The scientific objectives of ASPI are the design, analysis and implementation of interacting Monte Carlo methods, also known as particle methods, with focus on

statistical inference in hidden Markov models and particle filtering,

risk evaluation and simulation of rare events,

global optimization.

The whole problematic is multidisciplinary, not only because of the many scientific and engineering areas in which particle methods are used, but also because of the diversity of the scientific communities which have already contributed to establish the foundations of the field

target tracking, interacting particle systems, empirical processes, genetic algorithms (GA), hidden Markov models and nonlinear filtering, Bayesian statistics, Markov chain Monte Carlo (MCMC) methods, etc.

Intuitively speaking, interacting Monte Carlo methods are sequential simulation methods, in which particles

*explore* the state space by mimicking the evolution
of an underlying random process,

*learn* their environment by evaluating a fitness function,

and *interact* so that only the most successful particles
(in view of the fitness function) are allowed to survive
and to get offsprings at the next generation.

The effect of this mutation / selection mechanism is to automatically concentrate particles (i.e. the available computing power) in regions of interest of the state space. In the special case of particle filtering, which has numerous applications under the generic heading of positioning, navigation and tracking, in

target tracking, computer vision, mobile robotics, wireless communications, ubiquitous computing and ambient intelligence, sensor networks, etc.,

each particle represents a possible hidden state, and is replicated or terminated at the next generation on the basis of its consistency with the current observation, as quantified by the likelihood function. With these genetic–type algorithms, it becomes easy to efficiently combine a prior model of displacement with or without constraints, sensor–based measurements, and a base of reference measurements, for example in the form of a digital map (digital elevation map, attenuation map, etc.). In the most general case, particle methods provide approximations of Feynman–Kac distributions, a pathwise generalization of Gibbs–Boltzmann distributions, by means of the weighted empirical probability distribution associated with an interacting particle system, with applications that go far beyond filtering, in

simulation of rare events, global optimization, molecular simulation, etc.

The main applications currently considered are geolocalisation and tracking of mobile terminals, terrain–aided navigation, data fusion for indoor localisation, optimization of sensors location and activation, risk assessment in air traffic management, protection of digital documents.

Monte Carlo methods are numerical methods that are widely used
in situations where
(i) a stochastic (usually Markovian) model is given for some underlying
process, and (ii) some quantity of interest should be evaluated, that
can be expressed in terms of the expected value of a functional of the
process trajectory, which includes as an important special case the
probability that a given event has occurred.
Numerous examples can be found, e.g. in financial engineering (pricing of options and derivative
securities) ,
in performance evaluation of communication networks (probability of buffer
overflow), in statistics of hidden Markov models (state estimation,
evaluation of contrast and score functions), etc.
Very often in practice, no analytical expression is available for
the quantity of interest, but it is possible to simulate trajectories
of the underlying process. The idea behind Monte Carlo methods is
to generate independent trajectories of this process
or of an alternate instrumental process,
and to build an approximation (estimator) of the quantity of interest
in terms of the weighted empirical probability distribution
associated with the resulting independent sample.
By the law of large numbers, the above estimator converges
as the size *blindly*,
and only afterwards are the corresponding weights evaluated.
Some of the weights can happen to be negligible, in which case the
corresponding trajectories are not going to contribute to the estimator,
i.e. computing power has been wasted.

A recent and major breakthrough,
has been the introduction of interacting Monte Carlo methods,
also known as sequential Monte Carlo (SMC) methods,
in which a whole (possibly weighted) sample,
called *system of particles*, is propagated in time, where
the particles

*explore* the state space under the effect of
a *mutation* mechanism which mimics the evolution of the
underlying process,

and are *replicated* or *terminated*, under
the effect of a *selection* mechanism which automatically
concentrates the particles, i.e. the available computing power,
into regions of interest of the state space.

In full generality, the underlying process is a discrete–time Markov chain, whose state space can be

finite, continuous, hybrid (continuous / discrete), graphical, constrained, time varying, pathwise, etc.,

the only condition being that it can easily be *simulated*.

In the special case of particle filtering,
originally developed within the tracking community,
the algorithms yield a numerical approximation of the optimal Bayesian
filter, i.e. of the conditional probability distribution
of the hidden state given the past observations, as a (possibly
weighted) empirical probability distribution of the system of particles.
In its simplest version, introduced in several different scientific
communities under the name of
*bootstrap filter* ,
*Monte Carlo filter*
or *condensation* (conditional density propagation)
algorithm ,
and which historically has been the first algorithm to include
a redistribution step,
the selection mechanism is governed by the likelihood function:
at each time step, a particle is more likely to survive
and to replicate at the next generation if it is consistent with
the current observation.
The algorithms also provide as a by–product a numerical approximation
of the likelihood function, and of many other contrast functions for
parameter estimation in hidden Markov models, such as the prediction
error or the conditional least–squares criterion.

Particle methods are currently being used in many scientific and engineering areas

positioning, navigation, and tracking , , visual tracking , mobile robotics , , ubiquitous computing and ambient intelligence, sensor networks, risk evaluation and simulation of rare events , genetics, molecular simulation , etc.

Other examples of the many applications of particle filtering can be
found in the contributed volume and in the special
issue of *IEEE Transactions on Signal Processing* devoted
to *Monte Carlo Methods for Statistical Signal Processing*
in February 2002,
where the tutorial paper can be found,
and in the textbook devoted
to applications in target tracking.
Applications of sequential Monte Carlo methods to other areas,
beyond signal and image processing, e.g. to genetics,
can be found in .
A recent overview can also be found in .

Particle methods are very easy to implement, since it is sufficient in principle to simulate independent trajectories of the underlying process. The whole problematic is multidisciplinary, not only because of the already mentioned diversity of the scientific and engineering areas in which particle methods are used, but also because of the diversity of the scientific communities which have contributed to establish the foundations of the field

target tracking, interacting particle systems, empirical processes, genetic algorithms (GA), hidden Markov models and nonlinear filtering, Bayesian statistics, Markov chain Monte Carlo (MCMC) methods.

These algorithms can be interpreted as numerical approximation schemes
for Feynman–Kac distributions, a pathwise generalization of Gibbs–Boltzmann
distributions,
in terms of the weighted empirical probability distribution
associated with a system of particles.
This abstract point of view , ,
has proved to be extremely fruitful in providing a very general
framework to the design and analysis of numerical approximation schemes,
based on systems of branching and / or interacting particles,
for nonlinear dynamical systems with values in the space of probability
distributions, associated with Feynman–Kac distributions.
Many asymptotic results have been proved as the number

convergence in

The objective here is to systematically study the impact of the many algorithmic variants on the convergence results.

Hidden Markov models (HMM) form a special case of partially observed stochastic dynamical systems, in which the state of a Markov process (in discrete or continuous time, with finite or continuous state space) should be estimated from noisy observations. The conditional probability distribution of the hidden state given past observations is a well–known example of a normalized (nonlinear) Feynman–Kac distribution, see . These models are very flexible, because of the introduction of latent variables (non observed) which allows to model complex time dependent structures, to take constraints into account, etc. In addition, the underlying Markovian structure makes it possible to use numerical algorithms (particle filtering, Markov chain Monte Carlo methods (MCMC), etc.) which are computationally intensive but whose complexity is rather small. Hidden Markov models are widely used in various applied areas, such as speech recognition, alignment of biological sequences, tracking in complex environment, modeling and control of networks, digital communications, etc.

Beyond the recursive estimation of a hidden state from noisy observations, the problem arises of statistical inference of HMM with general state space , including estimation of model parameters, early monitoring and diagnosis of small changes in model parameters, etc.

**Large time asymptotics** A fruitful approach is the asymptotic study, when the observation
time increases to infinity, of an extended Markov chain, whose
state includes (i) the hidden state, (ii) the observation,
(iii) the prediction filter (i.e. the conditional probability
distribution of the hidden state given observations at all previous
time instants), and possibly (iv) the derivative of the prediction
filter with respect to the parameter.
Indeed, it is easy to express the log–likelihood function,
the conditional least–squares criterion, and many other clasical
contrast processes, as well as their derivatives with respect to
the parameter, as additive functionals of the extended Markov chain.

The following general approach has been proposed

first, prove an exponential stability property (i.e. an exponential forgetting property of the initial condition) of the prediction filter and its derivative, for a misspecified model,

from this, deduce a geometric ergodicity property and the existence of a unique invariant probability distribution for the extended Markov chain, hence a law of large numbers and a central limit theorem for a large class of contrast processes and their derivatives, and a local asymptotic normality property,

finally, obtain the consistency (i.e. the convergence to the set of minima of the associated contrast function), and the asymptotic normality of a large class of minimum contrast estimators.

This programme has been completed in the case of a finite state space , and has been generalized under an uniform minoration assumption for the Markov transition kernel, which typically does only hold when the state space is compact. Clearly, the whole approach relies on the existence of an exponential stability property of the prediction filter, and the main challenge currently is to get rid of this uniform minoration assumption for the Markov transition kernel , , so as to be able to consider more interesting situations, where the state space is noncompact.

**Small noise asymptotics** Another asymptotic approach can also be used, where it is rather easy
to obtain interesting explicit results, in terms close to the language
of nonlinear deterministic control theory .
Taking the simple example where the hidden state is the solution to
an ordinary differential equation, or a nonlinear state model, and
where the observations are subject to additive Gaussian white noise,
this approach consists in assuming that covariances matrices
of the state noise and of the observation noise go simultaneously
to zero. If it is reasonable in many applications to consider that
noise covariances are small, this asymptotic approach is less natural
than the large time asymptotics, where it is enough (provided a
suitable ergodicity assumption holds) to accumulate observations
and to see the expected limit laws (law of large numbers, central
limit theorem, etc.). In opposition, the expressions obtained in the
limit (Kullback–Leibler divergence, Fisher information matrix, asymptotic
covariance matrix, etc.) take here a much more explicit form than in the
large time asymptotics.

The following results have been obtained using this approach

the consistency of the maximum likelihood estimator (i.e. the convergence to the set

if the abovementioned set

it has been shown
that (i) the parameter dependent
probability distributions of the observations are locally asymptotically
normal (LAN) , from which the asymptotic
normality of the maximum likelihood estimator follows, with an explicit
expression for the asymptotic covariance matrix, i.e. for the Fisher
information matrix

The estimation of the small probability of a rare but critical event, is a crucial issue in industrial areas such as

nuclear power plants, food industry, telecommunication networks, finance and insurance industry, air traffic management, etc.

In such complex systems, analytical methods cannot be used, and naive Monte Carlo methods are clearly unefficient to estimate accurately very small probabilities. Besides importance sampling, an alternate widespread technique consists in multilevel splitting , where trajectories going towards the critical set are given offsprings, thus increasing the number of trajectories that eventually reach the critical set. As shown in , the Feynman–Kac formalism of is well suited for the design and analysis of splitting algorithms for rare event simulation.

**Propagation of uncertainty** Multilevel splitting can be used in static situations. Here, the
objective is to learn the probability distribution of an output random
variable

The key issue is to learn as fast as possible regions of the input space which contribute most to the computation of the target quantity. The proposed splitting methods consists in (i) introducing a sequence of intermediate regions in the input space, implicitly defined by exceeding an increasing sequence of thresholds or levels, (ii) counting the fraction of samples that reach a level given that the previous level has been reached already, and (iii) improving the diversity of the selected samples, usually using an artificial Markovian dynamics. In this way, the algorithm learns

the transition probability between successive levels, hence the probability of reaching each intermediate level,

and the probability distribution of the input random variable, conditionned on the output variable reaching each intermediate level.

A further remark, is that this conditional probability distribution is precisely the optimal (zero variance) importance distribution needed to compute the probability of reaching the considered intermediate level.

**Rare event simulation** To be specific, consider a complex dynamical system modelled as a Markov
process, whose state can possibly contain continuous components and
finite components (mode, regime, etc.), and the objective is to
compute the probability, hopefully very small, that a critical region
of the state space is reached by the Markov process before a final
time

The proposed splitting method consists in (i) introducing a decreasing
sequence of intermediate, more and more critical, regions in the state
space, (ii) counting the fraction of trajectories that reach an
intermediate region before time

the branching rate (number of offsprings allocated to a successful trajectory) is fixed, which allows for depth–first exploration of the branching tree, but raises the issue of controlling the population size,

the population size is fixed, which requires a breadth–first exploration of the branching tree, with random (multinomial) or deterministic allocation of offsprings, etc.

Just as in the static case, the algorithm learns

the transition probability between successive levels, hence the probability of reaching each intermediate level,

and the entrance probability distribution of the Markov process in each intermediate region.

Contributions have been given to

minimizing the asymptotic variance, obtained through a central limit theorem, with respect to the shape of the intermediate regions (selection of the importance function), to the thresholds (levels), to the population size, etc.

controlling the probability of extinction (when not even one trajectory reaches the next intermediate level),

designing and studying variants suited for hybrid state space (resampling per mode, marginalization, mode aggregation),

and in the static case, to

minimizing the asymptotic variance, obtained through a central limit theorem, with respect to intermediate levels, to the Metropolis kernel introduced in the mutation step, etc.

A related issue is global optimization. Indeed, the difficult problem
of finding the set

This additional topic was not present in the initial list of objectives, and has emerged only recently.

In pattern recognition and statistical learning, also known as machine
learning, nearest neighbor (NN) algorithms are amongst the simplest but
also very powerful algorithms available.
Basically, given a training set of data, i.e. an

In general, there is no way to guess exactly the value of the feature
associated with the new object, and the minimal error that can be done
is that of the Bayes estimator, which cannot be computed by lack of knowledge
of the distribution of the object–feature pair, but the Bayes estimator
can be useful to characterize the strength of the method.
So the best that can be expected is that the NN estimator converges, say
when the sample size

The asymptotic behavior when the sample size grows is well understood in finite dimension, but the situation is radically different in general infinite dimensional spaces, when the objects to be classified are functions, images, etc.

**Nearest neighbor classification in infinite dimension** In finite dimension, the

**Rates of convergence of the functional $k$–nearest neighbor
estimator** Motivated by a broad range of potential applications, such as regression
on curves, rates of convergence of the

This emerging topic has produced several theoretical advances , in collaboration with Gérard Biau (université Pierre et Marie Curie, ENS Paris and EPI CLASSIC, Inria Paris—Rocquencourt), and a possible target application domain has been identified in the statistical analysis of recommendation systems, that would be a source of interesting problems.

Among the many application domains of particle methods, or interacting Monte Carlo methods, ASPI has decided to focus on applications in localisation (or positioning), navigation and tracking , , which already covers a very broad spectrum of application domains. The objective here is to estimate the position (and also velocity, attitude, etc.) of a mobile object, from the combination of different sources of information, including

a prior dynamical model of typical evolutions of the mobile, such as inertial estimates and prior model for inertial errors,

measurements provided by sensors,

and possibly a digital map providing some useful feature (terrain altitude, power attenuation, etc.) at each possible position.

In some applications, another useful source of information is provided by

a map of constrained admissible displacements, for instance in the form of an indoor building map,

which particle methods can easily handle (map-matching). This Bayesian dynamical estimation problem is also called filtering, and its numerical implementation using particle methods, known as particle filtering, has been introduced by the target tracking community , , which has already contributed to many of the most interesting algorithmic improvements and is still very active, and has found applications in

target tracking, integrated navigation, points and / or objects tracking in video sequences, mobile robotics, wireless communications, ubiquitous computing and ambient intelligence, sensor networks, etc.

ASPI is contributing (or has contributed recently) to several applications of particle filtering in positioning, navigation and tracking, such as geolocalisation and tracking in a wireless network, terrain–aided navigation, and data fusion for indoor localisation.

Another application domain of particle methods, or interacting Monte Carlo methods, that ASPI has decided to focus on is the estimation of the small probability of a rare but critical event, in complex dynamical systems. This is a crucial issue in industrial areas such as

nuclear power plants, food industry, telecommunication networks, finance and insurance industry, air traffic management, etc.

In such complex systems, analytical methods cannot be used, and naive Monte Carlo methods are clearly unefficient to estimate accurately very small probabilities. Besides importance sampling, an alternate widespread technique consists in multilevel splitting , where trajectories going towards the critical set are given offsprings, thus increasing the number of trajectories that eventually reach the critical set. This approach not only makes it possible to estimate the probability of the rare event, but also provides realizations of the random trajectory, given that it reaches the critical set, i.e. provides realizations of typical critical trajectories, an important feature that methods based on importance sampling usually miss.

ASPI is contributing (or has contributed recently) to several applications of multilevel splitting for rare event simulation, such as risk assessment in air traffic management, detection in sensor networks, and protection of digital documents.

This work has been presented at the 10th International Workshop on Rare Event Simulation (RESIM), held in Amsterdam in August 2014.

The problem is to accurately estimate the (very small) probability that a rare but critical event (such as a score function exceeding a given threshold) occurs before some fixed final time. Multilevel splitting is a very efficient solution, in which sample paths are propagated and are eliminated or replicated when some intermediate events (defined by some intermediate thresholds) occur. A common and efficient design is to define the next intermediate level as an empirical quantile of the running maximum of the score function along a surviving trajectory. However, it is practically impossible to remember when (at which time instant) and where (in which state) did each successful trajectory cross the empirically defined threshold. The proposed design is a two–step adaptive multilevel splitting algorithm: In the first step, a first set of trajectories is sampled in order to obtain the next intermediate threshold as an empirical quantile. In the second step, once the new intermediate threshold is obtained, a second set of trajectories is sampled in order to evaluate the transition probability to the new empirically defined intermediate region. This two–step procedure is repeated until some trajectories do hit the critical region before final time.

This work has been presented at the 10th International Workshop on Rare Event Simulation (RESIM), held in Amsterdam in August 2014.

This is a collaboration with Christian Musso (ONERA, Palaiseau) and with Sébastien Paris (LSIS, université du Sud Toulon Var), related with the supervision of the PhD thesis of Yannick Kenné.

The problem considered here can be described as follows: a limited number of sensors should be deployed by a carrier in a given area, and should be activated at a limited number of time instants within a given time period, so as to maximize the probability of detecting a target (present in the given area during the given time period). There is an information dissymmetry in the problem: if the target is sufficiently close to a sensor position when it is activated, then the target can learn about the presence and exact position of the sensor, and can temporarily modify its trajectory so as to escape away before it is detected. This is referred to as the target intelligence. Two different simulation–based algorithms have been designed to solve separately or jointly this optimization problem, with different and complementary features. One is fast, and sequential: it proceeds by running a population of targets and by dropping and activating a new sensor (or re–activating a sensor already available) where and when this action seems appropriate. The other is slow, iterative, and non–sequential; it proceeds by updating a population of deployment plans with guaranteed and increasing criterion value at each iteration, and for each given deployment plan, there is a population of targets running to evaluate the criterion. Finally, the two algorithms can cooperate in many different ways, to try and get the best of both approaches. A simple and efficient way is to use the deployment plans provided by the sequential algorithm as the initial population for the iterative algorithm.

This work has been presented at the Conference on Optimization and Practices in Industry (COPI), held in Palaiseau in October 2014.

This is a collaboration with Pierre Ailliot (UBO) and Françoise Pène (UBO).

This is a collaboration with Pierre Ailliot (UBO).

A multi–site stochastic generator for wind speed has been developped . It aims at simulating realistic wind conditions with a focus on reproducing the space-time motions of the meteorological systems. A Gaussian linear state–space model is used where the latent state may be interpreted as regional wind conditions and the observation equation links regional and local scales. The model is fitted to 6–hourly reanalysis data in the North–East Atlantic. It is shown that it is interpretable and provides a good description of important properties of the space–time covariance function of the data, such as the non full–symmetry induced by prevailing flows in this area.

Many records in environmental science exhibit asymmetries. In this project, we introduce a time deformation to produce asymmetric path from a Gaussian process with symmetric path. A simple case is obtained by assuming that

with

This is a collaboration with Frédéric Lavancier (université de Nantes) and Souleymane Kadri–Harouna (université de la Rochelle)

This is a collaboration with Cédéric Herzet (EPI FLUMINANCE, Inria Rennes–Bretagne Atlantique) and Angélique Drémeau (ENSTA Bretagne, Brest).

Following recent contributions in non–linear sparse representations,
this work ,
focuses on a particular non–linear model, defined as the nested
composition of functions. This family includes in particular discrete–time
hidden Markov models. Recalling that most linear sparse representation
algorithms can be straightforwardly extended to non–linear models,
we emphasize that their performance highly relies on an efficient computation
of the gradient of the objective function. In the particular case of interest,
we propose to resort to a well–known technique from the theory of optimal
control to evaluate the gradient.
This computation is then implemented into the

This work has also been presented at Congrès National d'Assimilation, a national event held in Toulouse in December 2014.

Inria contract ALLOC 7326 — April 2013 to December 2016.

This is a collaboration with Christian Musso (ONERA, Palaiseau) and with Sébastien Paris (LSIS, université du Sud Toulon Var), related with the supervision of the PhD thesis of Yannick Kenné.

The objective of this project is to optimize the position and activation times of a few sensors deployed by one or several platforms over a search zone, so as to maximize the probability of detecting a moving target. The difficulty here is that the target can detect an activated sensor before it is detected itself, and it can then modify its own trajectory to escape from the sensor. This makes the optimization problem a spatio–temporal problem. The activity in the beginning of this project has been to study different ways to merge two different solutions to the optimization problem : a fast, though suboptimal, solution developped by ONERA in which sensors are deployed where and when the probability of presence of a target is high enough, and the optimal population–based solution developped by LSIS and Inria in a previous contract (Inria contract ALLOC 4233) with DGA / Techniques navales.

January 2013 to December 2016.

Piecewise deterministic Markov processes (PDMP) are non-diffusive stochastic processes which naturally appear in many areas of applications as communication networks, neuron activities, biological populations or reliability of complex systems. Their mathematical study has been intensively carried out in the past two decades but many challenging problems remain completely open. This project aims at federating a group of experts with different backgrounds (probability, statistics, analysis, partial derivative equations, modelling) in order to pool everyone's knowledge and create new tools to study PDMPs. The main lines of the project relate to estimation, simulation and asymptotic behaviors (long time, large populations, multi-scale problems) in the various contexts of application.

March 2014 to February 2018.

The GERONIMO project aims at devising new efficient and effective techniques for the design of geophysical reduced–order models (ROMs) from image data. The project both arises from the crucial need of accurate low–order descriptions of highly–complex geophysical phenomena and the recent numerical revolution which has supplied the geophysical scientists with an unprecedented volume of image data. Our research activities are concerned by the exploitation of the huge amount of information contained in image data in order to reduce the uncertainty on the unknown parameters of the models and improve the reduced–model accuracy. In other words, the objective of our researches to process the large amount of incomplete and noisy image data daily captured by satellites sensors to devise new advanced model reduction techniques. The construction of ROMs is placed into a probabilistic Bayesian inference context, allowing for the handling of uncertainties associated to image measurements and the characterization of parameters of the reduced dynamical system.

Arnaud Guyader collaborates with the group of Nicolas Hengartner at Los Alamos National Laboratories, on the development of fast algorithms to simulate rare events, and on iterative bias reduction techniques in nonparametric estimation. This collaboration has a long record of bilateral visits.

Valérie Monbet has co–organized the worshop
on *Stochastic Weather Generators*,
held in Avignon in September 2014.

François Le Gland has been a member of the organizing committee
of the *46èmes Journées de Statistique*,
held in Bruz in June 2014.

François Le Gland gives

a course on Kalman filtering and hidden Markov models, at université de Rennes 1, within the SISEA (signal, image, systèmes embarqués, automatique, école doctorale MATISSE) track of the master in electronical engineering and telecommunications,

a 3rd year course on Bayesian filtering and particle approximation, at ENSTA (école nationale supérieure de techniques avancées), Paris, within the systems and control module,

a 3rd year course on linear and nonlinear filtering, at ENSAI (école nationale de la statistique et de l'analyse de l'information), Ker Lann, within the statistical engineering track,

and a 3rd year course on hidden Markov models, at Télécom Bretagne, Brest.

He has also animated a set of training sessions on particle filtering, with an application to video multi–object tracking, to engineers from Canon Research France.

Patrick Héas gives a course on statistical image analysis at université de Rennes 1, within the SISEA (signal, image, systèmes embarqués, automatique, école doctorale MATISSE) track of the master in electronical engineering and telecommunications.

Valérie Monbet gives several courses on data analysis, on time series, and on mathematical statistics, all at université de Rennes 1 within the master on statistics and econometrics. She is also the director of the master on statistics and econometry at université de Rennes 1.

François Le Gland has been supervising one PhD student

Damien–Barthélémy Jacquemart,
title: *Contributions to multilevel splitting for rare events,
and applications to air traffic*,
université de Rennes 1,
started in October 2011,
defense in December 2014,
funding: DGA / ONERA grant,
co–direction: Jérôme Morio (ONERA, Palaiseau).

and he is currently supervising two PhD students

Alexandre Lepoutre,
provisional title: *Detection issues in track–before–detect*,
université de Rennes 1,
started in October 2010,
expected defense in 2015,
funding: ONERA grant,
co–direction: Olivier Rabaste (ONERA, Palaiseau),

Kersane Zoubert–Ousseni,
provisional title: *Particle filters for hybrid indoor navigation
with smartphones*,
université de Rennes 1,
started in December 2014,
expected defense in 2017,
funding: CEA grant,
co–direction: Christophe Villien (CEA LETI, Grenoble).

Valérie Monbet has been supervising one PhD student

Julie Bessac,
title: *On the construction of stochastic wind data generators
off–shore Brittany*,
université de Rennes 1,
started in October 2011,
defense in October 2014,
co–direction : Pierre Ailliot (université de Bretagne Occidentale).

François Le Gland has been a reviewer for the PhD theses of Paul Lemaître (université de Bordeaux 1, advisors: Pierre Del Moral and Bertrand Iooss), Achille Murangira (université de technologie de Troyes, advisors: Igor Nikoforov and Karim Dahia) and El houcine Bergou (université de Toulouse, advisor: Serge Gratton).

Valérie Monbet has been a member of the committee for the PhD thesis of Emmanuelle Autret (IFREMER).

In addition to presentations with a publication in the proceedings, which are listed at the end of the document in the bibliography, members of ASPI have also given the following presentations.

Frédéric Cérou has given a talk on rare event simulation for molecular dynamics, at the ICMS workshop on Computational Methods for Statistical Mechanics — at the Interface between Mathematical Statistics and Molecular Simulation, held in Edinburgh in June 2014, and a talk on a central limit theorem for adaptive splitting, at the 10th International Workshop on Rare Event Simulation (RESIM'14), held in Amsterdam in August 2014. He has been invited to give two seminar talks on rare event simulation with multilevel splitting, in Marseilles in May 2014.

François Le Gland has given a talk on a two–step multilevel splitting algorithm for rare event simulation, at the 10th International Workshop on Rare Event Simulation (RESIM'14), held in Amsterdam in August 2014, and a talk on simulation–based algorithms for the optimization of sensor deployment, at the Conference on Optimization and Practices in Industry (COPI), held in Palaiseau in October 2014.

François Le Gland is a member of the “conseil d'UFR” of the department of mathematics of université de Rennes 1.

Valérie Monbet is a member of the two “comité de direction” and “conseil” of IRMAR (institut de recherche mathématiques de Rennes, UMR 6625). She is also the deputy head, and a member of the two “conseil scientifique” and “conseil d'UFR” of the department of mathematics of université de Rennes 1.