arXiv
(422,153 recursos)
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Mostrando recursos 101 - 110 de 110
101.
Long Memory in Nonlinear Processes - Deo, Rohit; Hsieh, Meng-Chen; Hurvich, Clifford M.; Soulier, Philippe
It is generally accepted that many time series of practical interest exhibit
strong dependence, i.e., long memory. For such series, the sample
autocorrelations decay slowly and log-log periodogram plots indicate a
straight-line relationship. This necessitates a class of models for describing
such behavior. A popular class of such models is the autoregressive
fractionally integrated moving average (ARFIMA) which is a linear process.
However, there is also a need for nonlinear long memory models. For example,
series of returns on financial assets typically tend to show zero correlation,
whereas their squares or absolute values exhibit long memory. Furthermore, the
search for a realistic mechanism for generating long memory has led...
102.
Subgeometric ergodicity of Markov chains - Douc, Randal; Moulines, Eric; Soulier, Philippe
The goal of this paper is to give a short and self contained proof of general
bounds for subgeometric rates of convergence, under practical conditions. The
main result whose proof, based on coupling, provides an intuitive understanding
of the results of Nummelin and Tuominen (1983) and Tuominen and Tweedie (1994).
To obtain practical rates, a very general drift condition, recently introduced
in Douc et al (2004) is used.
103.
Probabilistic graphical models in computational biology - Airoldi, Edoardo M
Probabilistic graphical models (PGMs) have become a popular tool for
computational analysis of biological data in a variety of domains. But, what
exactly are they and how do they work? How can we use PGMs to discover patterns
that are biologically relevant? And to what extent can PGMs help us formulate
new hypotheses that are testable at the bench? This note sketches out some
answers and illustrates the main ideas behind this probabilistic approach to
biological pattern discovery.
104.
Extreme values for Benedicks-Carleson quadratic maps - Freitas, Ana Cristina Moreira; Freitas, Jorge Milhazes
We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with
$x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these
chaotic dynamical systems we study the extreme value distribution of the
stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for
every integer $n\geq0$, where each random variable $X_n$ is distributed
according to the unique absolutely continuous, invariant probability of $f_a$.
Using techniques developed by Benedicks and Carleson, we show that the limiting
distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that which would
apply if the sequence $X_0,X_1,...$ was independent and identically
distributed. This result allows us to conclude that the asymptotic distribution
of $M_n$ is of Type...
105.
Inferring dynamic genetic networks with low order independencies - Lèbre, Sophie
In this paper, we propose a novel inference method for dynamic genetic
networks which makes it possible to face with a number of time measurements n
much smaller than the number of genes p. The approach is based on the concept
of low order conditional dependence graph that we extend here to Dynamic
Bayesian Networks. Most of our results are based on the theory of graphical
models associated with the Directed Acyclic Graphs (DAGs). In this way, we
define a minimal DAG G which describes exactly the full order conditional
dependencies given the past of the process. Then, to face with the large p and
small n estimation...
106.
Morphing Ensemble Kalman Filters - Beezley, Jonathan D.; Mandel, Jan
A new type of ensemble filter is proposed, which combines an ensemble Kalman
filter (EnKF) with the ideas of morphing and registration from image
processing. This results in filters suitable for nonlinear problems whose
solutions exhibit moving coherent features, such as thin interfaces in wildfire
modeling. The ensemble members are represented as the composition of one common
state with a spatial transformation, called registration mapping, plus a
residual. A fully automatic registration method is used that requires only
gridded data, so the features in the model state do not need to be identified
by the user. The morphing EnKF operates on a transformed state consisting of
the registration mapping...
107.
A volume inequality for quantum Fisher information and the uncertainty
principle - Gibilisco, P.; Imparato, D.; Isola, T.
Let $A_1,...,A_N$ be complex self-adjoint matrices and let $\rho$ be a
density matrix. The Robertson uncertainty principle $$ det(Cov_\rho(A_h,A_j))
\geq det(- \frac{i}{2} Tr(\rho [A_h,A_j])) $$ gives a bound for the quantum
generalized covariance in terms of the commutators $[A_h,A_j]$. The right side
matrix is antisymmetric and therefore the bound is trivial (equal to zero) in
the odd case $N=2m+1$.
Let $f$ be an arbitrary normalized symmetric operator monotone function and
let $<\cdot, \cdot >_{\rho,f}$ be the associated quantum Fisher information. In
this paper we conjecture the inequality $$ det (Cov_\rho(A_h,A_j)) \geq det
(\frac{f(0)}{2} < i[\rho, A_h],i[\rho,A_j] >_{\rho,f}) $$ that gives a
non-trivial bound for any natural number $N$ using...
108.
Power-law distributions in empirical data - Clauset, Aaron; Shalizi, Cosma Rohilla; Newman, M. E. J.
Power-law distributions occur in many situations of scientific interest and
have significant consequences for our understanding of natural and man-made
phenomena. Unfortunately, the empirical detection and characterization of power
laws is made difficult by the large fluctuations that occur in the tail of the
distribution. In particular, standard methods such as least-squares fitting are
known to produce systematically biased estimates of parameters for power-law
distributions and should not be used in most circumstances. Here we describe
statistical techniques for making accurate parameter estimates for power-law
data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic.
We also show how to tell whether the data follow a power-law distribution at
all,...
109.
Consistent reasoning about a continuum of hypotheses on the basis of
finite evidence - Rau, Jochen
In the modern Bayesian view classical probability theory is simply an
extension of conventional logic, i.e., a quantitative tool that allows for
consistent reasoning in the presence of uncertainty. Classical theory
presupposes, however, that--at least in principle--the amount of evidence that
an experimenter can accumulate always matches the size of the hypothesis space.
I investigate how the framework for consistent reasoning must be modified in
non-classical situations where hypotheses form a continuum, yet the maximum
evidence accessible through experiment is not allowed to exceed some finite
upper bound. Invoking basic consistency requirements pertaining to the
preparation and composition of systems, as well as to the continuity of
probabilities, I show...
110.
Practical wavelet design on the sphere - Guilloux, Frédéric; Fay, Gilles; Cardoso, Jean-François
We address the question of designing isotropic analysis functions on the
sphere which are perfectly limited in the spectral domain and optimally
localized in the spatial domain. This work is motivated by the need of
localized analysis tools in domains where the data is lying on the sphere,
e.g.{} the science of the Cosmic Microwave Background. Our construction is
derived from the localized frames introduced by Narcowich, Petrushev, Ward,
2006. The analysis frames are optimized for given applications and compared
numerically using various criteria.
101.
