46,522 research outputs found
State estimation for temporal point processes
This paper is concerned with combined inference for point processes on the
real line observed in a broken interval. For such processes, the classic
history-based approach cannot be used. Instead, we adapt tools from sequential
spatial point processes. For a range of models, the marginal and conditional
distributions are derived. We discuss likelihood based inference as well as
parameter estimation using the method of moments, conduct a simulation study
for the important special case of renewal processes and analyse a data set
collected by Diggle and Hawtin
Loop-free Markov chains as determinantal point processes
We show that any loop-free Markov chain on a discrete space can be viewed as
a determinantal point process. As an application, we prove central limit
theorems for the number of particles in a window for renewal processes and
Markov renewal processes with Bernoulli noise.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP115 the Annales de
l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques
(http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Constrained exchangeable partitions
For a class of random partitions of an infinite set a de Finetti-type
representation is derived, and in one special case a central limit theorem for
the number of blocks is shown
Zeros of random tropical polynomials, random polytopes and stick-breaking
For , let be independent and identically
distributed random variables with distribution with support .
The number of zeros of the random tropical polynomials is also the number of faces of the lower convex
hull of the random points in . We show that this
number, , satisfies a central limit theorem when has polynomial decay
near . Specifically, if near behaves like a
distribution for some , then has the same asymptotics as the
number of renewals on the interval of a renewal process with
inter-arrival distribution . Our proof draws on connections
between random partitions, renewal theory and random polytopes. In particular,
we obtain generalizations and simple proofs of the central limit theorem for
the number of vertices of the convex hull of uniform random points in a
square. Our work leads to many open problems in stochastic tropical geometry,
the study of functionals and intersections of random tropical varieties.Comment: 22 pages, 5 figure
Processes with Long Memory: Regenerative Construction and Perfect Simulation
We present a perfect simulation algorithm for stationary processes indexed by
Z, with summable memory decay. Depending on the decay, we construct the process
on finite or semi-infinite intervals, explicitly from an i.i.d. uniform
sequence. Even though the process has infinite memory, its value at time 0
depends only on a finite, but random, number of these uniform variables. The
algorithm is based on a recent regenerative construction of these measures by
Ferrari, Maass, Mart{\'\i}nez and Ney. As applications, we discuss the perfect
simulation of binary autoregressions and Markov chains on the unit interval.Comment: 27 pages, one figure. Version accepted by Annals of Applied
Probability. Small changes with respect to version
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