Hierarchical Bayesian modeling of large point-referenced space-time data is increasingly becoming feasible in many environmental applications due to the recent advances in both statistical methodology and computation power. Implementation of these methods using the Markov chain Monte Carlo (MCMC) computational techniques, however, requires development of problem-specific and user-written computer code, possibly in a low-level language. This programming requirement is hindering the widespread use of the Bayesian model-based methods among practitioners and, hence there is an urgent need to develop high-level software that can analyze large data sets rich in both space and time.This paper develops the package spTimer for hierarchical Bayesian modeling of stylized environmental space-time monitoring data as a contributed software package in the R language that is fast becoming a very popular statistical computing platform. The package is able to fit, spatially and temporally predict large amounts of space-time data using three recently developed Bayesian models. The user is given control over many options regarding covariance function selection, distance calculation, prior selection and tuning of the implemented MCMC algorithms, although suitable defaults are provided. The package has many other attractive features such as on the fly transformations and an ability to spatially predict temporally aggregated summaries on the original scale, which saves the problem of storage when using MCMC methods for large datasets. A simulation example, with more than a million observations, and a real life data example are used to validate the underlying code and to illustrate the software capabilities.

Despite a broad pattern of warming in minimum temperatures over the past 50years, regions of southeastern Australia have experienced increases in frost frequency in recent decades, and more broadly across southern Australia, an extension of the frost window due to an earlier onset and later cessation. Consistent across southern Australia is a later cessation of frosts, with some areas of southeastern Australia experiencing the last frost an average 4weeks later than in the 1960s (i.e. mean date of last frost for the period 1960-1970 was 19 September versus 22 October for the period [2000][2001][2002][2003][2004][2005][2006][2007][2008][2009]. We seek to model the spatial changes in frosts for a region exhibiting the strongest individual station trends, i.e. northern Victoria and southern New South Wales. We identify statistically significant trends at low-lying stations for the month of August and construct and validate a Bayesian space-time model of minimum temperatures, using rates of greenhouse gas (GHG) emissions, as well as other well-understood causal factors including solar radiation, the El Niño Southern Oscillation (ENSO 3.4) and times series data relating to the position (STRP) and intensity (STRI) of subtropical highs and blocking high pressure systems. We assess the performance of this modelling approach against observational records as well as against additive and linear regression modelling approaches using root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) as well as false alarm and hit rate metrics. The spatiotemporal modelling approach demonstrated considerably better predictive skill than the others, with enhanced performance across all the metrics analysed. This enhanced performance was consistent across each decade and for temperature extremes below 2°C. Crimp, S., Bakar, K., Kokic, P., Jin, H., Nicholls, N. & Howden, M. (2015) ABSTRACT: Despite a broad pattern of warming in minimum temperatures over the past 50 years, regions of southeastern Australia have experienced increases in frost frequency in recent decades, and more broadly across southern Australia, an extension of the frost window due to an earlier onset and later cessation. Consistent across southern Australia is a later cessation of frosts, with some areas of southeastern Australia experiencing the last frost an average 4 weeks later than in the 1960s (i.e. mean date of last frost for the period 1960-1970 was 19 September versus 22 October for the period [2000][2001][2002][2003][2004][2005][2006][2007][2008][2009]. We seek to model the spatial changes in frosts for a region exhibiting the strongest individual station trends, i.e. northern Victoria and southern New South Wales. We identify statistically significant trends at low-lying stations for the month of August and construct and validate a Bayesian space-time model of minimum temperatures, using rates of greenhouse gas (GHG) emissions, as well as other well-understood causal factors including solar radiation, the El Niño S...

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases temporal data are obtained by registering events, for example telecommunication or web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time auto-regressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method (Banerjee et al. [1]) is extended to include auto-regressive terms of latent space-time processes. Specifically, a spacetime auto-regressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-hour average ground level ozone concentration data from 1997 to 2006 from a large study region in the eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of non-compliance with respect to the standard, are obtained and illustrated.

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Random matrix theory has been widely applied in physics, and even beyond physics. Here, we apply such tools to study catastrophic events, which occur rarely but cause devastating effects. It is important to understand the complexity of the underlying dynamics and signatures of catastrophic events in complex systems, such as the financial market or the environment. We choose the USA S&P-500 and Japanese Nikkei-225 financial markets, as well as the environmental ozone system in the USA. We study the evolution of the cross-correlation matrices and their eigen spectra over different short time-intervals or ‘epochs’. A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues, mainly around zero. The statistical properties of the emerging spectrum are intriguing—the smallest eigenvalues and the shape of the emerging spectrum (characterized by the spectral entropy) capture the system instability or criticality. Importantly, the smallest eigenvalue could also signal a precursor to a market catastrophe as well as a ‘market bubble’. We demonstrate in two paradigms the capacity of the emerging spectrum to understand the nature of instability; this is a new and robust feature that can be broadly applied to other physical or complex systems.