A hierarchical multivariate spatio-temporal model for clustered climate data with annual cycles

Mastrantonio, Gianluca; Lasinio, Giovanna Jona; Pollice, Alessio; Capotorti, Giulia; Teodonio, Lorenzo; Genova, Giulio; Blasi, C.

doi:10.1214/18-aoas1212

Cited by 23 publications

(15 citation statements)

References 50 publications

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“…This has been advocated in recent papers: Random fields defined over

scriptD \times S^{1}

, where

scriptD

is the spatial domain (a path or a planar surface) and

S^{1}

is time wrapped over the circle, have been considered by Benigni and Furrer (2012) to analyze improvised explosive device attacks along a main supply route in Baghdad, or by Shirota and Gelfand (2017) to analyze daily crime events in San Francisco. Similar approaches are then adopted by Mastrantonio et al (2019), who consider Bayesian hierarchical modeling where seasonality is modeled through conditioning sets. A similar approach under the Bayesian framework has been adopted by White and Porcu (2019a).…”

Section: Discussionmentioning

confidence: 99%

30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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“…This has been advocated in recent papers: Random fields defined over

scriptD \times S^{1}

, where

scriptD

is the spatial domain (a path or a planar surface) and

S^{1}

Section: Discussionmentioning

confidence: 99%

30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

View full text Add to dashboard Cite

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“…In some practical scenarios, several spatial phenomena are monitored simultaneously [5]. Though each spatially distributed process can be modelled individually, crosscorrelation between them is ubiquitous [10].…”

Section: B Multivariate Spatial Predictionmentioning

confidence: 99%

“…In cases there exist multiple or multivariate spatial processes in the same environment, e.g. indoor temperature and humidity, they may have cross-correlation [5]. If those spatial phenomena are simultaneously observed, presence of their cross-correlation may influence on results of the spatial sensor selection for monitoring multivariate spatial fields, which here we define as the multivariate sensor selection.…”

Section: Introductionmentioning

confidence: 99%

Multivariate versus Univariate Sensor Selection for Spatial Field Estimation

Nguyen¹,

Thiyagarajan²,

Ulapane³

et al. 2021

Preprint

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The paper discusses the sensor selection problem in estimating spatial ﬁelds. It is demonstrated that selecting a subset of sensors depends on modelling spatial processes. It is ﬁrst proposed to exploit Gaussian process (GP) to model a univariate spatial ﬁeld and multivariate GP (MGP) to jointly represent multivariate spatial phenomena. A Mat´ern cross covariance function is employed in the MGP model to guarantee its cross-covariance matrices to be positive semi-deﬁnite. We then consider two corresponding univariate and multivariate sensor selection problems in effectively monitoring multiple spatial random ﬁelds. The sensor selection approaches were implemented in the real-world experiments and their performances were compared. Difference of results obtained by the univariate and multivariate sensor selection techniques is insigniﬁcant; that is, either of the methods can be efﬁciently used in practice.

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“…The usual choice is the Cholesky decomposition, however it is well known that this induces an ordering between the variables [56] that is against one of the principle of compositional data analysis. We follow the approach of [43] by setting…”

Section: A New Parametrizationmentioning

confidence: 99%

New formulation of the logistic-Gaussian process to analyze trajectory tracking data

Mastrantonio¹,

Grazian²,

Mancinelli³

et al. 2019

Ann. Appl. Stat.

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Improved communication systems, shrinking battery sizes and the price drop of tracking devices have led to an increasing availability of trajectory tracking data. These data are often analyzed to understand animals behavior using mixture-type model.In this work we propose a new model based on the Logistic-Normal process. Due to a new formalization and the way we specify the coregionalization matrix of the associated multivariate Gaussian process, we show that our model, differently from other proposals, is invariant with respect to the choice of the reference element and of the ordering of the components of the probability vectors. We estimate the model under a Bayesian framework, using an approximation of the Gaussian process needed to avoid impractical computational time.We perform a simulation study with the aim of showing the ability of the model to retrieve the parameters used to simulate the data. The model is then applied to the real data where a wolf is observed before and after the procreation. Results are easy interpretable showing differences in the two phases.We record a time series of spatial locations of the female wolf called F24 (2-3 years old), that was live-trapped in May 2009 in the Abruzzo, Lazio and Molise National Park (central Apennines, Italy) and equipped with a Vectronic Pro Light-1 collar (Vectronic Aerospace GmbH, Berlin, Germany). Details on wolf capture and handling are provided in [36]. During winter months (January -April), fix attempts were scheduled every 30 minutes for 10 days, and every 3 hours for 20 days for the rest of the year. The lower acquisition interval during winter months was programmed with the aim to estimate wolf kill rate through field investigations of GPS clusters [58].When first captured, F24 was a member of the Villa pack, where it remained for 7.9 months before dispersing and establishing a new pack (i.e., Bisegna pack) in January 2010. The wolf reproduced in May 2010 and, using information derived from its GPS locations, we were able to determine the actual position of the den. Between May 28th and June 4th, F24 restricted its movements in the proximity of the den. We therefore assumed that F24 entered the den on May 28th and reproduced in the following days. Until collars failure on June 16th, F24 systematically revisited the den to feed and attend the cubs. We collected locations from F24's collar with a mean acquisition rate of 91.5%. We decided to The modelIn a mixture-type model the clustering is generally encoded using a discrete (latent) random variable z = {z t } t∈T , where z t ∈ {1, 2, . . . , K} ≡ K is a membership variable such that z t = k indicates the behavior at time t.

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A hierarchical multivariate spatio-temporal model for clustered climate data with annual cycles

Cited by 23 publications

References 50 publications

30 Years of space–time covariance functions

30 Years of space–time covariance functions

Multivariate versus Univariate Sensor Selection for Spatial Field Estimation

New formulation of the logistic-Gaussian process to analyze trajectory tracking data

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