Sequential Monte Carlo

The sequential Monte Carlo quantum mechanics methodology is used to obtain the solvent effects on the Stokes shift of acetone in water. One of the great advantages of this methodology is that all the important statistical information is known before running into the costly quantum mechanical calculations. This advantage is discussed not only with respect to the statistical correlation between the different structures generated by the simulation but also in the proper identification of hydrogen bonds in liquids. To obtain the solvent effects in the Stokes shift of the n -p p absorption transition of acetone in water, quantum-mechanical calculations are performed in super-molecular structures generated by NVT Monte Carlo simulation. The statistical correlation between configurations is analyzed using the auto-correlation function of the energy. The largest calculations include one acetone and 170 water molecules. One-hundred INDO/CIS super-molecular calculations are performed for each solvation shell to obtain the statistical average value. The calculated solvatochromic shift of the n -p p absorption transition of acetone in water, compared to gas phase, is , 1310 cm 21 in good agreement with the experimental blue shift of 1500^200 cm 21 . For the emission of the relaxed excited state, the calculated shift is , 1850 cm 21 . The total calculated solvent effect on the Stokes shift of acetone in aqueous solution is thus 540 cm 21 . A detailed analysis of the sampling of the configurations obtained in the Monte Carlo simulation is made and it is shown that all results represent statistically converged values. q

Reliability assessment is of primary importance in designing and planning distribution systems that operate in an economical manner with minimal interruption of customer loads. With the advances in renewable energy sources, Distributed Generation (DG), is forecasted to increase in distribution networks. This paper presents a new methodology that can be used to quantitatively analyze the reliability of such distribution systems and can be applied in preliminary planning studies for such systems. The method uses a sequential Monte Carlo simulation of the distribution system's stochastic model to generate the operating behavior. This is combined with a path augmenting Max flow algorithm to evaluate the load status for each state change of operation in the system. Overall system and load point reliability indices such as hourly loss of load, frequency of loss of load and expected energy unserved can be computed using this technique. The reliability indices can be compared for different scenarios and strategies for placement of DG using this methodology.

He is engaged in research and teaching in digital communications and wireless systems, equalization and channel estimation in multicarrier (OFDM) communication systems, and efficient modulation and coding techniques (TCM and turbo coding). He spent two years (1979-

Mon mémoire a pour objectif d’étudier le comportement de l’algorithme du filtrage particulaire pour des espaces d’état de grandes dimension. Cette méthode est utilisée dans de nombreux domaines, et particulièrement dans les statistiques bayésiennes. Elle permet par exemple d’estimer l’état d’un système à partir d’observations bruitées qu’on pourrait en faire. On retrouve ainsi, lorsqu’on augmente la dimension, des effets de bord et des problème de convergence assez rapidement, compte tenu de la croissance exponentielle de l’erreur. Ce mémoire essaye de comprendre les tenants et aboutissants de cette situation.

The problem of dynamically estimating a timevarying set of targets can be cast as a filtering problem using the random finite set (or point process) framework. The probability hypothesis density (PHD) filter is a recursion that propagates the posterior intensity function-a 1st-order moment-of the random set of multiple targets in time. Like the Bayesian single-target filter, the PHD recursion also suffers from the curse of dimensionality.

In this review, we describe applications of the pruned-enriched Rosenbluth method (PERM), a sequential Monte Carlo algorithm with resampling, to various problems in polymer physics. PERM produces samples according to any given prescribed weight distribution, by growing configurations step by step with controlled bias, and correcting "bad" configurations by "population control". The latter is implemented, in contrast to other population based algorithms like e.g. genetic algorithms, by depth-first recursion which avoids storing all members of the population at the same time in computer memory. The problems we discuss all concern single polymers (with one exception), but under various conditions: Homopolymers in good solvents and at the Θ point, semi-stiff polymers, polymers in confining geometries, stretched polymers undergoing a forced globule-linear transition, star polymers, bottle brushes, lattice animals as a model for randomly branched polymers, DNA melting, and finally -as the only system at low temperatures, lattice heteropolymers as simple models for protein folding. PERM is for some of these problems the method of choice, but it can also fail. We discuss how to recognize when a result is reliable, and we discuss also some types of bias that can be crucial in guiding the growth into the right directions.

Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically detailed models are not designed to deal with this. We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo (''particle filtering'') methods, in combination with a detailed biophysical description of a cell, are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a non-parametric manner. Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances, and observation noise) are inferred automatically from noisy data via expectation-maximisation. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.

Historical Linguistics studies language change over time. If a group of languages derives from changes to a common ancestor language (proto-language) then they are said to be related. Whenever there exists a lack of written records for an ancestor language, a relevant question in Historical Linguistics is to determine whether two languages are related.

The gold standard for finding these relationships is the Comparative Method. Despite the success of the Comparative Method in finding language relationships, it suffers from at least two limitations. First, the Comparative Method involves the manual comparison of various features from a group of languages. Second, the Comparative Method doesn't provide a numerical measure of evidence for how much the database under consideration corroborates an hypothesis.

Given the above limitations, the field of Computational Historical Linguistics is presented as a complement to the Comparative Method. This field has experienced a recent expansion with the adaptation of methods from biological phylogenetics. Nevertheless, there is debate whether the evolutionary models used in phylogenetics also incorporate valid linguistical assumptions.

In this thesis, I propose a new (probability) model for the evolution of the phonology of languages. A relevant innovation of this model is that it captures the regularity of sound changes. I also describe the software that I created in order to assist in incorporating into the model a linguist's expert knowledge. I show that the knowledge obtained in this way agrees with qualitative statements known to linguists. Finally, I present a new algorithm used to compute the probability of linguistic hypotheses regarding language relationships and the occurence of regular sound changes. The main problem that this algorithm overcomes is that it efficiently explores
the possible regular sound changes, mutations in languages that simultaneously affect several words. In order to overcome this challange, I present a new variant of Nested Sequential Monte Carlo that is used to explore the large space of language relationships and regular sound changes. To the best of my knowledge, this is the first algorithm that can perform joint inference on regular sound changes and evolutionary trees. I show that this algorithm is a special case of Sequential Importance Resampling.

In reliability assessment of bulk power systems, two methods have been largely studied and used: contingency enumeration and non-sequential Monte Carlo simulation. Both have their wellknown advantages and drawbacks. Contingency enumeration is conceptually simple and usually requires low computational effort. Conversely, Monte Carlo simulation is computationally harder, but much more versatile to model random aspects. This paper depicts some major aspects regarding both methods. It also shows that it is not a matter of choosing the definite and unique technique, but how they can be used in a complementary way. A real power system, based on the Brazilian interconnected electrical system, and the commercial program NH2 are used to illustrate that both methods are feasible to bulk power systems, and can be used in order to achieve complementary results.

In this paper we propose a sequential Monte Carlo algorithm to estimate a stochastic volatility model with leverage eect, non constant conditional mean and jumps. Our idea relies on the auxiliary particle lter algorithm together with the Markov Chain Monte Carlo (MCMC) method- ology. Our method allows to sequentially evaluate the parameters and the latent processes involved in the dynamic of interest. An empirical applica- tion on simulated data and on the Standard & Poor's 500 index is presented to study the performance of the algorithm implemented.

A new spacecraft attitude estimation approach using particle filtering is derived. Based on sequential Monte Carlo simulation, the particle filter approximately represents the probability distribution of the state vector with random samples. The filter formulation is based on the star camera measurements using a gyro-based or attitude dynamics-based model for attitude propagation. Modified Rodrigues parameters are used for attitude parametrization when the sample mean and covariance of the attitude are computed. The ambiguity problem associated with the modified Rodrigues parameters in the mean and covariance computation is addressed as well. By using the uniform attitude probability distribution as the initial attitude distribution and using a gradually decreasing measurement variance in the computation of the importance weights, the particle filter based attitude estimator possesses global convergence properties. Simulation results indicate that the particular particle filter, known as bootstrap filter, with as many as 2000 particles is able to converge from arbitrary initial attitude error and initial gyro bias errors as large as 4500 degrees per hour per axis.

Let P(E) be the space of probability measures on a measurable space (E, E). In this paper we introduce a class of non-linear Markov Chain Monte Carlo (MCMC) methods for simulating from a probability measure π ∈ P(E). Non-linear Markov kernels (e.g. Del ; Del ) K : P(E) × E → P(E) can be constructed to admit π as an invariant distribution and have superior mixing properties to ordinary (linear) MCMC kernels. However, such non-linear kernels cannot be simulated exactly, so, in the spirit of particle approximations of Feynman-Kac formulae (Del Moral 2004), we construct approximations of the non-linear kernels via Self-Interacting Markov Chains (Del Moral & Miclo 2004) (SIMC). We present several non-linear kernels and demonstrate that, under some conditions, the associated self-interacting approximations exhibit a strong law of large numbers; our proof technique is via the Poisson equation and Foster-Lyapunov conditions. We investigate the performance of our approximations with some simulations, combining the methodology with population-based Markov chain Monte Carlo (e.g. Jasra et al. ). We also provide a comparison of our methods with sequential Monte Carlo samplers when applied to a continuous-time stochastic volatility model.

With the advent of Big Data, inference in very large datasets is becoming increasingly common. Furthermore, business models and operational strategies demand ever more often an online, user real-time feedback solution in contrast with standard batch methods. This involves performing inference on streaming data even before it is persisted. A flexible and elegant way of performing this task is by modelling data as a Dynamic Generalised Linear Model (DGLM), fundamentally a State-Space Model (SSM) which combines a linear transition state model with an observational model following a distribution from the exponential family. Here we will explain the basics of a fully Bayesian online and sequential state estimation using sequential Monte Carlo (SMC) methods and how this class of algorithms can be implemented to perform state and parameter estimation simultaneously. The merits and shortcomings of these methods will also be discussed.

We introduce a new class of Sequential Monte Carlo (SMC) methods, which we call free energy SMC. This class is inspired by free energy methods, which originate from Physics, and where one samples from a biased distribution such that a given function ξ(θ) of the state θ is forced to be uniformly distributed over a given interval. From an initial sequence of distributions (πt) of interest, and a particular choice of ξ(θ), a free energy SMC sampler computes sequentially a sequence of biased distributions (πt) with the following properties: (a) the marginal distribution of ξ(θ) with respect toπt is approximatively uniform over a specified interval, and (b)πt and πt have the same conditional distribution with respect to ξ. We apply our methodology to mixture posterior distributions, which are highly multimodal. In the mixture context, forcing certain hyper-parameters to higher values greatly faciliates mode swapping, and makes it possible to recover a symetric output. We illustrate our approach with univariate and bivariate Gaussian mixtures and two real-world datasets.

In this paper we present an online approach for joint detection and tracking for multiple targets using variable rate particle filters (VRPFs). Unlike conventional models and particle filters, the proposed method utilises the applied forces (tangential and radial components) to model target motions and does not assume the hidden state to change at the same rate as the observations. In effect not only does the proposed method enable us to model parsimoniously the manoeuvring behaviours of targets with a single dynamical model but it also provides a more efficient framework for recursive estimation of the targets' positions since much fewer states will be estimated. In addition, a target detection/termination module will be integrated in the proposed method in which a track initiation, termination, or maintenance move is randomly executed using Bayesian Monte Carlo methods. To model a more realistic observation environment Poisson process is chosen for all target originating and spurious measurements. Unlike other observation models, the proposed model does not require extensive computation for data association between active targets and observations, prior to target state estimation, as a result. To improve the quality of the particles we adopt a data-dependent importance sampling strategy in which the latest observations are involved when new particles are updated. This enables the target states to be updated as new observations arrive while keeping the number of states sufficiently low to track the manoeuvres of the targets. Computer simulations demonstrate the potential of the proposed method for detecting and tracking multiple highly manoeuverable targets in a hostile environment with high clutter density and low detection probability.

We apply sequential Monte Carlo (SMC) to the detection of turning points in the business cycle and to the evaluation of useful statistics employed in business cycle analysis. The proposed nonlinear filtering method is very useful for sequentially estimating the latent variables and the parameters of nonlinear and non-Gaussian time-series models, such as the Markov-switching (MS) models studied in this work. We show how to combine SMC with Monte Carlo Markov Chain for estimating time series models with MS latent factors. We illustrate the effectiveness of the methodology and measure, in a full Bayesian and realtime context, the ability of a pool of MS models to identify turning points in the European economic activity. We also compare our results with the business cycle datation existing in the literature and provide a sequential evaluation of the forecast accuracy of the competing MS models.

— Random finite sets are natural representations of multi-target states and observations that allow multi-sensor multi-target filtering to fit in the unifying random set framework for Data Fusion. Although the foundation has been established in the form of Finite Set Statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multi-target filtering is not yet practical due to the inherent computational hurdle. Even the Probability Hypothesis Density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multi-target posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multi-target filter. In addition, a SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving non-linear non-Gaussian dynamics. Convergence results for these filters are also established.

This reprint differs from the original in pagination and typographic detail. 1 2 IONIDES, BHADRA, ATCHADÉ AND KING and Koopman (2001)], dynamic models [West and Harrison (1997)] and hidden Markov models [Cappé, Moulines and Rydén (2005)]. Applications include ecology [Newman et al. (2009)], economics [Fernández-Villaverde and Rubio-Ramírez (2007)], epidemiology [King et al. (2008)], finance [Johannes, Polson and Stroud (2009)], meteorology [Anderson and Collins (2007)], neuroscience [Ergün et al. (2007)] and target tracking [ ]. This article investigates convergence of a Monte Carlo technique for estimating unknown parameters of POMPs, called iterated filtering, which was proposed by Ionides, . Iterated filtering algorithms repeatedly carry out a filtering procedure to explore the likelihood surface at increasingly local scales in search of a maximum of the likelihood function. In several case-studies, iterated filtering algorithms have been shown capable of addressing scientific challenges in the study of infectious disease transmission, by making likelihood-based inference computationally feasible in situations where this was previously not the case [King et al. ; Bretó et al. (2009); He, Ionides and King (2010); Laneri et al. (2010)]. The partially observed nonlinear stochastic systems arising in the study of disease transmission and related ecological systems are a challenging environment to test statistical methodology [Bjørnstad and Grenfell (2001)], and many statistical methodologies have been tested on these systems in the past fifty years [e.g., Cauchemez and Ferguson (2008); Toni et al. (2008); Keeling and Ross (2008); Ferrari et al. (2008); Morton and Finkenstädt (2005); Grenfell, Bjornstad and Finkenstädt (2002); Kendall et al. (1999); Bartlett (1960); Bailey (1955)].

Localization schemes for wireless sensor networks can be classified as range-based or range-free. They differ in the information used for localization. Range-based methods use range measurements, while range-free techniques only use the content of the messages. None of the existing algorithms evaluate both types of information. Most of the localization schemes do not consider mobility. In this paper, a Sequential

This paper presents a new approach for channel tracking and parameter estimation in cooperative wireless relay networks. We consider a system with multiple relay nodes operating under an amplify and forward relay function. We develop a novel algorithm to efficiently solve the challenging problem of joint channel tracking and parameters estimation of the Jakes' system model within a mobile wireless relay network. This is based on a novel particle Markov chain Monte Carlo (PMCMC) method. In particular, it first involves developing a Bayesian state space model, then estimating the associated high dimensional posterior using an adaptive Markov chain Monte Carlo (MCMC) sampler relying on a proposal built using a Rao-Blackwellised Sequential Monte Carlo (SMC) filter.

We apply sequential Monte Carlo (SMC) to the detection of turning points in the business cycle and to the evaluation of useful statistics employed in business cycle analysis. The proposed nonlinear filtering method is very useful for sequentially estimating the latent variables and the parameters of nonlinear and non-Gaussian time-series models, such as the Markov-switching (MS) models studied in this work. We show how to combine SMC with Monte Carlo Markov Chain for estimating time series models with MS latent factors. We illustrate the effectiveness of the methodology and measure, in a full Bayesian and realtime context, the ability of a pool of MS models to identify turning points in the European economic activity. We also compare our results with the business cycle datation existing in the literature and provide a sequential evaluation of the forecast accuracy of the competing MS models.

We present a Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given a data vector Y corresponding to the regression model f (β), find plausible values of β. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of β given Y using MCMC. To reduce computational cost, we limit evaluation of f to a small number of points chosen on a high posterior density region found by optimization. Then, we approximate the logarithm of the posterior density using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC.

An algorithm for reliability simulation of equipment and systems using a parallel computing environment is developed. A sequential Monte Carlo simulation-based method is applied for generating reliability and maintainability history charts for equipment, from which the reliability indices, as well as their probability distributions, are calculated. A parallel methodology is developed to discretize the simulation into periods, and the simulation of individual periods is dispatched to different processors for efficient computing. Case studies utilizing the proposed method for reliability evaluation of equipment and simple systems are presented. Simulation results are compared with the analytical approach results for the same cases. The study provides the basis for using a parallel computing environment in power system reliability and cost evaluations. The environment used in this paper is Rock-131 from the San Diego Supercomputer Center in La Jolla, CA.

In this paper we propose a sequential Monte Carlo algorithm to estimate a stochastic volatility model with leverage effects and non constant conditional mean and jumps. We are interested in estimating the time invariant parameters and the non-observable dynamics involved in the model. Our idea relies on the auxiliary particle filter algorithm mixed together with Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm.

The hydration of the hydroxyl OH radical has been investigated by microsolvation modeling and statistical mechanics Monte Carlo simulations. The microsolvation approach was based on density functional theory (DFT) calculations for OH-(H2O)(1-6) and (H2O)(1-7) clusters. The results from microsolvation indicate that the binding enthalpies of the OH radical and water molecule to small water clusters are similar. Monte Carlo simulations predict that the hydration enthalpy of the OH radical, Delta(hyd)H(OH,g), is -39.1 kJ mol(-1). From this value we have estimated that the band gap of liquid water is 6.88 eV, which is in excellent agreement with the result of Coe [J. Chem. Phys. 107, 6023 (1997)]. We have compared the structure of the hydrated OH solution with the structure of pure liquid water. The structural differences between the two systems reflect the strong role played by the OH radical as a proton donor in water. From sequential Monte Carlo/DFT calculations the dipole moment of the OH radical in liquid water is 2.2+/-0.1 D, which is similar to33% above the experimental gas phase value (1.66 D).

In indoor and urban canyon environments, where the Global Navigation Satellite System (GNSS) line-of-sight signals are very weak, accurate localization using GNSS alone is very challenging. So, it becomes necessary to combine GNSS technology with other wireless systems for proper localization. Recently, various forms of Bayesian filters have been used for combining the sensor information in order to estimate the location of a moving receiver. However the performance of most of these filters relies on the accuracy of the assumed probabilistic model of the system. In this paper, we show how the performance of these filters vary by applying them to various applications with different probabilistic models. We mainly focus on a new type of sequential Monte Carlo (MC) filter, called the cost reference particle filter, and show that this filter is more robust compared to the other filters as it does not make any assumption about the statistical distribution of the noise. Apart from the analysis of results of synthetic experiments, we also present a detailed analysis of the results obtained in a real world application where the trajectory of a robot has been tracked by integrating the measurements obtained using a set of ZigBee and Ultra-Wide Band (UWB) sensors into the filtering algorithms.

Extended objects are characterised with multiple measurements originated from different locations of the object surface. This paper presents a novel Sequential Monte Carlo (SMC) approach for extended object tracking based on border parametrisation. The problem is formulated for general nonlinear problems. The main contribution of this work is in the derivation of the likelihood function for nonlinear measurement functions, with sets of measurements belonging to a bounded region. Simulation results are presented when the object is surrounded by a circular region. Accurate estimation results are presented both for the object kinematic state and object extent.

The time sequential Monte Carlo simulation used in power systems for the estimation of reliability indices is a computationally expensive method. The accuracy of the results depends on the number of samples used in the simulation and the variance of the estimate. Variance reduction techniques can be employed to reduce the sample size needed to achieve a given precision in the estimate values. This paper discusses the Antithetic Variates application to the time sequential Monte Carlo simulation. The study cases are conducted on a small isolated distribution system with dispersed generation (DG).

Quantifying the uncertainty in the location and nature of change points in time series is important in a variety of applications. Many existing methods for estimation of the number and location of change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst others require explicit simulation of large vectors of dependent latent variables. This paper proposes methodology for approximating the full posterior distribution of various change point characteristics in the presence of parameter uncertainty. The methodology combines recent work on evaluation of exact change point distributions conditional on model parameters via Finite Markov Chain Imbedding in a Hidden Markov Model setting, and accounting for parameter uncertainty and estimation via Bayesian modelling and Sequential Monte Carlo. The combination of the two leads to a flexible and computationally efficient procedure, which does not require estimates of the underlying state sequence.

The reliability performance of transmission system substations is critical for overall system reliability. Failure events at main grid substations can lead to multiple outages with possible cascading consequences and widespread loss of customer load. Considerable knowledge on substation reliability analysis has been gained from the application of primarily analytical methods. The complexity, however, of substation switching operations does not lend itself to pure analytical treatment. Simulation methods are more suitable as the mathematical modeling of the relationship between events and outcomes is not always possible. The paper expands the existing methodology and describes a method to perform reliability evaluation of substation switching arrangements based on the sequential Monte Carlo simulation. The method is applied in the reliability analysis and comparison of the most commonly used substation switching configurations. The paper shows how the results of the analysis can be applied to model substations in a composite system reliability evaluation.

An essential step in the reliability evaluation of a power system containing Wind Energy Conversion Systems (WECS) using sequential Monte Carlo analysis is to simulate the hourly wind speed. This paper presents two different time-series models generated using different available wind data. Wind data from Environment Canada and SaskPower are used to illustrate these models. No assumptions or previously estimated factors are included in the models. In order to check the adequacy of the proposed models, the F-criterion and Q-test are used, and the statistical characteristics of the simulated wind speeds are compared with those obtained from the actual wind speeds. The proposed wind models satisfy the basic statistical tests and preserve the high-order auto-correlation, seasonal property and diurnal distributions of the actual wind speed.

The electronic polarization of acetone in liquid water is obtained using an iterative procedure in the sequential Monte Carlo/quantum mechanics methodology. MP2/aug-cc-pVDZ calculations of the dipole moment of acetone in water are performed on statistically uncorrelated structures extracted from isothermic-isobaric MC simulations. After electrostatic equilibrium the calculated dipole moment of acetone is obtained as 4.80 ± 0.03 D, with an increase of 60% compared to the gas phase value. This solute polarization is used to obtain the shift of 1650 ± 42 cm -1 for the n-π ∗ transition of acetone in water, in agreement with the experimental result of 1500-1700 cm -1.

Given the actual context of increased dispersed generation and highly loaded lines, probabilistic methods are more and more required to take into account the stochastic behavior of electrical network components (possible spate of outages by use of the electrical network near its physical limits) in reliability studies. To implement those probabilistic methods, numerical Monte Carlo simulations are typically used and can be divided in two categories: sequential and non-sequential techniques.This paper deals with two wind speed sampling methods adapted for non-sequential Monte Carlo simulations, among which an original approach based on the combination of a mean statistical law (for a large geographical area like a country) and Normal distributions (to characterize smaller wind speed zones inside the country). Both proposed techniques are then applied on a self-developed non-sequential Monte Carlo simulation only taking into account generation units outages and load changes (hierarchical level HL-I). Finally, the collected simulation results allow, not only, to evaluate the impact of sampling methods on the collected reliability indices but also to decide which proposed technique will lead to the most interesting situations (larger wind power fluctuations from one state to the other) for the electrical network operation management. Note that our simulations are applied to the Belgian production park. Copyright © 2008 John Wiley & Sons, Ltd.

This paper shows how one can use Sequential Monte Carlo methods to perform what is typically done using Markov chain Monte Carlo methods. This leads to a general class of principled integration and genetic type optimization methods based on interacting particle systems.