778 research outputs found
Fully Adaptive Gaussian Mixture Metropolis-Hastings Algorithm
Markov Chain Monte Carlo methods are widely used in signal processing and
communications for statistical inference and stochastic optimization. In this
work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw
samples from generic multi-modal and multi-dimensional target distributions.
The proposal density is a mixture of Gaussian densities with all parameters
(weights, mean vectors and covariance matrices) updated using all the
previously generated samples applying simple recursive rules. Numerical results
for the one and two-dimensional cases are provided
Improved Adaptive Rejection Metropolis Sampling Algorithms
Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH)
algorithm, are widely used for Bayesian inference. One of the most important
issues for any MCMC method is the convergence of the Markov chain, which
depends crucially on a suitable choice of the proposal density. Adaptive
Rejection Metropolis Sampling (ARMS) is a well-known MH scheme that generates
samples from one-dimensional target densities making use of adaptive piecewise
proposals constructed using support points taken from rejected samples. In this
work we pinpoint a crucial drawback in the adaptive procedure in ARMS: support
points might never be added inside regions where the proposal is below the
target. When this happens in many regions it leads to a poor performance of
ARMS, with the proposal never converging to the target. In order to overcome
this limitation we propose two improved adaptive schemes for constructing the
proposal. The first one is a direct modification of the ARMS procedure that
incorporates support points inside regions where the proposal is below the
target, while satisfying the diminishing adaptation property, one of the
required conditions to assure the convergence of the Markov chain. The second
one is an adaptive independent MH algorithm with the ability to learn from all
previous samples except for the current state of the chain, thus also
guaranteeing the convergence to the invariant density. These two new schemes
improve the adaptive strategy of ARMS, thus simplifying the complexity in the
construction of the proposals. Numerical results show that the new techniques
provide better performance w.r.t. the standard ARMS.Comment: Matlab code provided in http://a2rms.sourceforge.net
Heat asymmetries in nanoscale conductors: The role of decoherence and inelasticity
We investigate the heat flow between different terminals in an interacting
coherent conductor when inelastic scattering is present. We illustrate our
theory with a two-terminal quantum dot setup. Two types of heat asymmetries are
investigated: electric asymmetry , which describes deviations of the
heat current in a given contact when voltages are exchanged, and contact
asymmetry , which quantifies the difference between the power
measured in two distinct electrodes. In the linear regime, both asymmetries
agree and are proportional to the Seebeck coefficient, the latter following at
low temperature a Mott-type formula with a dot transmission renormalized by
inelasticity. Interestingly, in the nonlinear regime of transport we find
and this asymmetry departure depends on the applied bias
configuration. Our results may be important for the recent experiments by Lee
et al. [Nature (London) 498, 209 (2013)], where these asymmetries were
measured.Comment: 9 pages, 5 figures. Minor changes; published versio
Latent variable analysis of causal interactions in atrial fibrillation electrograms
Multi-channel intracardiac electrocardiograms of atrial fibrillation (AF) patients are acquired at the electrophysiology laboratory in order to guide radiofrequency (RF) ablation surgery. Unfortunately, the success rate of RF ablation is still moderate, since the mechanisms underlying AF initiation and maintenance are still not precisely known. In this paper, we use an advanced machine learning model, the Gaussian process latent force model (GP-LFM), to infer the relationship between the observed signals and the unknown (latent or exogenous) sources causing them. The resulting GP-LFM provides valuable information about signal generation and propagation inside the heart, and can then be used to perform causal analysis. Results on realistic synthetic signals, generated using the FitzHugh-Nagumo model, are used to showcase the potential of the proposed approach
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