On the Sum of Order Statistics and Applications to Wireless Communication Systems Performances

We consider the problem of evaluating the cumulative distribution function (CDF) of the sum of order statistics, which serves to compute outage probability (OP) values at the output of generalized selection combining receivers. Generally, closed-form expressions of the CDF of the sum of order statistics are unavailable for many practical distributions. Moreover, the naive Monte Carlo (MC) method requires a substantial computational effort when the probability of interest is sufficiently small. In the region of small OP values, we propose instead two effective variance reduction techniques that yield a reliable estimate of the CDF with small computing cost. The first estimator, which can be viewed as an importance sampling estimator, has bounded relative error under a certain assumption that is shown to hold for most of the challenging distributions. An improvement of this estimator is then proposed for the Pareto and the Weibull cases. The second is a conditional MC estimator that achieves the bounded relative error property for the Generalized Gamma case and the logarithmic efficiency in the Log-normal case. Finally, the efficiency of these estimators is compared via various numerical experiments

Policy Gradients for CVaR-Constrained MDPs

We study a risk-constrained version of the stochastic shortest path (SSP) problem, where the risk measure considered is Conditional Value-at-Risk (CVaR). We propose two algorithms that obtain a locally risk-optimal policy by employing four tools: stochastic approximation, mini batches, policy gradients and importance sampling. Both the algorithms incorporate a CVaR estimation procedure, along the lines of Bardou et al. [2009], which in turn is based on Rockafellar-Uryasev's representation for CVaR and utilize the likelihood ratio principle for estimating the gradient of the sum of one cost function (objective of the SSP) and the gradient of the CVaR of the sum of another cost function (in the constraint of SSP). The algorithms differ in the manner in which they approximate the CVaR estimates/necessary gradients - the first algorithm uses stochastic approximation, while the second employ mini-batches in the spirit of Monte Carlo methods. We establish asymptotic convergence of both the algorithms. Further, since estimating CVaR is related to rare-event simulation, we incorporate an importance sampling based variance reduction scheme into our proposed algorithms

Hadron energy response of the Iron Calorimeter detector at the India-based Neutrino Observatory

The results of a Monte Carlo simulation study of the hadron energy response for the magnetized Iron CALorimeter detector, ICAL, proposed to be located at the India-based Neutrino Observatory (INO) is presented. Using a GEANT4 modeling of the detector ICAL, interactions of atmospheric neutrinos with target nuclei are simulated. The detector response to hadrons propagating through it is investigated using the hadron hit multiplicity in the active detector elements. The detector response to charged pions of fixed energy is studied first, followed by the average response to the hadrons produced in atmospheric neutrino interactions using events simulated with the NUANCE event generator. The shape of the hit distribution is observed to fit the Vavilov distribution, which reduces to a Gaussian at high energies. In terms of the parameters of this distribution, we present the hadron energy resolution as a function of hadron energy, and the calibration of hadron energy as a function of the hit multiplicity. The energy resolution for hadrons is found to be in the range 85% (for 1GeV) -- 36% (for 15 GeV).Comment: 14 pages, 10 figures (24 eps files

Sequential quasi-Monte Carlo: Introduction for Non-Experts, Dimension Reduction, Application to Partly Observed Diffusion Processes

SMC (Sequential Monte Carlo) is a class of Monte Carlo algorithms for filtering and related sequential problems. Gerber and Chopin (2015) introduced SQMC (Sequential quasi-Monte Carlo), a QMC version of SMC. This paper has two objectives: (a) to introduce Sequential Monte Carlo to the QMC community, whose members are usually less familiar with state-space models and particle filtering; (b) to extend SQMC to the filtering of continuous-time state-space models, where the latent process is a diffusion. A recurring point in the paper will be the notion of dimension reduction, that is how to implement SQMC in such a way that it provides good performance despite the high dimension of the problem.Comment: To be published in the proceedings of MCMQMC 201

Co-existence in the two-dimensional May-Leonard model with random rates

We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state in two-dimensional stochastic May--Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May--Leonard system (for small system sizes): (1) As the mobility rate exceeds a threshold that separates a species coexistence (quasi-)steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ~ e^{cN} / N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.Comment: 9 pages, 4 figures; to appear in Eur. Phys. J. B (2011