Free Energy Methods for Bayesian Inference: Efficient Exploration of Univariate Gaussian Mixture Posteriors

Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure which originates from computational Statistical Physics. The principle is first to choose a "reaction coordinate", that is, a "direction" in which the target distribution is multimodal. In a second step, the marginal log-density of the reaction coordinate with respect to the posterior distribution is estimated; minus this quantity is called "free energy" in the computational Statistical Physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their targeted invariant distribution on the fly, in order to overcome sampling barriers along the chosen reaction coordinate. Finally, we perform an importance sampling step in order to remove the bias and recover the true posterior. The efficiency factor of the importance sampling step can easily be estimated \emph{a priori} once the bias is known, and appears to be rather large for the test cases we considered. A crucial point is the choice of the reaction coordinate. One standard choice (used for example in the classical Wang-Landau algorithm) is minus the log-posterior density. We discuss other choices. We show in particular that the hyper-parameter that determines the order of magnitude of the variance of each component is both a convenient and an efficient reaction coordinate. We also show how to adapt the method to compute the evidence (marginal likelihood) of a mixture model. We illustrate our approach by analyzing two real data sets

Importance sampling large deviations in nonequilibrium steady states. I

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states, and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult, because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.Comment: Published in JC

Measurement of forward photon production cross-section in proton-proton collisions at s\sqrt{s} = 13 TeV with the LHCf detector

In this paper, we report the production cross-section of forward photons in the pseudorapidity regions of $\eta\,>\,10.94$ and $8.99\,>\,\eta\,>\,8.81$, measured by the LHCf experiment with proton--proton collisions at $\sqrt{s}$ = 13 TeV. The results from the analysis of 0.191 $\mathrm{nb^{-1}}$ of data obtained in June 2015 are compared to the predictions of several hadronic interaction models that are used in air-shower simulations for ultra-high-energy cosmic rays. Although none of the models agree perfectly with the data, EPOS-LHC shows the best agreement with the experimental data among the models.Comment: 21 pages, 4 figure

Wireless magnetic sensor network for road traffic monitoring and vehicle classification

Efficiency of transportation of people and goods is playing a vital role in economic growth. A key component for enabling effective planning of transportation networks is the deployment and operation of autonomous monitoring and traffic analysis tools. For that reason, such systems have been developed to register and classify road traffic usage. In this paper, we propose a novel system for road traffic monitoring and classification based on highly energy efficient wireless magnetic sensor networks. We develop novel algorithms for vehicle speed and length estimation and vehicle classification that use multiple magnetic sensors. We also demonstrate that, using such a low-cost system with simplified installation and maintenance compared to current solutions, it is possible to achieve highly accurate estimation and a high rate of positive vehicle classification

An Off-line Scan of the BATSE Daily Records and a Large Uniform Sample of Gamma-Ray Bursts

During a scan of the archival BATSE daily records covering the entire 9.1 years (TJD 8369-11690) of the BATSE operation, 3906 gamma-ray bursts (GRBs) have been detected. 2068 of these GRBs are previously known BATSE triggers while 1838 of them are new non-triggered bursts. It is important that all events were detected in the same type of data and were processed with the same procedure. Therefore these 3906 GRBs constitute a uniform sample. We have created a publically available electronic data base containing this sample. We describe the procedures of the data reduction, the selection of the GRB candidates, and the statistical tests for possible non-GRB contaminations. We also describe a novel test burst method used to measure the scan efficiency and the information obtained using the test bursts. Our scan decreases the BATSE detection threshold to ~0.1 photons/sec/cm2. As a first result, we show that the differential log N - log P distribution corrected for the detection efficiency extends to low brightnesses without any indication of a turn-over. Any reasonable extrapolation of the new log N - log P to lower brightnesses imply a rate of several thousands of GRBs in the Universe per year.Comment: 14 pages; 23 figures; revised version accepted to ApJ; electronic version of Table 2 is available at ftp://ftp.astro.su.se/pub/head/grb/catalogs/etable2.txt The GRB archive is available at http://www.astro.su.se/groups/head/grb_archive.htm

Time dependence of the e^- flux measured by PAMELA during the July 2006 - December 2009 solar minimum

Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy not accessible from the study of the cosmic-ray nuclear components due to their differing diffusion and energy-loss processes. However, when measured near Earth, the effects of propagation and modulation of galactic cosmic rays in the heliosphere, particularly significant for energies up to at least 30 GeV, must be properly taken into account. In this paper the electron (e^-) spectra measured by PAMELA down to 70 MeV from July 2006 to December 2009 over six-months time intervals are presented. Fluxes are compared with a state-of-the-art three-dimensional model of solar modulation that reproduces the observations remarkably well.Comment: 40 pages, 18 figures, 1 tabl