Modulated Poisson Process Research Articles

Filtering and smoothing formulas of AR(p)-modulated Poisson processes

Recursive formulas are presented to compute smoothed estimates and online filtered estimates for a hidden AR(p) processes, using modulated Poisson observations. We utilize techniques of a transformation of probability, a duality between a forward equation and a backward equation, and develop a new partial fraction decomposition of rational polynomials with several variables. The established polynomial time algorithm computes efficiently closed-form expressions of estimates for the hidden AR(p) process. With a truncating technique, complexity of the algorithm can be reduced further. Finally, we discuss some computational issues related to the proposed algorithm and compare it with other numerical methods.

A Stochastic Model for Highway Accident Predictions with Winter Data

In this paper, we consider the problem of modeling and predicting highway accidents in the presence of randomly changing winter driving conditions. Unlike most accident prediction models in the literature, which are typically formulated in a static (e.g. regression models) or discrete time (e.g. time-series models) setting, we propose a continuous- time stochastic model to describe the relation between highway accidents and winter weather dynamics. We believe this to be a more natural way to describe discrete-event highway accidents that occur in continuous-time. In particular, the accident counting process is viewed as a non-homogeneous Poisson process (NHPP) with an intensity function that depends on a (Markovian) weather process. Such a model is known in the stochastic process literature as a Markov- modulated Poisson process (MMPP) and has been successfully applied to queuing and telecommunications problems. One main advantage of such an approach, is its ability to provide explicit closed-form prediction formulae for both weather and accidents over any future time horizon (i.e. short or long-term predictions). To illustrate the effectiveness of the proposed stochastic model, we study a large winter data set provided by Ministry of Transportation of Ontario (MTO) that includes motor vehicle accidents on Highway 401, the busiest highway in North America.

Fluctuation relations with intermittent non-Gaussian variables

Nonequilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FRs). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a thermodynamiclike change of measure. Taking one of them as a modulated Poisson process, it is demonstrated that intermittence and FRs are compatible properties that may coexist naturally. Strong non-Gaussian features characterize the probability distribution and its generating function. Their associated large deviation functions develop a "kink" at the origin and a plateau regime respectively. Application of this model in different stationary nonequilibrium situations is discussed.

Letter: Cell level modelling of H.261 coded video sequences at different bit rates

AbstractA video source, with a low to medium activity, coded with an H.261 type video codec can be modelled at the frame level as an M state Markov chain. For cell level modelling, the generated cells within the frame are distributed using a modulated Poisson process with interarrivals of Gamma function. Sequences with scene cuts use an. additional state in the Markov chain to represent the scene cut bit rate. The multiplexed model of N homogeneous sources is represented by a linear Markov model of N × M states. The transition probabilities in the multiplexed model are approximated by a truncated discrete normal distribution bounded within ±N states. The proposed single and multiplexed models exhibit similar cell loss performance with the real coded data at both cell and burst scale levels. The multiplexed model is then generalised to represent the aggregate traffic of several homogeneous sources at different bit rates.

Burst-firing sharpens frequency-tuning in primary auditory cortex.

Frequency-tuning in 46 high-firing single units from primary auditory cortex of ketamine-anaesthetized cats was studied separately for isolated-spike firing and burst spike firing. The tuning curve for burst firing was significantly narrower than for the overall firing rate condition and, consequently, much narrower than for the isolated spikes. The burst firing was found in excess of that predicted from a modulated Poisson process, so the results cannot be explained on basis of a change in firing rate criterion. We propose that burst firing in auditory cortex may selectively enhance frequency tuning dynamically controlled by the behavioural state of the animal as well as its stimulus history. Thus burst firing may have functional implications for cortical processing.