the simple example of a first-order autoregressive model with missing values, that the lower bound surface can be very similar in shape to the true log-likelihood in non-asymptotic situations.
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| 4. |
- Björkström, Anders, et al.
(författare)
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Continuum regression is not always continuous
- 1996
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - 1369-7412 .- 1467-9868. ; B 58:4, s. 703-710
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Bolin, David, 1983, et al.
(författare)
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Excursion and contour uncertainty regions for latent Gaussian models
- 2015
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - : Oxford University Press (OUP). - 1369-7412 .- 1467-9868. ; 77:1, s. 85-106
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Tidskriftsartikel (refereegranskat)abstract
- In several areas of application ranging from brain imaging to astrophysics and geostatistics, an important statistical problem is to find regions where the process studied 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 connected to the problem of multiple significance testing. In this work, a method for solving this problem, as well as the related problem of finding credible 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 by using simulated data and an environmental application is presented.
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| 6. |
- Bolin, David, 1983, et al.
(författare)
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Multivariate type G Matern stochastic partial differential equation random fields
- 2020
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Ingår i: Journal of the Royal Statistical Society Series B-Statistical Methodology. - : Oxford University Press (OUP). - 1369-7412 .- 1467-9868.
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Tidskriftsartikel (refereegranskat)abstract
- For many applications with multivariate data, random-field models capturing departures from Gaussianity within realizations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of stochastic partial differential equations with additive type G noise whose marginal covariance functions are of Matern type. We consider four increasingly flexible constructions of the noise, where the first two are similar to existing copula-based models. In contrast with these, the last two constructions can model non-Gaussian spatial data without replicates. Computationally efficient methods for likelihood-based parameter estimation and probabilistic prediction are proposed, and the flexibility of the models suggested is illustrated by numerical examples and two statistical applications.
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| 7. |
- Johansson, Per, et al.
(författare)
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On optimal rerandomization designs
- 2021
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - : John Wiley & Sons. - 1369-7412 .- 1467-9868. ; 83:2, s. 395-403
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Tidskriftsartikel (refereegranskat)abstract
- Blocking is commonly used in randomized experiments to increase efficiency of estimation. A generalization of blocking removes allocations with imbalance in covariate distributions between treated and control units, and then randomizes within the remaining set of allocations with balance. This idea of rerandomization was formalized by Morgan and Rubin (Annals of Statistics, 2012, 40, 1263-1282), who suggested using Mahalanobis distance between treated and control covariate means as the criterion for removing unbalanced allocations. Kallus (Journal of the Royal Statistical Society, Series B: Statistical Methodology, 2018, 80, 85-112) proposed reducing the set of balanced allocations to the minimum. Here we discuss the implication of such an 'optimal' rerandomization design for inferences to the units in the sample and to the population from which the units in the sample were randomly drawn. We argue that, in general, it is a bad idea to seek the optimal design for an inference because that inference typically only reflects uncertainty from the random sampling of units, which is usually hypothetical, and not the randomization of units to treatment versus control.
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| 8. |
- Karwa, Vishesh, et al.
(författare)
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Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels
- 2024
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - : Oxford University Press (OUP). - 1369-7412 .- 1467-9868. ; 86:1, s. 90-121
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Tidskriftsartikel (refereegranskat)abstract
- We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.
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| 9. |
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| 10. |
- Wijayatunga, Priyantha, 1967-
(författare)
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Discussion on the paper by Caron and Fox
- 2017
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - USA : John Wiley & Sons. - 1369-7412 .- 1467-9868. ; 79:5, s. 1359-1359
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- A measure of dependence for graph models
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| 11. |
- Wijayatunga, Priyantha, 1967-
(författare)
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Discussion on the paper titled "Gaussian differential privacy"
- 2022
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Ingår i: Journal of The Royal Statistical Society Series B-statistical Methodology. - : John Wiley & Sons. - 1369-7412 .- 1467-9868. ; 84:1, s. 49-50
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 12. |
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| 13. |
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