Data augmentation and parameter expansion for independent or spatially correlated ordinal data

Schliep, Erin M.; Hoeting, Jennifer A.

doi:10.1016/j.csda.2015.03.020

Cited by 15 publications

(9 citation statements)

References 23 publications

(37 reference statements)

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“…Next, because we label the mixture components based on ordering such that , we can model as an ordered multinomial, spatial random variable. As such, we can employ the methods of Higgs and Hoeting ( 2010 ) and Schliep and Hoeting ( 2015 ) and further augment the parameter space with another latent variable such that, Notably, integrating out the , we have which is equivalently defined by Eq. ( 2 ).…”

Section: Model Descriptionmentioning

confidence: 99%

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Distributional Validation of Precipitation Data Products with Spatially Varying Mixture Models

Warr

Heaton

Christensen

et al. 2022

JABES

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The high mountain regions of Asia contain more glacial ice than anywhere on the planet outside of the polar regions. Because of the large population living in the Indus watershed region who are reliant on melt from these glaciers for fresh water, understanding the factors that affect glacial melt along with the impacts of climate change on the region is important for managing these natural resources. While there are multiple climate data products (e.g., reanalysis and global climate models) available to study the impact of climate change on this region, each product will have a different amount of skill in projecting a given climate variable, such as precipitation. In this research, we develop a spatially varying mixture model to compare the distribution of precipitation in the High Mountain Asia region as produced by climate models with the corresponding distribution from in situ observations from the Asian Precipitation—Highly Resolved Observational Data Integration Towards Evaluation (APHRODITE) data product. Parameter estimation is carried out via a computationally efficient Markov chain Monte Carlo algorithm. Each of the estimated climate distributions from each climate data product is then validated against APHRODITE using a spatially varying Kullback–Leibler divergence measure. Supplementary materials accompanying this paper appear online.

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Section: Model Descriptionmentioning

confidence: 99%

“…Hence, we draw from their complete conditional using an adaptive Metropolis accept–reject algorithm. We again follow the convention of Schliep and Hoeting ( 2015 ) and integrate out the latent to sample from their posterior distribution given and .…”

Section: Model Descriptionmentioning

confidence: 99%

Distributional Validation of Precipitation Data Products with Spatially Varying Mixture Models

Warr

Heaton

Christensen

et al. 2022

JABES

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“…For the other variables, we need to specify the prior distributions. Following Schliep and Hoeting (2015), we specify conjugate priors for η l , µ sj , and…”

Section: Bayesian Approachmentioning

confidence: 99%

A Sample Covariance-Based Approach For Spatial Binary Data

Zarmehri

Hanks

Lin

2020

Preprint

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AbstractThe field of landscape genetics enables the study of infectious disease dynamics by connecting the landscape features with evolutionary changes. Quantifying genetic correlation across space is helpful in providing insight into the rate of spread of an infectious disease. We investigate two genetic patterns in spatially referenced single-nucleotide polymorphisms (SNPs): isolation by distance and isolation by resistance. We model the data using a Generalized Linear Mixed effect Model (GLMM) with spatially referenced random effects and provide a novel approach for estimating parameters in spatial GLMMs. In this approach, we use the links between binary probit models and bivariate normal probabilities to directly compute the model-based covariance function for spatial binary data. Parameter estimation is based on minimizing sum of squared distance between the elements of sample covariance and model-based covariance matrices. We analyze data including Brucella Abortus SNPs from spatially referenced hosts in the Greater Yellowstone Ecosystem (GYE).

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“…(1) are the spatial binary model with probit link (considered by Berrett and Calder, 2016) and spatial probit model for correlated ordinal data (Schliep and Hoeting, 2015); examples for case (2) are already considered in this manuscript.…”

Section: S6 Sglmms With Small-scale (Nugget) Spatial Effectmentioning

confidence: 99%

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

Guan

Haran

2018

Journal of Computational and Graphical Statistics

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Inference for spatial generalized linear mixed models (SGLMMs) for high-dimensional non-Gaussian spatial data is computationally intensive. The computational challenge is due to the high-dimensional random effects and because Markov chain Monte Carlo (MCMC) algorithms for these models tend to be slow mixing. Moreover, spatial confounding inflates the variance of fixed effect (regression coefficient) estimates. Our approach addresses both the computational and confounding issues by replacing the high-dimensional spatial random effects with a reduced-dimensional representation based on random projections. Standard MCMC algorithms mix well and the reduceddimensional setting speeds up computations per iteration. We show, via simulated examples, that Bayesian inference for this reduced-dimensional approach works well both in terms of inference as well as prediction; our methods also compare favorably to 1 arXiv:1609.02501v3 [stat.CO] 7 Oct 2018 existing reduced-rank approaches. We also apply our methods to two real world data examples, one on bird count data and the other classifying rock types.

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Data augmentation and parameter expansion for independent or spatially correlated ordinal data

Cited by 15 publications

References 23 publications

Distributional Validation of Precipitation Data Products with Spatially Varying Mixture Models

Distributional Validation of Precipitation Data Products with Spatially Varying Mixture Models

A Sample Covariance-Based Approach For Spatial Binary Data

A Computationally Efficient Projection-Based Approach for Spatial Generalized Linear Mixed Models

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