1,909 research outputs found
New coins from old, smoothly
Given a (known) function , we consider the problem of
simulating a coin with probability of heads by tossing a coin with
unknown heads probability , as well as a fair coin, times each, where
may be random. The work of Keane and O'Brien (1994) implies that such a
simulation scheme with the probability equal to 1 exists iff
is continuous. Nacu and Peres (2005) proved that is real analytic in an
open set iff such a simulation scheme exists with the
probability decaying exponentially in for every . We
prove that for non-integer, is in the space if
and only if a simulation scheme as above exists with , where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}.
The key to the proof is a new result in approximation theory:
Let \B_n be the cone of univariate polynomials with nonnegative Bernstein
coefficients of degree . We show that a function is in
if and only if has a series representation
with F_n \in \B_n and for all and . We also provide a
counterexample to a theorem stated without proof by Lorentz (1963), who claimed
that if some \phi_n \in \B_n satisfy for all and , then .Comment: 29 pages; final version; to appear in Constructive Approximatio
Fast simulation of new coins from old
Let S\subset (0,1). Given a known function f:S\to (0,1), we consider the
problem of using independent tosses of a coin with probability of heads p
(where p\in S is unknown) to simulate a coin with probability of heads f(p). We
prove that if S is a closed interval and f is real analytic on S, then f has a
fast simulation on S (the number of p-coin tosses needed has exponential
tails). Conversely, if a function f has a fast simulation on an open set, then
it is real analytic on that set.Comment: Published at http://dx.doi.org/10.1214/105051604000000549 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
A cyclic time-dependent Markov process to model daily patterns in wind turbine power production
Wind energy is becoming a top contributor to the renewable energy mix, which
raises potential reliability issues for the grid due to the fluctuating nature
of its source. To achieve adequate reserve commitment and to promote market
participation, it is necessary to provide models that can capture daily
patterns in wind power production. This paper presents a cyclic inhomogeneous
Markov process, which is based on a three-dimensional state-space (wind power,
speed and direction). Each time-dependent transition probability is expressed
as a Bernstein polynomial. The model parameters are estimated by solving a
constrained optimization problem: The objective function combines two maximum
likelihood estimators, one to ensure that the Markov process long-term behavior
reproduces the data accurately and another to capture daily fluctuations. A
convex formulation for the overall optimization problem is presented and its
applicability demonstrated through the analysis of a case-study. The proposed
model is capable of reproducing the diurnal patterns of a three-year dataset
collected from a wind turbine located in a mountainous region in Portugal. In
addition, it is shown how to compute persistence statistics directly from the
Markov process transition matrices. Based on the case-study, the power
production persistence through the daily cycle is analysed and discussed
Quantum Branching Programs and Space-Bounded Nonuniform Quantum Complexity
In this paper, the space complexity of nonuniform quantum computations is
investigated. The model chosen for this are quantum branching programs, which
provide a graphic description of sequential quantum algorithms. In the first
part of the paper, simulations between quantum branching programs and
nonuniform quantum Turing machines are presented which allow to transfer lower
and upper bound results between the two models. In the second part of the
paper, different variants of quantum OBDDs are compared with their
deterministic and randomized counterparts. In the third part, quantum branching
programs are considered where the performed unitary operation may depend on the
result of a previous measurement. For this model a simulation of randomized
OBDDs and exponential lower bounds are presented.Comment: 45 pages, 3 Postscript figures. Proofs rearranged, typos correcte
Bayesian multivariate Bernstein polynomial density estimation
This paper introduces a new approach to Bayesian nonparametric inference for densities
on the hypercube, based on the use of a multivariate Bernstein polynomial prior.
Posterior convergence rates under the proposed prior are obtained. Furthermore, a
novel sampling scheme, based on the use of slice sampling techniques, is proposed for
estimation of the posterior predictive density. The approach is illustrated with both
simulated and real data example
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