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Irreversible and rejection-free Monte Carlo methods, recently developed in Physics under the name Event-Chain and known in Statistics as Piecewise Deterministic Monte Carlo (PDMC), have proven to produce clear acceleration over standard Monte Carlo methods, thanks to the reduction of their random-walk behavior. However, while applying such schemes to standard statistical models, one generally needs to introduce an additional randomization for sake of correctness. We propose here a new class of Event-Chain Monte Carlo methods that reduces this extra-randomization to a bare minimum. We compare the efficiency of this new methodology to standard PDMC and Monte Carlo methods. Accelerations up to several magnitudes and reduced dimensional scalings are exhibited.The Hamiltonian dynamics used in Hybrid/Hamiltonian Monte Carlo algorithms [14,27] provides an example of such alternative frameworks [18,34,21]. These methods require however a fine tuning of several parameters, alleviated recently by the development of the statistical software Stan [9]. Also, while aiming at introducing persistency in the successive steps of the Markov chain, these methods still rely on reversible chains with an acceptance-reject scheme.In Physics, recent advances were made in the field of irreversible and rejection-free MCMC simulation methods. These new schemes, referred to as Event-Chain Monte Carlo [2,25], generalize the concept of lifting developed by [12], while drawing on the lines of the recent rejection-free Monte Carlo scheme of [30]. The lifting concept is indeed based upon the transformation of rejections into direction changes. Their successes in different applications [1,22] have motivated the research community to pursue a general framework for implementing irreversible MCMC algorithms beyond Physics. In the statistical community, these methods have been cast into the framework of Piecewise Deterministic Markov Processes (PDMP), see [8,5,4]. In particular, the Bouncy Particle Sampler (BPS) have shown a promising acceleration in comparison to the Hamiltonian MC, as reported in [8]. However, when considering common target distributions encountered in statistics, the PDMC methods can still suffer from some random-walk behavior, partly because they still rely on an additional randomization step to ensure ergodicity.In this paper, we introduce a generalized PDMC framework, the Forward Event-Chain Monte Carlo. This method allows for a fast and global exploration of the sampling space, thanks to a new lifting implementation which leads to a minimal randomization. In this framework, the successive directions are picked according to a full probability distribution conditional on the local potential gradient, contrary to previous PDMC schemes. In addition of being rejection-free, the Forward Event-Chain Monte Carlo algorithm does not require any critical parameter tuning. This paper is organized as follows. Section 2 first recalls and describes the standard MCMC sampling methodologies, as well as classical PDMC sampling schemes. Then, it ...

We propose a new network model framework, denoted heterogeneous fluid model network, which allows to derive closed formula for the Signal to Interference plus Noise Ratio (SINR) received by a mobile in heterogeneous cellular networks, composed of macro cells and femto cells. Quality of service (QoS) and performance of wireless networks can therefore be analyzed in a simple way. We apply our model to Long Term Evolution (LTE) and indoor/outdoor environment. This model allows to analyze the deployment of a femto cells network when the femto base stations share the same bandwidth as deployed macro cells. We propose an analysis of the impact of transmitting power femto base stations on the performance in terms of coverage, throughput and QoS.