A point process is a set of points randomly located in a space, such as time or abstract
spaces. Point process models have found numerous applications in epidemiology,
ecology, geophysics, social networks and many other areas.
The Poisson process is the most widely known point process. Poisson intensity
estimation is a vital task in various applications including medical imaging,
astrophysics and network traffic analysis. A Bayesian Additive Regression Trees
(BART) scheme for estimating the intensity of inhomogeneous Poisson processes
is introduced. The new approach enables full posterior inference of the intensity
in a non-parametric regression setting. The performance of the novel scheme is
demonstrated through simulation studies on synthetic and real datasets up to five
dimensions, and the new scheme is compared with alternative approaches. A drawback
of the proposed algorithm is its axis-alignment nature. We discuss this problem
and suggest alternative approaches to remedy the drawback.
The novel coronavirus disease (COVID-19) has been declared a Global Health
Emergency of International Concern with over 557 million cases and 6.36 million
deaths as of 3 August 2022 according to the World Health Organization. Understanding
the spread of COVID-19 has been the subject of numerous studies, highlighting
the significance of reliable epidemic models. We introduce a novel epidemic
model using a latent Hawkes process with temporal covariates for modelling the infections.
Unlike other Hawkes models, we model the reported cases via a probability
distribution driven by the underlying Hawkes process. Modelling the infections via
a Hawkes process allows us to estimate by whom an infected individual was infected.
We propose a Kernel Density Particle Filter (KDPF) for inference of both latent
cases and reproduction number and for predicting new cases in the near future. The
computational effort is proportional to the number of infections making it possible
to use particle filter-type algorithms, such as the KDPF. We demonstrate the performance
of the proposed algorithm on synthetic data sets and COVID-19 reported
cases in various local authorities in the UK, and benchmark our model to alternative
approaches.
We extend the unstructured homogeneously mixing epidemic model considering
a finite population stratified by age bands. We model the actual unobserved infections
using a latent marked Hawkes process and the reported aggregated infections
as random quantities driven by the underlying Hawkes process. We apply a Kernel
Density Particle Filter (KDPF) to infer the marked counting process, the instantaneous
reproduction number for each age group and forecast the epidemic’s future
trajectory in the near future. We demonstrate the performance of the proposed
inference algorithm on synthetic data sets and COVID-19 reported cases in various
local authorities in the UK. Taking into account the individual heterogeneity in age
provides a real-time measurement of interventions and behavioural changes.Open Acces
