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Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to…

The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…

Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance…

The availability of large spatial data geocoded at accurate locations has fueled a growing interest in spatial modeling and analysis of point processes. The proposed research is motivated by the intensity estimation problem for large…

Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…

In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…

Variable selection for Gaussian process models is often done using automatic relevance determination, which uses the inverse length-scale parameter of each input variable as a proxy for variable relevance. This implicitly determined…

The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…

The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…

In this paper, a modification of the conventional approximations to the quasi-maximum likelihood method is introduced for the parameter estimation of diffusion processes from discrete observations. This is based on a convergent…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

This paper presents a parametric estimation method for ill-observed linear stationary Hawkes processes. When the exact locations of points are not observed, but only counts over time intervals of fixed size, methods based on the likelihood…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

In this paper, we harness a result in point process theory, specifically the expectation of the weighted $K$-function, where the weighting is done by the true first-order intensity function. This theoretical result can be employed as an…

Computer experiments are becoming increasingly important in scientific investigations. In the presence of uncertainty, analysts employ probabilistic sensitivity methods to identify the key-drivers of change in the quantities of interest.…

Covariance tapering is a popular approach for reducing the computational cost of spatial prediction and parameter estimation for Gaussian process models. However, tapering can have poor performance when the process is sampled at spatially…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

Estimation of the four generalized lambda distribution parameters is not straightforward, and available estimators that perform best have large computation times. In this paper, we introduce a simple two-step estimator of the parameters…

An algorithm for non-stationary spatial modelling using multiple secondary variables is developed. It combines Geostatistics with Quantile Random Forests to give a new interpolation and stochastic simulation algorithm. This paper introduces…