298,334 research outputs found
Group invariant inferred distributions via noncommutative probability
One may consider three types of statistical inference: Bayesian, frequentist,
and group invariance-based. The focus here is on the last method. We consider
the Poisson and binomial distributions in detail to illustrate a group
invariance method for constructing inferred distributions on parameter spaces
given observed results. These inferred distributions are obtained without using
Bayes' method and in particular without using a joint distribution of random
variable and parameter. In the Poisson and binomial cases, the final formulas
for inferred distributions coincide with the formulas for Bayes posteriors with
uniform priors.Comment: Published at http://dx.doi.org/10.1214/074921706000000563 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Analytical Results For The Steady State Of Traffic Flow Models With Stochastic Delay
Exact mean field equations are derived analytically to give the fundamental
diagrams, i.e., the average speed - car density relations, for the
Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high
speed vehicles with stochastic delay. Starting with the basic
equation describing the time evolution of the number of empty sites in front of
each car, the concepts of inter-car spacings longer and shorter than are
introduced. The probabilities of having long and short spacings on the road are
calculated. For high car densities , it is shown that
inter-car spacings longer than will be shortened as the traffic flow
evolves in time, and any initial configurations approach a steady state in
which all the inter-car spacings are of the short type. Similarly for low car
densities , it can be shown that traffic flow approaches an
asymptotic steady state in which all the inter-car spacings are longer than
. The average traffic speed is then obtained analytically as a function of
car density in the asymptotic steady state. The fundamental diagram so obtained
is in excellent agreement with simulation data.Comment: 12 pages, latex, 2 figure
Closed loop identification based on quantization
This paper proposes a new closed-loop identification scheme for a single-input-single-output control loop. It is based upon a quantizer inserted into the feedback path. The quantizer can be used to generate an equivalent persistently exciting signal with which the well known two-stage and/or two-step method can be used directly. Simulation examples and an experimental demonstration are used to illustrate the proposed scheme
Probability-dependent gain-scheduled filtering for stochastic systems with missing measurements
Copyright @ 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This brief addresses the gain-scheduled filtering problem for a class of discrete-time systems with missing measurements, nonlinear disturbances, and external stochastic noise. The missing-measurement phenomenon is assumed to occur in a random way, and the missing probability is time-varying with securable upper and lower bounds that can be measured in real time. The multiplicative noise is a state-dependent scalar Gaussian white-noise sequence with known variance. The addressed gain-scheduled filtering problem is concerned with the design of a filter such that, for the admissible random missing measurements, nonlinear parameters, and external noise disturbances, the error dynamics is exponentially mean-square stable. The desired filter is equipped with time-varying gains based primarily on the time-varying missing probability and is therefore less conservative than the traditional filter with fixed gains. It is shown that the filter parameters can be derived in terms of the measurable probability via the semidefinite program method.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61074016 and 60974030, the Shanghai Natural
Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany
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