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

Simpson, Daniel; Rue, Håvard; Martins, Thiago G.; Riebler, Andrea; Sørbye, Sigrunn Holbek

doi:10.48550/arxiv.1403.4630

Cited by 6 publications

(6 citation statements)

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“…Therefore, a single hyperparameter value cannot be used in all situations. Some recent studies have focused on methods for more careful and principled specification of priors for complex hierarchical models (Fong et al, 2010;Simpson et al, 2014;Sørbye and Rue, 2014). The method of Sørbye and Rue (2014) was developed for intrinsic GMRF priors and we adapt their approach to our specific models in what follows.…”

Section: Parameterizing the Global Smoothing Priormentioning

confidence: 99%

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Faulkner¹,

Minin²

2018

Bayesian Anal.

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We present a locally adaptive nonparametric curve fitting method that operates within a fully Bayesian framework. This method uses shrinkage priors to induce sparsity in order-k differences in the latent trend function, providing a combination of local adaptation and global control. Using a scale mixture of normals representation of shrinkage priors, we make explicit connections between our method and kth order Gaussian Markov random field smoothing. We call the resulting processes shrinkage prior Markov random fields (SPMRFs). We use Hamiltonian Monte Carlo to approximate the posterior distribution of model parameters because this method provides superior performance in the presence of the high dimensionality and strong parameter correlations exhibited by our models. We compare the performance of three prior formulations using simulated data and find the horseshoe prior provides the best compromise between bias and precision. We apply SPMRF models to two benchmark data examples frequently used to test nonparametric methods. We find that this method is flexible enough to accommodate a variety of data generating models and offers the adaptive properties and computational tractability to make it a useful addition to the Bayesian nonparametric toolbox.

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Section: Parameterizing the Global Smoothing Priormentioning

confidence: 99%

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Faulkner¹,

Minin²

2018

Bayesian Anal.

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“…This is an efficient computational alternative to the Markov Chain Monte Carlo (MCMC) methods, especially when data has a spatial or space-temporal structure 26 . In the modeling, minimally informative priors were considered for fixed effects and priors with penalized complexity for random effects 32 . The analyses were performed in the R-INLA 31 and INLAOutputs 33 packages of the R program 34 .…”

Section: Methodsmentioning

confidence: 99%

Variabilidade espacial intraurbana da mortalidade por câncer de mama e do colo do útero no município de São Paulo: análise dos fatores associados

Aguiar

Pellini

Rebolledo

et al. 2023

Rev. bras. epidemiol.

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RESUMO Objetivo: Identificar a variabilidade espacial da mortalidade por câncer de mama e colo do útero e avaliar fatores associados à mortalidade por esses cânceres no município de São Paulo. Métodos: Entre 2009 e 2016 foram registrados, no Sistema de Informações sobre Mortalidade, 10.124 óbitos por câncer de mama e 2.116 óbitos por câncer do colo do útero em mulheres com 20 anos e mais. Os registros foram geocodificados por endereço de residência e agregados segundo território adstrito. Foram realizadas modelagens de regressão espacial utilizando-se a abordagem bayesiana com estrutura de Besag-York-Mollié para verificar a associação dos óbitos com indicadores selecionados. Resultados: As taxas de mortalidade por esses cânceres apresentaram padrões espaciais inversos. As variáveis associadas à mortalidade por câncer de mama foram: tempo de deslocamento para o trabalho entre uma e duas horas (risco relativo — RR 0,97; intervalo de credibilidade — IC95% 0,93–1,00); mulheres responsáveis pelo domicílio (RR 0,97; IC95% 0,94–0,99) e óbitos por câncer de mama ocorridos em estabelecimentos privados (RR 1,04; IC95% 1,00–1,07). À mortalidade por câncer do colo do útero, estiveram associados: tempo de deslocamento para o trabalho entre meia e uma hora (RR 0,92; IC95% 0,87–0,98); rendimento domiciliar até três salários-mínimos (RR 1,27; IC95% 1,18–1,37); e razão de menores de um ano em relação à população feminina de 15 a 49 anos (RR 1,09; IC95% 1,01–1,18). Conclusão: Foram calculados os RR preditos para a mortalidade por esses cânceres, que estiveram associados às condições socioeconômicas das áreas de abrangência.

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“…With too restrictive a training set, fits would suffer from additional systematic bias. As such, our SFH template parameters are intended to have weakly informative priors (Simpson et al 2014;Gelman & Hennig 2015) which encompass the areas of parameter space that are physically allowable and in line with previous studies (to this point, see the below description of the mass weighted mean stellar age distribution, Figure 6), while allowing only a relatively small proportion of more complex models (e.g., those involving bursts or a transition in SFH behavior).…”

Section: Sfhs and Stellar Population Propertiesmentioning

confidence: 99%

Resolved and Integrated Stellar Masses in the SDSS-iv/MaNGA Survey. I. PCA Spectral Fitting and Stellar Mass-to-light Ratio Estimates

Pace

Tremonti²,

Chen³

et al. 2019

ApJ

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We present a method of fitting optical spectra of galaxies using a basis set of six vectors obtained from principal component analysis (PCA) of a library of synthetic spectra of 40000 star formation histories (SFHs). Using this library, we provide estimates of resolved effective stellar mass-to-light ratio (Υ * ) for thousands of galaxies from the SDSS-IV/MaNGA integral-field spectroscopic survey. Using a testing framework built on additional synthetic SFHs, we show that the estimates of log Υ * i are reliable (as are their uncertainties) at a variety of signal-to-noise ratios, stellar metallicities, and dust attenuation conditions. Finally, we describe the future release of the resolved stellar mass-to-light ratios as a SDSS-IV/MaNGA Value-Added Catalog (VAC) and provide a link to the software used to conduct this analysis a)Corresponding author: Zachary J. Pace zpace@astro.wisc.edu a) The software can be found at https://github.com/zpace/pcay.

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

Cited by 6 publications

References 0 publications

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Locally Adaptive Smoothing with Markov Random Fields and Shrinkage Priors

Variabilidade espacial intraurbana da mortalidade por câncer de mama e do colo do útero no município de São Paulo: análise dos fatores associados

Resolved and Integrated Stellar Masses in the SDSS-iv/MaNGA Survey. I. PCA Spectral Fitting and Stellar Mass-to-light Ratio Estimates

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