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We introduce a new class of spatial Cox processes driven by a Hilbert--valued random log--intensity. We adopt a parametric framework in the spectral domain, to estimate its spatial functional correlation structure. Specifically, we consider…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…
In this paper, a Bayesian method for piecewise regression is adapted to handle counting processes data distributed as Poisson. A numerical code in Mathematica is developed and tested analyzing simulated data. The resulting method is…
The Cox proportional hazards model (Cox model) is a popular model for survival data analysis. When the sample size is small relative to the dimension of the model, the standard maximum partial likelihood inference is often problematic. In…
Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…
Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates.…
Spatial point pattern data are routinely encountered. A flexible regression model for the underlying intensity is essential to characterizing the spatial point pattern and understanding the impacts of potential risk factors on such pattern.…
Given data from a Poisson point process with intensity $(x,y) \mapsto n \mathbf{1}(f(x)\leq y),$ frequentist properties for the Bayesian reconstruction of the support boundary function $f$ are derived. We mainly study compound Poisson…
In this paper, we use the Hawkes process to model the sequence of failure, i.e., events of compressor station and conduct survival analysis on various failure events of the compressor station. However, until now, nearly all relevant…
Hawkes processes are point process models that have been used to capture self-excitatory behavior in social interactions, neural activity, earthquakes and viral epidemics. They can model the occurrence of the times and locations of events.…
Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The…
We propose a novel Bayesian nonparametric method for hierarchical modelling on a set of related density functions, where grouped data in the form of samples from each density function are available. Borrowing strength across the groups is a…
Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through…
In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a…