arXiv subjects

Arnab Hazra

Publications and source records attributed to Arnab Hazra.

28 records · Page 2Linked to original sources

arXiv2023

Spatial wildfire risk modeling using mixtures of tree-based multivariate Pareto distributions

Wildfires pose a severe threat to the ecosystem and economy, and risk assessment is typically based on fire danger indices such as the McArthur Forest Fire Danger Index (FFDI) used in Australia. Studying the joint tail dependence structure of high-resolution spatial FFDI data is thus crucial for estimating current and future extreme wildfire risk. However, existing likelihood-based inference approaches are computationally prohibitive in high dimensions due to the need to censor observations in the bulk of the distribution. To address this, we construct models for spatial FFDI extremes by leveraging the sparse conditional independence structure of Hüsler--Reiss-type generalized Pareto processes defined on trees. These models allow for a simplified likelihood function that is computationally efficient. Our framework involves a mixture of tree-based multivariate Pareto distributions with randomly generated tree structures, resulting in a flexible model that can capture nonstationary spatial dependence structures. We fit the model to summer FFDI data from different spatial clusters in Mainland Australia and 14 decadal windows between 1999--2022 to study local spatiotemporal variability with respect to the magnitude and extent of extreme wildfires. Our results demonstrate that our proposed method fits the margins and spatial tail dependence structure adequately, and is helpful to provide extreme wildfire risk measures.

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arXiv2021

A combined statistical and machine learning approach for spatial prediction of extreme wildfire frequencies and sizes

Motivated by the Extreme Value Analysis 2021 (EVA 2021) data challenge we propose a method based on statistics and machine learning for the spatial prediction of extreme wildfire frequencies and sizes. This method is tailored to handle large datasets, including missing observations. Our approach relies on a four-stage high-dimensional bivariate sparse spatial model for zero-inflated data, which is developed using stochastic partial differential equations(SPDE). In Stage 1, the observations are categorized in zero/nonzero categories and are modeled using a two-layered hierarchical Bayesian sparse spatial model to estimate the probabilities of these two categories. In Stage 2, before modeling the positive observations using spatially-varying coefficients, smoothed parameter surfaces are obtained from empirical estimates using fixed rank kriging. This approximate Bayesian method inference was employed to avoid the high computational burden of large spatial data modeling using spatially-varying coefficients. In Stage 3, the standardized log-transformed positive observations from the second stage are further modeled using a sparse bivariate spatial Gaussian process. The Gaussian distribution assumption for wildfire counts developed in the third stage is computationally effective but erroneous. Thus in Stage 4, the predicted values are rectified using Random Forests. The posterior inference is drawn for Stages 1 and 3 using Markov chain Monte Carlo (MCMC) sampling. A cross-validation scheme is then created for the artificially generated gaps, and the EVA 2021 prediction scores of the proposed model are compared to those obtained using certain natural competitors.

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arXiv2021

Contamination mapping in Bangladesh using a multivariate spatial Bayesian model for left-censored data

Arsenic (As) and other toxic elements contamination of groundwater in Bangladesh poses a major threat to millions of people on a daily basis. Understanding complex relationships between arsenic and other elements can provide useful insights for mitigating arsenic poisoning in drinking water and requires multivariate modeling of the elements. However, environmental monitoring of such contaminants often involves a substantial proportion of left-censored observations falling below a minimum detection limit (MDL). This problem motivates us to propose a multivariate spatial Bayesian model for left-censored data for investigating the abundance of arsenic in Bangladesh groundwater and for creating spatial maps of the contaminants. Inference about the model parameters is drawn using an adaptive Markov Chain Monte Carlo (MCMC) sampling. The computation time for the proposed model is of the same order as a multivariate Gaussian process model that does not impute the censored values. The proposed method is applied to the arsenic contamination dataset made available by the Bangladesh Water Development Board (BWDB). Spatial maps of arsenic, barium (Ba), and calcium (Ca) concentrations in groundwater are prepared using the posterior predictive means calculated on a fine lattice over Bangladesh. Our results indicate that Chittagong and Dhaka divisions suffer from excessive concentrations of arsenic and only the divisions of Rajshahi and Rangpur have safe drinking water based on recommendations by the World Health Organization (WHO).

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arXiv2021

Latent Gaussian Models for High-Dimensional Spatial Extremes

In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in practice for the computation of long-term return levels. The extended LGM framework assumes that the data follow a specific parametric distribution, whose unknown parameters are transformed using a multivariate link function and are then further modeled at the latent level in terms of fixed and random effects that have a joint Gaussian distribution. In the extremal context, we here assume that the data level distribution is described in terms of a Poisson point process likelihood, motivated by asymptotic extreme-value theory, and which conveniently exploits information from all threshold exceedances. This contrasts with the more common data-wasteful approach based on block maxima, which are typically modeled with the generalized extreme-value (GEV) distribution. When conditional independence can be assumed at the data level and latent random effects have a sparse probabilistic structure, fast approximate Bayesian inference becomes possible in very high dimensions, and we here present the recently proposed inference approach called "Max-and-Smooth", which provides exceptional speed-up compared to alternative methods. The proposed methodology is illustrated by application to satellite-derived precipitation data over Saudi Arabia, obtained from the Tropical Rainfall Measuring Mission, with 2738 grid cells and about 20 million spatio-temporal observations in total. Our fitted model captures the spatial variability of extreme precipitation satisfactorily and our results show that the most intense precipitation events are expected near the south-western part of Saudi Arabia, along the Red Sea coastline.

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arXiv2020

A semiparametric spatiotemporal Bayesian model for the bulk and extremes of the Fosberg Fire Weather Index

Large wildfires pose a major environmental concern, and precise maps of fire risk can improve disaster relief planning. Fosberg Fire Weather Index (FFWI) is often used to measure wildfire risk; FFWI exhibits non-Gaussian marginal distributions as well as strong spatiotemporal extremal dependence and thus, modeling FFWI using geostatistical models like Gaussian processes is questionable. Extreme value theory (EVT)-driven models like max-stable processes are theoretically appealing but are computationally demanding and applicable only for threshold exceedances or block maxima. Disaster management policies often consider moderate-to-extreme quantiles of climate parameters and hence, joint modeling of the bulk and the tail of the data is required. In this paper, we consider a Dirichlet process mixture of spatial skew-t processes that can flexibly model the bulk as well as the tail. The proposed model has nonstationary mean and covariance structure, and also nonzero spatiotemporal extremal dependence. A simulation study demonstrates that the proposed model has better spatial prediction performance compared to some competing models. We develop spatial maps of FFWI medians and extremes, and discuss the wildfire risk throughout the Santa Ana region of California.

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arXiv2020

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

In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., 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 16703 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 spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student-$t$ 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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arXiv2018

A multivariate spatial skew-t process for joint modeling of extreme precipitation indexes

To study trends in extreme precipitation across US over the years 1951-2017, we consider 10 climate indexes that represent extreme precipitation, such as annual maximum of daily precipitation, annual maximum of consecutive 5-day average precipitation, which exhibit spatial correlation as well as mutual dependence. We consider the gridded data, produced by the CLIMDEX project (http://www.climdex.org/gewocs.html), constructed using daily precipitation data. In this paper, we propose a multivariate spatial skew-t process for joint modeling of extreme precipitation indexes and discuss its theoretical properties. The model framework allows Bayesian inference while maintaining a computational time that is competitive with common multivariate geostatistical approaches. In a numerical study, we find that the proposed model outperforms multivariate spatial Gaussian processes, multivariate spatial t-processes including their univariate alternatives in terms of various model selection criteria. We apply the proposed model to estimate the average decadal change in the extreme precipitation indexes throughout the United States and find several significant local changes.

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arXiv2017

Analysis of Annual Cyclone Frequencies over Bay of Bengal: Effect of 2004 Indian Ocean Tsunami

This paper discusses the time series trend and variability of the cyclone frequencies over Bay of Bengal, particularly in order to conclude if there is any significant difference in the pattern visible before and after the disastrous 2004 Indian ocean tsunami based on the observed annual cyclone frequency data obtained by India Meteorological Department over the years 1891-2015. Three different categories of cyclones- depression (<34 knots), cyclonic storm (34-47 knots) and severe cyclonic storm (>47 knots) have been analyzed separately using a non-homogeneous Poisson process approach. The estimated intensity functions of the Poisson processes along with their first two derivatives are discussed and all three categories show decreasing trend of the intensity functions after the tsunami. Using an exact change-point analysis, we show that the drops in mean intensity functions are significant for all three categories. As of author's knowledge, no study so far have discussed the relation between cyclones and tsunamis. Bay of Bengal is surrounded by one of the most densely populated areas of the world and any kind of significant change in tropical cyclone pattern has a large impact in various ways, for example, disaster management planning and our study is immensely important from that perspective.

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arXiv2015

A Time-varying Parameter Based Seasonally-adjusted Bayesian State-space Model for Forecasting

In this paper, we develop a time-varying parameter based seasonally-adjusted Bayesian state-space model for non-stationary time series datasets where both the trend and seasonal components are present and it is the general scenario for most of the real datasets in various scientific disciplines. In spite of removing such terms using some do-and-check procedure to make the data stationary, our model directly fits a dataset and forecasts a number of future observations. For a specific prior construction we have considered, every parameter update is one-dimensional so that we don't need to invert any matrix and also we overcome the difficulty of Metropolis-Hastings steps simply by Gibbs sampling which is another advantage of this model. It can handle missing data as well which occurs very often in time series contexts. We implement it on the sufficiently large (24 years of monthly average temperature series, i.e. the number of observations =288) for 57 meteorological stations across India and show that for most of the cases, our method forecasts quite accurately for the months of the 25-th year.

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arXiv2014

A Note on the Misuse of the Variance Test in Meteorological Studies

The erroneous assumption "for all distributions for which the theoretical variance can be computed independently from parameters estimated by any method different from the method of moments" has been used in the case of fitting the gamma distribution to a rainfall data by Mooley (1973) which was followed by several researchers. We show that the asymptotic distribution of the test statistic is generally not even comparable to any central chi-square distribution. We also describe a method for checking the validity of the asymptotic distribution for a class of distributions.

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