scholarly journals Score-matching estimators for continuous-time point-process regression models

2016 ◽  
Author(s):  
Maneesh Sahani ◽  
Gergo Bohner ◽  
Arne Meyer
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Regression Models ◽  
Matching Estimators ◽  
Time Point

Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (3) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

Continuous-time point-queue models in dynamic network loading

2012 ◽  
Vol 46 (3) ◽  
pp. 360-380 ◽  
Author(s):  
Xuegang (Jeff) Ban ◽  
Jong-Shi Pang ◽  
Henry X. Liu ◽  
Rui Ma
Keyword(s):  
Continuous Time ◽  
Dynamic Network ◽  
Dynamic Network Loading ◽  
Network Loading ◽  
Time Point

Proportional intensities and strong ergodicity for Markov processes

1983 ◽  
Vol 20 (01) ◽  
pp. 185-190 ◽  
Author(s):  
Mark Scott ◽  
Dean L. Isaacson
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Homogeneous Markov Process ◽  
Strong Ergodicity ◽  
Transition Functions ◽  
The Matrix ◽  
Intensity Functions ◽  
Time Point

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

MMAE-Based Control with Space-Time Point Process Observations

1985 ◽  
Vol AES-21 (3) ◽  
pp. 292-300 ◽  
Author(s):  
Peter Maybeck ◽  
William Zicker
Keyword(s):  
Point Process ◽  
Space Time ◽  
Time Point

scholarly journals Likelihood Methods for Point Processes with Refractoriness

2014 ◽  
Vol 26 (2) ◽  
pp. 237-263 ◽  
Author(s):  
Luca Citi ◽  
Demba Ba ◽  
Emery N. Brown ◽  
Riccardo Barbieri
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Process Model ◽  
Point Processes ◽  
Linear Models ◽  
Continuous Time Model ◽  
Time Model ◽  
Fitting Procedures ◽  
Continuous Time Process ◽  
Conditional Intensity Function

Likelihood-based encoding models founded on point processes have received significant attention in the literature because of their ability to reveal the information encoded by spiking neural populations. We propose an approximation to the likelihood of a point-process model of neurons that holds under assumptions about the continuous time process that are physiologically reasonable for neural spike trains: the presence of a refractory period, the predictability of the conditional intensity function, and its integrability. These are properties that apply to a large class of point processes arising in applications other than neuroscience. The proposed approach has several advantages over conventional ones. In particular, one can use standard fitting procedures for generalized linear models based on iteratively reweighted least squares while improving the accuracy of the approximation to the likelihood and reducing bias in the estimation of the parameters of the underlying continuous-time model. As a result, the proposed approach can use a larger bin size to achieve the same accuracy as conventional approaches would with a smaller bin size. This is particularly important when analyzing neural data with high mean and instantaneous firing rates. We demonstrate these claims on simulated and real neural spiking activity. By allowing a substantive increase in the required bin size, our algorithm has the potential to lower the barrier to the use of point-process methods in an increasing number of applications.

scholarly journals On a Model for the Storage of Files on a Hardware: Statistics at a Fixed Time and Asymptotic Regimes

2009 ◽  
Vol 2009 ◽  
pp. 1-24
Author(s):  
Vincent Bansaye
Keyword(s):  
Point Process ◽  
Real Line ◽  
Continuous Time ◽  
Poisson Point Process ◽  
Fixed Time ◽  
The Real ◽  
Parking Problem ◽  
The Right

We consider a version in continuous time of the parking problem of Knuth. Files arrive following a Poisson point process and are stored on a hardware identified with the real line, in the closest free portions at the right of the arrival location. We specify the distribution of the space of unoccupied locations at a fixed time and give asymptotic regimes when the hardware is becoming full.

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