219 research outputs found
Explicit equilibria in a kinetic model of gambling
We introduce and discuss a nonlinear kinetic equation of Boltzmann type which
describes the evolution of wealth in a pure gambling process, where the entire
sum of wealths of two agents is up for gambling, and randomly shared between
the agents. For this equation the analytical form of the steady states is found
for various realizations of the random fraction of the sum which is shared to
the agents. Among others, Gibbs distribution appears as steady state in case of
a uniformly distributed random fraction, while Gamma distribution appears for a
random fraction which is Beta distributed. The case in which the gambling game
is only conservative-in-the-mean is shown to lead to an explicit heavy tailed
distribution
Large Deviations for the solution of a Kac-type kinetic equation
The aim of this paper is to study large deviations for the self-similar
solution of a Kac-type kinetic equation. Under the assumption that the initial
condition belongs to the domain of normal attraction of a stable law of index
and under suitable assumptions on the collisional kernel, precise
asymptotic behavior of the large deviations probability is given
Bayesian Nonparametric Calibration and Combination of Predictive Distributions
We introduce a Bayesian approach to predictive density calibration and
combination that accounts for parameter uncertainty and model set
incompleteness through the use of random calibration functionals and random
combination weights. Building on the work of Ranjan, R. and Gneiting, T. (2010)
and Gneiting, T. and Ranjan, R. (2013), we use infinite beta mixtures for the
calibration. The proposed Bayesian nonparametric approach takes advantage of
the flexibility of Dirichlet process mixtures to achieve any continuous
deformation of linearly combined predictive distributions. The inference
procedure is based on Gibbs sampling and allows accounting for uncertainty in
the number of mixture components, mixture weights, and calibration parameters.
The weak posterior consistency of the Bayesian nonparametric calibration is
provided under suitable conditions for unknown true density. We study the
methodology in simulation examples with fat tails and multimodal densities and
apply it to density forecasts of daily S&P returns and daily maximum wind speed
at the Frankfurt airport.Comment: arXiv admin note: text overlap with arXiv:1305.2026 by other author
Beta-Product Poisson-Dirichlet Processes
Time series data may exhibit clustering over time and, in a multiple time
series context, the clustering behavior may differ across the series. This
paper is motivated by the Bayesian non--parametric modeling of the dependence
between the clustering structures and the distributions of different time
series. We follow a Dirichlet process mixture approach and introduce a new
class of multivariate dependent Dirichlet processes (DDP). The proposed DDP are
represented in terms of vector of stick-breaking processes with dependent
weights. The weights are beta random vectors that determine different and
dependent clustering effects along the dimension of the DDP vector. We discuss
some theoretical properties and provide an efficient Monte Carlo Markov Chain
algorithm for posterior computation. The effectiveness of the method is
illustrated with a simulation study and an application to the United States and
the European Union industrial production indexes
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