1,024 research outputs found
Characterisation of exchangeable sequences through empirical distributions
The fact that the empirical distributions of an exchangeable sequence form a
reverse-martingale is a well-know result. The converse statement is proved,
under the additional assumption of stationarity. A similar reverse-martingale
for separately exchangeable matrices is found and marginal characterisations
are considered.Comment: 7 pages, 0 figure
Simulation of multivariate diffusion bridge
We propose simple methods for multivariate diffusion bridge simulation, which
plays a fundamental role in simulation-based likelihood and Bayesian inference
for stochastic differential equations. By a novel application of classical
coupling methods, the new approach generalizes a previously proposed simulation
method for one-dimensional bridges to the multi-variate setting. First a method
of simulating approximate, but often very accurate, diffusion bridges is
proposed. These approximate bridges are used as proposal for easily
implementable MCMC algorithms that produce exact diffusion bridges. The new
method is much more generally applicable than previous methods. Another
advantage is that the new method works well for diffusion bridges in long
intervals because the computational complexity of the method is linear in the
length of the interval. In a simulation study the new method performs well, and
its usefulness is illustrated by an application to Bayesian estimation for the
multivariate hyperbolic diffusion model.Comment: arXiv admin note: text overlap with arXiv:1403.176
Mortality modeling and regression with matrix distributions
In this paper we investigate the flexibility of matrix distributions for the
modeling of mortality. Starting from a simple Gompertz law, we show how the
introduction of matrix-valued parameters via inhomogeneous phase-type
distributions can lead to reasonably accurate and relatively parsimonious
models for mortality curves across the entire lifespan. A particular feature of
the proposed model framework is that it allows for a more direct interpretation
of the implied underlying aging process than some previous approaches.
Subsequently, towards applications of the approach for multi-population
mortality modeling, we introduce regression via the concept of proportional
intensities, which are more flexible than proportional hazard models, and we
show that the two classes are asymptotically equivalent. We illustrate how the
model parameters can be estimated from data by providing an adapted EM
algorithm for which the likelihood increases at each iteration. The practical
feasibility and competitiveness of the proposed approach are illustrated for
several sets of mortality data
Expert Kaplan--Meier estimation
The setting of a right-censored random sample subject to contamination is
considered. In various fields, expert information is often available and used
to overcome the contamination. This paper integrates expert knowledge into the
product-limit estimator in two different ways with distinct interpretations.
Strong uniform consistency is proved for both cases under certain assumptions
on the kind of contamination and the quality of expert information, which sheds
light on the techniques and decisions that practitioners may take. The nuances
of the techniques are discussed -- also with a view towards semi-parametric
estimation -- and they are illustrated using simulated and real-world insurance
data
Multivariate matrix-exponential distributions
We review what is currently known about one-dimensional distributions on
the non-negative reals with rational Laplace transform, also known as
matrix-exponential distributions. In particular we discuss a flow
interpreation which enables one to mimic certain probabilisticly
inspired arguments which are known from the theory of phase-type distributions.
We then move on to present ongoing research for higher dimensions.
We discuss a characterization result, some closure properties, and
a number of examples. Finally we present open problems and future
perspectives
A vision of leadership : a reflective essay
My interest in the field of education was sparked before I entered kindergarten. My mom was a teacher and I had two high school-aged siblings planning to enter the educational field. These three individuals greatly influenced my desire to enter the educational profession. By the age of eight, I had decided that I was going to make a difference in the lives of children and to right all of the wrongs that I had heard about from various family conversations. My maturity and experiences have allowed me to reflect upon the roles of leadership
Point processes with finite-dimensional conditional probabilities
AbstractWe study the structure of point processes N with the property that the P(θtN∈·|Ft) vary in a finite-dimensional space where θt is the shift and Ft the σ-field generated by the counting process up to time t. This class of point processes is strictly larger than Neuts’ class of Markovian arrival processes. On the one hand, it allows for more general features like interarrival distributions which are matrix-exponential rather than phase type, on the other the probabilistic interpretation is a priori less clear. Nevertheless, the properties are very similar. In particular, finite-dimensional distributions of interarrival times, moments, Laplace transforms, Palm distributions, etc., are shown to be given by two fundamental matrices C,D just as for the Markovian arrival process. We also give a probabilistic interpretation in terms of a piecewise deterministic Markov process on a compact convex subset of Rp, whose jump times are identical to the epochs of N
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