An Exact Gibbs Sampler for the Markov-Modulated Poisson Process
SummaryA Markov-modulated Poisson process is a Poisson process whose intensity varies according to a Markov process. We present a novel technique for simulating from the exact distribution of a continuous time Markov chain over an interval given the start and end states and the infinitesimal generator, and we use this to create a Gibbs sampler which ...
Fearnhead, P, Sherlock, C
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Estimating the parameters of a seasonal Markov-modulated Poisson process [PDF]
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Guillou, Armelle +2 more
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A Markov modulated Poisson process model for rainfall increments
The problems encountered when using traditional rectangular pulse hierarchical point process models for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly.
C, Onof +3 more
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Learning to detect events with Markov-modulated poisson processes [PDF]
Time-series of count data occur in many different contexts, including Internet navigation logs, freeway traffic monitoring, and security logs associated with buildings. In this article we describe a framework for detecting anomalous events in such data using an unsupervised learning approach.
Alexander T. Ihler +2 more
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Markov modulated Poisson process models incorporating covariates for rainfall intensity
Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework ...
R, Thayakaran, N I, Ramesh
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Control problem for the Markov-modulated Poisson process in the diffusion schema
This paper addresses the optimal control problem for a stochastic evolution system perturbed by a Markov-modulated Poisson process within a diffusion approximation framework. The considered system captures complex dynamics involving continuous evolution
S. A. Semenyuk +3 more
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Modelling approaches via (batch) Markov modulated poisson processes [PDF]
This dissertation is mainly motivated by the problem of statistical modeling via a specific point process, namely, the (Batch) Markov Modulated Poisson process. Point processes arise in a wide range of situations in physics, biology, engineering, or economics.
Yera Mora, Yoel Gustavo
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Markov-Modulated Poisson Process Modeling for Machine-to-Machine Heterogeneous Traffic
Theoretical mathematics is a key evolution factor of artificial intelligence (AI). Nowadays, representing a smart system as a mathematical model helps to analyze any system under development and supports different case studies found in real life ...
Ahmad Hani El Fawal +2 more
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Renewal characterization of Markov modulated Poisson processes [PDF]
A Markov Modulated Poisson Process (MMPP) M(t) defined on a Markov chain J(t) is a pure jump process where jumps of M(t) occur according to a Poisson process with intensity λi whenever the Markov chain J(t) is in state i. M(t) is called strongly renewal (SR) if M(t) is a renewal process for an arbitrary initial probability vector of J(t) with full ...
Neuts, Marcel F. +2 more
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The random walk Metropolis : linking theory and practice through a case study. [PDF]
The random walk Metropolis (RWM) is one of the most common Markov Chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important ...
Fearnhead, Paul +6 more
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