Related papers: Estimating Inhomogeneous Spatio-Temporal Backgroun…
We develop nonparametric Bayesian modelling approaches for Poisson processes, using weighted combinations of structured beta densities to represent the point process intensity function. For a regular spatial domain, such as the unit square,…
Non-homogeneous Poisson processes are used in a wide range of scientific disciplines, ranging from the environmental sciences to the health sciences. Often, the central object of interest in a point process is the underlying intensity…
Seasonal point processes refer to stochastic models for random events which are only observed in a given season. We develop nonparametric Bayesian methodology to study the dynamic evolution of a seasonal marked point process intensity. We…
The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point-processes continue to provide an important tool for…
Intensity estimation is a common problem in statistical analysis of spatial point pattern data. This paper proposes a nonparametric Bayesian method for estimating the spatial point process intensity based on mixture of finite mixture (MFM)…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…
Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…
Estimates of seismic wave speeds in the Earth (seismic velocity models) are key input parameters to earthquake simulations for ground motion prediction. Owing to the non-uniqueness of the seismic inverse problem, typically many velocity…
Seismic processing transforms raw data into subsurface images essential for geophysical applications. Traditional methods face challenges, such as noisy data, and manual parameter tuning, among others. Recently deep learning approaches have…
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…
Recent years have seen an increased interest in the application of methods and techniques commonly associated with machine learning and artificial intelligence to spatial statistics. Here, in a celebration of the ten-year anniversary of the…
Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains…
We propose a general modeling framework for marked Poisson processes observed over time or space. The modeling approach exploits the connection of the nonhomogeneous Poisson process intensity with a density function. Nonparametric Dirichlet…
Induced seismicity has emerged as a source of a significant earthquake hazard associated with recent development of unconventional energy resources. Therefore, it is imperative to develop stochastic models that can accurately describe the…
We study online change point detection for multivariate inhomogeneous Poisson point process time series. This setting arises commonly in applications such as earthquake seismology, climate monitoring, and epidemic surveillance, yet remains…
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.…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…
Intensity estimation for Poisson processes is a classical problem and has been extensively studied over the past few decades. Practical observations, however, often contain compositional noise, i.e. a nonlinear shift along the time axis,…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The…
Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets…