The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-consistency of Dirichlet mixtures in multivariate Bayesian density estimation

Wu, Yuefeng; Ghosal, Subhashis

doi:10.1016/j.jmva.2010.06.012

Cited by 24 publications

(2 citation statements)

References 12 publications

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“…Thus, for L, K = ∞, the covariance of the proposed model satisfies the criteria of the Karhunen-Loève Theorem (Alexanderian (2015)) and spans the covariance structure of all squared-integrable stochastic processes with continuous covariance functions. Under suitable regularity conditions, posterior consistency of the proposed model holds (Wu and Ghosal (2010), Ghosal and van der Vaart (2017)).…”

Section: Low-rank Student's T Process (Ltp) Ltps Are Richer Thanmentioning

confidence: 98%

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

Hazra

Huser

2021

Ann. Appl. Stat.

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In this work, we estimate extreme sea surface temperature (SST) hotspots, that is, high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16,703 grid cells across the Red Sea over the period 1985-2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatiallyvarying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student's t processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance, and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives. Moreover, we show how hotspots can be identified, and we estimate extreme SST hotspots for the whole Red Sea, projected until the year 2100, based on the Representative Concentration Pathways 4.5 and 8.5. The estimated 95% credible region, for joint high threshold exceedances include large areas covering major endangered coral reefs in the southern Red Sea.

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Section: Low-rank Student's T Process (Ltp) Ltps Are Richer Thanmentioning

confidence: 98%

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

Hazra

Huser

2021

Ann. Appl. Stat.

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“…With advancements in computing and general inference schemes such as Markov chain Monte Carlo (MCMC), BNP mixtures can be easily implemented. Moreover, well-established theory validates the use of BNP mixtures for asymptotically optimal density estimation [141–144]. Together these properties and developments have led to the huge growth and adoption of BNP mixtures, especially DP mixtures, for a variety of applications in statistics and machine learning in the twenty-first century.…”

Section: Estimating the Number Of Clusters And Model Misspecificationmentioning

confidence: 99%

Bayesian cluster analysis

Wade

2023

Phil. Trans. R. Soc. A.

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Bayesian cluster analysis offers substantial benefits over algorithmic approaches by providing not only point estimates but also uncertainty in the clustering structure and patterns within each cluster. An overview of Bayesian cluster analysis is provided, including both model-based and loss-based approaches, along with a discussion on the importance of the kernel or loss selected and prior specification. Advantages are demonstrated in an application to cluster cells and discover latent cell types in single-cell RNA sequencing data to study embryonic cellular development. Lastly, we focus on the ongoing debate between finite and infinite mixtures in a model-based approach and robustness to model misspecification. While much of the debate and asymptotic theory focuses on the marginal posterior of the number of clusters, we empirically show that quite a different behaviour is obtained when estimating the full clustering structure. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.

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Dirichlet process mixtures under affine transformations of the data

2020

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Location-scale Dirichlet process mixtures of Gaussians (DPM-G) have proved extremely useful in dealing with density estimation and clustering problems in a wide range of domains. Motivated by an astronomical application, in this work we address the robustness of DPM-G models to affine transformations of the data, a natural requirement for any sensible statistical method for density estimation and clustering. First, we devise a coherent prior specification of the model which makes posterior inference invariant with respect to affine transformations of the data. Second, we formalise the notion of asymptotic robustness under data transformation and show that mild assumptions on the true data generating process are sufficient to ensure that DPM-G models feature such a property. Our investigation is supported by an extensive simulation study and illustrated by the analysis of an astronomical dataset consisting of physical measurements of stars in the field of the globular cluster NGC 2419.

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The L1-consistency of Dirichlet mixtures in multivariate Bayesian density estimation

Cited by 24 publications

References 12 publications

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

Bayesian cluster analysis

Dirichlet process mixtures under affine transformations of the data

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