Fractional Gaussian noise: Prior specification and model comparison

Sørbye, Sigrunn Holbek; Rue, Haåvard

doi:10.1002/env.2457

Cited by 23 publications

(18 citation statements)

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“…The class of PC priors represents a recently developed framework to compute priors based on specific principles, including support for Occam's razor. The PC prior of the two scaling parameters σ f and σ can be computed to equal the exponential distribution, while the PC prior of H is computed numerically (Sørbye and Rue, 2018).…”

Section: Discrete-time Modeling and Statistical Inferencementioning

confidence: 99%

“…In addition to ensuring computational efficiency, this approximation also proves to be remarkably accurate. For further details about this approximation, see Sørbye et al (2019), who also provide a discussion from a statistical perspective. For a physical interpretation of this approximation we refer to Fredriksen and Rypdal (2017).…”

Section: Discrete-time Modeling and Statistical Inferencementioning

confidence: 99%

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Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling

et al. 2020

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Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach using a stochastic linear response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from one-box and two-box energy balance models. The software developed to perform the given analyses is publicly available as the R package INLA.climate.where σ dB(t) represents a white-noise forcing that gives rise to internal climate variability, and G is the response function, or Green's function, characterizing the relation between forcing and the temperature anomaly. A model of this form canPublished by Copernicus Publications on behalf of the European Geosciences Union.

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Section: Discrete-time Modeling and Statistical Inferencementioning

confidence: 99%

Section: Discrete-time Modeling and Statistical Inferencementioning

confidence: 99%

Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling

et al. 2020

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“…The PC priors proposed in this paper provide a solution to this issue as they are defined on a distance scale d(·), common to both M 1 and M 2 . Following Sørbye and Rue (2018) we assume PC priors on d(ρ) (for M 1 ) and d(φ) (for M 2 ) with equal rate λ; in this way, M 1 and M 2 have the same distance, at prior, from the iid base model. This strategy is reminiscent of the concept of compatible priors (Dawid and Lauritzen, 2001), i.e.…”

Section: Comparing Different Group Models Using the Bayes Factormentioning

confidence: 99%

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

2019

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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 penalized complexity (PC) prior for the correlation parameter of a generic group model. This prior has desirable properties from a practical point of view: i) it ensures appropriate shrinkage to the iid case; ii) it depends on a scaling parameter whose choice only requires a prior guess on the proportion of total variance explained by the grouping factor; iii) it is defined on a distance scale common to all group models, thus the scaling parameter can be chosen in the same manner regardless the adopted group model. We show the benefit of using these PC priors in a case study in community ecology where different group models are compared.

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“…PC priors now exist for models of tail dependence (Kereszturi, Tawn and Jonathan, 2016), the Hurst parameter for fractional Gaussian noise (Sørbye and Rue, 2016a), the degrees of freedom for P-splines (Ventrucci and Rue, 2016), parameters in the Matérn covariance function (Fuglstad et al, 2015), the correlation parameter in bivariate meta-analysis models (Guo, Rue and Riebler, 2015), the autoregressive parameters in an AR(p) process (Sørbye and Rue, 2016b) and the variance in the mean-variance parameterisation of the Beta distribution (Harjanto et al, 2016).…”

Section: Give the People What They Wantmentioning

confidence: 99%

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

Simpson¹,

Rue²,

Riebler³

et al. 2017

Statist. Sci.

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The entire reason that we wrote this paper was to provide a concrete object around which to focus a broader discussion about prior choice and we are extremely grateful to the editorial team at Statistical Science for this opportunity. David Dunson (DD), Jim Hodges (JH), Christian Robert, Judith Rousseau (RR) and James Scott (JS) have taken this discussion in diverse and challenging directions and over the next few pages, we will try to respond to the main points they have raised. "IF I COULD LOVE, I WOULD LOVE YOU ALL."-KIKI DURANEThe point of departure for our paper is that most modern statistical models are built to be flexible enough to model diverse data generating mechanisms. Good statistical practice requires us to limit this flexibility, which is typically controlled by a small number of parameters, to the amount "needed" to model the data at hand. The Bayesian framework provides a natural method for doing this although, as DD points out, this trend for penalising model complexity casts a broad shadow over all of modern statistics and data science.The PC prior framework argues for setting priors on these flexibility parameters that are specifically built to penalise a certain type of complexity and avoid overfitting. The discussants raised various points about this core idea. First, DD pointed out that while over-fitting a model is a bad thing, under-fitting is not better: we do not want Occam's razor to slit our throat. We saw this behaviour when using a half-Normal prior on the distance, while the exponential prior does not lead to obvious attenuation of the estimates. This is confirmed experimentally by Klein and Kneib (2016).Both DD and RR note our focus on a specific parameterisation and DD (as well as a large number of reviewers) note that our informal definition of overfitting is parameterisation dependent. We did this on purpose: most people who use complex statistical models do not understand prior mass conditions in terms of Kullback-Leibler balls and the theoretical results in the paper do not justify this level of mathematical sophistication. Our choice to sacrifice generality (and annoy reviewers) in the search for a clear exposition has lead us to a revelation: we can replace questions about prior choice with questions about parameterisation. This leads us to re-phrase DD's implied question: How should we parameterise a flexibility parameter so that we can use an exponential prior?The parameterisation we chose waswhere ξ is the original flexibility parameter indexing model f ξ and f 0 is the base model. JH correctly tweaks our nose over our inability to communicate this distance in a meaningful way (a heinous sin for people who abandoned measure theory in a quest for clarity). While we personally find our interpretationd(ξ ) is the amount of information you lose by abandoning the flexible component in favour of the base model-appealing, it is a bit dry and abstract. JH suggests communicating the distance by considering how much a coin would be weighted to achieve that distance from a fair co...

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Fractional Gaussian noise: Prior specification and model comparison

Cited by 23 publications

References 25 publications

Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling

Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling

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

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

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