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Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
We consider the problem of analyzing multivariate time series collected on multiple subjects, with the goal of identifying groups of subjects exhibiting similar trends in their recorded measurements over time as well as time-varying groups…
We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…
State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
Quantitative modeling of post-transcriptional regulation process is a challenging problem in systems biology. A mechanical model of the regulatory process needs to be able to describe the available spatio-temporal protein concentration and…
In this era of big data, all scientific disciplines are evolving fast to cope up with the enormity of the available information. So is statistics, the queen of science. Big data are particularly relevant to spatio-temporal statistics,…
Nonstationary non-Gaussian spatial data are common in many disciplines, including climate science, ecology, epidemiology, and social sciences. Examples include count data on disease incidence and binary satellite data on cloud mask…
I overview recent research advances in Bayesian state-space modeling of multivariate time series. A main focus is on the decouple/recouple concept that enables application of state-space models to increasingly large-scale data, applying to…
We propose a novel Bayesian approach to modelling nonlinear alignments of time series based on latent shared information. We apply the method to the real-world problem of finding common structure in the sensor data of wind turbines…
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…
Building spatial process models that capture nonstationary behavior while delivering computationally efficient inference is challenging. Nonstationary spatially varying kernels (see, e.g., Paciorek, 2003) offer flexibility and richness, but…
We introduce a dynamic spatiotemporal volatility model that extends traditional approaches by incorporating spatial, temporal, and spatiotemporal spillover effects, along with volatility-specific observed and latent factors. The model…
Time-dependent data often exhibit characteristics, such as non-stationarity and heavy-tailed errors, that would be inappropriate to model with the typical assumptions used in popular models. Thus, more flexible approaches are required to be…
We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently…
Data-informed predictive maintenance planning largely relies on stochastic deterioration models. Monitoring information can be utilized to update sequentially the knowledge on time-invariant deterioration model parameters either within an…
Bayesian computation crucially relies on Markov chain Monte Carlo (MCMC) algorithms. In the case of massive data sets, running the Metropolis-Hastings sampler to draw from the posterior distribution becomes prohibitive due to the large…
Gaussian and discrete non-Gaussian spatial datasets are common across fields like public health, ecology, geosciences, and social sciences. Bayesian spatial generalized linear mixed models (SGLMMs) are a flexible class of models for…
Simulation of rainfall over a region for long time-sequences can be very useful for planning and policy-making, especially in India where the economy is heavily reliant on monsoon rainfall. However, such simulations should be able to…