Related papers: Statistical inference for max-stable processes in …
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The…
The max-stable process is an asymptotically justified model for spatial extremes. In particular, we focus on the hierarchical extreme-value process (HEVP), which is a particular max-stable process that is conducive to Bayesian computing.…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…
The extremogram, proposed by Davis and Mikosch (2008), is a useful tool for measuring extremal dependence and checking model adequacy in a time series. We define the extremogram in the spatial domain when the data is observed on a lattice…
With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already…
The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope…
Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial…
Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
Gaussian process regression underpins countless academic and industrial applications of machine learning and statistics, with maximum likelihood estimation routinely used to select appropriate parameters for the covariance kernel. However,…
In this paper, we propose a doubly stochastic spatial point process model with both aggregation and repulsion. This model combines the ideas behind Strauss processes and log Gaussian Cox processes. The likelihood for this model is not…
Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically…
Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…