95,950 research outputs found
Bayesian estimation for the M/G/1 queue using a phase type approximation
This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase type distributions. Given this phase type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions
The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesics
We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime
where the norm closure of the Gibbs family fails due to discontinuities of the
maximum-entropy inference. The current discussion of maximum-entropy inference
and irreducible correlation in the area of quantum phase transitions is a major
motivation for this research. We extend a representation of the irreducible
correlation from finite temperatures to absolute zero.Comment: 8 pages, 3 figures, 34th International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, 21-26 September 2014,
Ch\^ateau du Clos Luc\'e, Amboise, Franc
BAYESIAN ESTIMATION FOR THE M/G/1 QUEUE USING A PHASE TYPE APPROXIMATION
This article deals with Bayesian inference and prediction for M/G/1 queueing systems. The general service time density is approximated with a class of Erlang mixtures which are phase type distributions. Given this phase type approximation, an explicit evaluation of measures such as the stationary queue size, waiting time and busy period distributions can be obtained. Given arrival and service data, a Bayesian procedure based on reversible jump Markov Chain Monte Carlo methods is proposed to estimate system parameters and predictive distributions.
Cooperative Synchronization in Wireless Networks
Synchronization is a key functionality in wireless network, enabling a wide
variety of services. We consider a Bayesian inference framework whereby network
nodes can achieve phase and skew synchronization in a fully distributed way. In
particular, under the assumption of Gaussian measurement noise, we derive two
message passing methods (belief propagation and mean field), analyze their
convergence behavior, and perform a qualitative and quantitative comparison
with a number of competing algorithms. We also show that both methods can be
applied in networks with and without master nodes. Our performance results are
complemented by, and compared with, the relevant Bayesian Cram\'er-Rao bounds
Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise
A new method is introduced for analysis of interactions between
time-dependent coupled oscillators, based on the signals they generate. It
distinguishes unsynchronized dynamics from noise-induced phase slips, and
enables the evolution of the coupling functions and other parameters to be
followed. It is based on phase dynamics, with Bayesian inference of the
time-evolving parameters achieved by shaping the prior densities to incorporate
knowledge of previous samples. The method is tested numerically and applied to
reveal and quantify the time-varying nature of cardiorespiratory interactions.Comment: 5 pages, 3 figures, accepted for Physical Review Letter
A Bayesian method for pulsar template generation
Extracting Times of Arrival from pulsar radio signals depends on the
knowledge of the pulsars pulse profile and how this template is generated. We
examine pulsar template generation with Bayesian methods. We will contrast the
classical generation mechanism of averaging intensity profiles with a new
approach based on Bayesian inference. We introduce the Bayesian measurement
model imposed and derive the algorithm to reconstruct a "statistical template"
out of noisy data. The properties of these "statistical templates" are analysed
with simulated and real measurement data from PSR B1133+16. We explain how to
put this new form of template to use in analysing secondary parameters of
interest and give various examples: We implement a nonlinear filter for
determining ToAs of pulsars. Applying this method to data from PSR J1713+0747
we derive ToAs self consistently, meaning all epochs were timed and we used the
same epochs for template generation. While the average template contains
fluctuations and noise as unavoidable artifacts, we find that the "statistical
template" derived by Bayesian inference quantifies fluctuations and remaining
uncertainty. This is why the algorithm suggested turns out to reconstruct
templates of statistical significance from ten to fifty single pulses. A moving
data window of fifty pulses, taking out one single pulse at the beginning and
adding one at the end of the window unravels the characteristics of the methods
to be compared. It shows that the change induced in the classical
reconstruction is dominated by random fluctuations for the average template,
while statistically significant changes drive the dynamics of the proposed
method's reconstruction. The analysis of phase shifts with simulated data
reveals that the proposed nonlinear algorithm is able to reconstruct correct
phase information along with an acceptable estimation of the remaining
uncertainty.Comment: 21 pages, 16 figures, submitted to MNRA
Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
We show that the phase sensitivity of a Mach-Zehnder
interferometer fed by a coherent state in one input port and squeezed-vacuum in
the other one is i) independent from the true value of the phase shift and ii)
can reach the Heisenberg limit , where is the
average number of particles of the input states. We also show that the
Cramer-Rao lower bound, , can be saturated for arbitrary values of the squeezing parameter
and the amplitude of the coherent mode by a Bayesian phase
inference protocol.Comment: 4 pages, 4 figure
A Tutorial on Time-Evolving Dynamical Bayesian Inference
In view of the current availability and variety of measured data, there is an
increasing demand for powerful signal processing tools that can cope
successfully with the associated problems that often arise when data are being
analysed. In practice many of the data-generating systems are not only
time-variable, but also influenced by neighbouring systems and subject to
random fluctuations (noise) from their environments. To encompass problems of
this kind, we present a tutorial about the dynamical Bayesian inference of
time-evolving coupled systems in the presence of noise. It includes the
necessary theoretical description and the algorithms for its implementation.
For general programming purposes, a pseudocode description is also given.
Examples based on coupled phase and limit-cycle oscillators illustrate the
salient features of phase dynamics inference. State domain inference is
illustrated with an example of coupled chaotic oscillators. The applicability
of the latter example to secure communications based on the modulation of
coupling functions is outlined. MatLab codes for implementation of the method,
as well as for the explicit examples, accompany the tutorial.Comment: Matlab codes can be found on http://py-biomedical.lancaster.ac.uk
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