1,122,813 research outputs found
Nonclassical stochastic flows and continuous products
Contrary to the classical wisdom, processes with independent values (defined
properly) are much more diverse than white noise combined with Poisson point
processes, and product systems are much more diverse than Fock spaces.
This text is a survey of recent progress in constructing and investigating
nonclassical stochastic flows and continuous products of probability spaces and
Hilbert spaces.Comment: A survey, 126 pages. Version 3 (final): former Question 9d4 is
solved; 8a1 reformulated. Ref [41] added. For readability, sections are
reordered (123456..->142536..). Cosmetic changes, mostly in 1b, 2a, 3d, (4a7)
(v3 numbers) and Introductio
Modelling mortality rates using GEE models
Generalised estimating equation (GEE) models are extensions of generalised
linear models by relaxing the assumption of independence. These models are appropriate
to analyze correlated longitudinal responses which follow any distribution that is a member
of the exponential family. This model is used to relate daily mortality rate of Maltese
adults aged 65 years and over with a number of predictors, including apparent temperature,
season and year. To accommodate the right skewed mortality rate distribution a Gamma
distribution is assumed. An identity link function is used for ease of interpretating the
parameter estimates. An autoregressive correlation structure of order 1 is used since
correlations decrease as distance between observations increases. The study shows that
mortality rate and temperature are related by a quadratic function. Moreover, the GEE
model identifies a number of significant main and interaction effects which shed light on
the effect of weather predictors on daily mortality rates.peer-reviewe
Stochastic Control Representations for Penalized Backward Stochastic Differential Equations
This paper shows that penalized backward stochastic differential equation
(BSDE), which is often used to approximate and solve the corresponding
reflected BSDE, admits both optimal stopping representation and optimal control
representation. The new feature of the optimal stopping representation is that
the player is allowed to stop at exogenous Poisson arrival times. The
convergence rate of the penalized BSDE then follows from the optimal stopping
representation. The paper then applies to two classes of equations, namely
multidimensional reflected BSDE and reflected BSDE with a constraint on the
hedging part, and gives stochastic control representations for their
corresponding penalized equations.Comment: 24 pages in SIAM Journal on Control and Optimization, 201
Edge Label Inference in Generalized Stochastic Block Models: from Spectral Theory to Impossibility Results
The classical setting of community detection consists of networks exhibiting
a clustered structure. To more accurately model real systems we consider a
class of networks (i) whose edges may carry labels and (ii) which may lack a
clustered structure. Specifically we assume that nodes possess latent
attributes drawn from a general compact space and edges between two nodes are
randomly generated and labeled according to some unknown distribution as a
function of their latent attributes. Our goal is then to infer the edge label
distributions from a partially observed network. We propose a computationally
efficient spectral algorithm and show it allows for asymptotically correct
inference when the average node degree could be as low as logarithmic in the
total number of nodes. Conversely, if the average node degree is below a
specific constant threshold, we show that no algorithm can achieve better
inference than guessing without using the observations. As a byproduct of our
analysis, we show that our model provides a general procedure to construct
random graph models with a spectrum asymptotic to a pre-specified eigenvalue
distribution such as a power-law distribution.Comment: 17 page
Stochastic Constraint Programming
To model combinatorial decision problems involving uncertainty and
probability, we introduce stochastic constraint programming. Stochastic
constraint programs contain both decision variables (which we can set) and
stochastic variables (which follow a probability distribution). They combine
together the best features of traditional constraint satisfaction, stochastic
integer programming, and stochastic satisfiability. We give a semantics for
stochastic constraint programs, and propose a number of complete algorithms and
approximation procedures. Finally, we discuss a number of extensions of
stochastic constraint programming to relax various assumptions like the
independence between stochastic variables, and compare with other approaches
for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial
Intelligenc
- …