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 major breakthrough made in the mid 90's,
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 resampling 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.

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 with an artificial Markovian dynamics for the input variable. 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

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 topic has produced several theoretical advances , in collaboration with Gérard Biau (université Pierre et Marie Curie). A few possible target application domains have been identified in

the statistical analysis of recommendation systems,

the design of reduced–order models and analog samplers,

that would be a source of interesting problems.

See .

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.

Frédéric Cérou and Arnaud Guyader have received the
prize
of the best recent paper published in the journal *Annales de l'Institut
Henri Poincaré, Probabilités et Statistiques*
for their joint paper
in collaboration with Gérard Biau (université Pierre et Marie Curie).
This paper analyzes ABC (approximate Bayesian computation) —
a family of computational techniques which offer an almost automated
solution in situations where evaluation of the likelihood is computationally
prohibitive, or whenever suitable likelihoods are not available —
from the point of view of

This is a collaboration with Bernard Delyon (université de Rennes 1).

In this work, we consider the adaptive multilevel splitting algorithm as a Fleming–Viot particle system: the particles are indexed by levels instead of time, and the associated states are given by first entrance into level sets, in a similar fashion as in . A rigorous proof of a central limit theorem has been obtained in for Fleming–Viot particle systems. The application to AMS (adaptive multilevel splitting) algorithm is in preparation.

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

This is a collaboration with Cédric Herzet (EPI FLUMINANCE, Inria Rennes–Bretagne Atlantique)

Dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This low-rank extension takes the form of a non–convex optimization problem. To the best of our knowledge, only sub–optimal algorithms have been proposed in the literature to compute the solution of this problem. In , we prove that there exists a closed-form optimal solution to this problem and design an effective algorithm to compute it based on singular value decomposition (SVD). Based on this solution, we then propose efficient procedures for reduced-order modeling and for the identification of the low-rank DMD modes and amplitudes. Experiments illustrates the gain in performance of the proposed algorithm compared to state-of-the-art techniques.

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

This is a collaboration with Pierre Ailliot (université de Bretagne Occidentale, Brest), Ronan Fablet and Pierre Tandéo (Télé́com Bretagne, Brest), Anne Cuzol (université de Bretagne Sud, Vannes) and Bernard Chapron (IFREMER, Brest).

Nowadays, ocean and atmosphere sciences face a deluge of data from spatial observations, in situ monitoring as well as numerical simulations. The availability of these different data sources offer new opportunities, still largely underexploited, to improve the understanding, modeling and reconstruction of geophysical dynamics. The classical way to reconstruct the space–time variations of a geophysical system from observations relies on data assimilation methods using multiple runs of the known dynamical model. This classical framework may have severe limitations including its computational cost, the lack of adequacy of the model with observed data, modeling uncertainties. In , we explore an alternative approach and develop a fully data–-driven framework, which combines machine learning and statistical sampling to simulate the dynamics of complex system. As a proof concept, we address the assimilation of the chaotic Lorenz–63 model and imputation of missing data in multisite wind and rain time series. We demonstrate that a nonparametric sampler from a catalog of historical datasets, namely local linear regression, combined with a classical stochastic data assimilation scheme, the ensemble Kalman filter and the particular filter, reach state–of–the–art performances, without online evaluations of the physical model. The use of local regression instead of analog sampler allows to improve the performance of the filters.

This is a collaboration with Jean–François Dupuy (INSA Rennes) and Laurent Rouvière (université de Haute Bretagne, Rennes).

Classification and discriminant analysis methods have grown in depths during the past 20 years. Fisher linear discriminant analysis (LDA) is the basic but standard approach. As the structure and dimension of the data becomes more complex in a wide range of applications, such as functional data, there is a need for more flexible nonparametric classification and discriminant analysis tools, especially when the ratio of learning sample size to number of covariates is low and the covariates are highly correlated and the covariance matrix is highly degenerated or when the large number of covariates are generally weak in predicting the class labels. For some data such as spectrometry data, only some parts of the observed curves are discriminant leading to groups of variables.

We proposed a classification tree based on groups of variables. Like usual tree-based methods, the algorithm partitions the feature space into M regions, by recursively performing binary splits. The main difference is that each split is based on groups of variables and the boundary between both classes is the hyperplane which minimizes the Bayes risk in the set generated by the selected group of variables. We demonstrate on several toy examples and real spectrometry data that the performances of the proposed tree groups algorithm are at least as good as the one of the standard CART algorithm and group Lasso logistic regression.

See .

This is a collaboration with Christophe Villien (CEA LETI, Grenoble).

The issue here is user localization, and more generally localization–based services (LBS). This problem is addressed by GPS for outdoor applications, but no such general solution has been provided so far for indoor applications. The desired solution should rely on sensors that are already available on smartphones and other tablet computers. Inertial solutions that use MEMS (microelectromechanical system, such as accelerometer, magnetometer, gyroscope and barometer) are already studied at CEA. An increase in performance should be possible, provided these data are combined with other available data: map of the building, WiFi signal, modeling of perturbations of the magnetic field, etc. To be successful, advanced data fusion techniques should be used, such as particle filtering and the like, to take into account displacement constraints due to walls in the building, to manage several possible trajectories, and to deal with rather heterogeneous information (map, radio signals, sensor signals).

The main objective of this thesis is to design and tune localization algorithms that will be tested on platforms already available at CEA. Special attention is paid to particle smoothing and particle MCMC algorithms, to exploit some very precise information available at special time instants, e.g. when the user is clearly localized near a landmark point.

In some applications, real time estimation of the trajectory is not needed, and a post processing framework may provide a better estimation of this trajectory. In , we present and compare three different algorithms to improve a real time trajectory estimation. Actually, two different smoothing algorithms and the Viterbi algorithm are implemented and evaluated. These methods improve the regularity of the estimated trajectory by reducing switches between hypotheses.

This is a collaboration with Dann Laneuville (DCNS Nantes).

After the introduction of MHT (multi–hypothesis tracking) techniques
in the nineties, multitarget tracking has recently seen promising
developpments with the introduction of new algorithms such
as the PHD (probability hypothesis density) filter ,
or the HISP (hypothesised filter for independent stochastic populations)
filter .
These techniques provide a unified multitarget model in a Bayesian
framework ,
which makes it possible to design recursive estimators of
a *multitarget probability density*.
Two main approaches can be used here: sequential Monte Carlo (SMC, also
kown as particle filtering), and Gaussian mixture (GM).
A third approach, based on discretizing the state–space in a possibly
adaptive way, could also be considered despite its larger computational load.
These methods are well studied and provide quite good results
for *contact output* data, which correspond to regularly spaced
measurements of targets with a large SNR (signal–to–noise ratio).
Here, the data is processed (compared with a detection threshold) in each
resolution cell of the sensor, so as to provide a list of detections at
a given time instant.
Among these methods, the HISP filter has the best performance/computational
cost ratio.

However, these classical methods are unefficient for targets with a low SNR,
e.g. targets in far range or small targets with a small detection
probability.
For such targets, preprocessing (thresholding) the data is not a good idea,
and a much better idea is to feed a tracking algorithm with the
raw *sensor output* data directly.
These new methods require a precise modeling of the
sensor physics and a direct access to the radar (or the sonar) raw data,
i.e. to the signal intensity level in each azimuth/range cell.
Note that these new methods seem well suited to new types of sensors such
as lidar, since manufacturers do not integrate a detection module and do
provide raw images of the signal intensity level in each azimuth/range cell.

The objective of the thesis is to study and design a tracking algorithm using raw data, and to implement it on radar (or sonar, or lidar) real data.

January 2015 to December 2017.

This is a joint research initiative supported by the three labex active in Brittany, CominLabs (Communication and Information Sciences Laboratory), Lebesgue (Centre de Mathématiques Henri Lebesgue) and LabexMER (Frontiers in Marine Research).

This project aims at exploring novel statistical and stochastic methods to address the emulation, reconstruction and forecast of fine–scale upper ocean dynamics. The key objective is to investigate new tools and methods for the calibration and implementation of novel sound and efficient oceanic dynamical models, combining

recent advances in the theoretical understanding, modeling and simulation of upper ocean dynamics,

and mass of data routinely available to observe the ocean evolution.

In this respect, the emphasis will be given to stochastic frameworks to encompass multi–scale/multi–source approaches and benefit from the available observation and simulation massive data. The addressed scientific questions constitute basic research issues at the frontiers of several disciplines. It crosses in particular advanced data analysis approaches, physical oceanography and stochastic representations. To develop such an interdisciplinary initiative, the project gathers a set of research groups associated with these different scientific domains, which have already proven for several years their capacities to interact and collaborate on topics related to oceanic data and models. This project will place Brittany with an innovative and leading expertise at the frontiers of computer science, statistics and oceanography. This transdisciplinary research initiative is expected to resort to significant advances challenging the current thinking in computational oceanography.

Inria contract ALLOC 9452 — January 2015 to December 2017.

The COSMOS project aims at developing numerical techniques dedicated to the sampling of high–dimensional probability measures describing a system of interest. There are two application fields of interest: computational statistical physics (a field also known as molecular simulation), and computational statistics. These two fields share some common history, but it seems that, in view of the quite recent specialization of the scientists and the techniques used in these respective fields, the communication between molecular simulation and computational statistics is not as intense as it should be.

We believe that there are therefore many opportunities in considering both fields at the same time: in particular, the adaption of a successful simulation technique from one field to the other requires first some abstraction process where the features specific to the original field of application are discarded and only the heart of the method is kept. Such a cross–fertilization is however only possible if the techniques developed in a specific field are sufficiently mature: this is why some fundamental studies specific to one of the application fields are still required. Our belief is that the embedding in a more general framework of specific developments in a given field will accelerate and facilitate the diffusion to the other field.

Inria contract ALLOC 8102 — 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.

January 2014 to December 2019.

PI: Tony Lelièvre, Civil Engineer in Chief, Ecole des Ponts Paris-Tech.

Note that

With the development of large-scale computing facilities, simulations of materials at the molecular scale are now performed on a daily basis. The aim of these simulations is to understand the macroscopic properties of matter from a microscopic description, for example, its atomistic configuration.

In order to make these simulations efficient and precise, mathematics have a crucial role to play. Indeed, specific algorithms have to be used in order to bridge the time and space scales between the atomistic level and the macroscopic level. The objective of the MSMath ERC project is thus to develop and study efficient algorithms to simulate high-dimensional systems over very long times. These developments are done in collaboration with physicists, chemists and biologists who are using these numerical methods in an academic or industrial context.

In particular, we are developping mathematical tools at the interface between the analysis of partial differential equations and stochastic analysis in order to characterize and to quantify the metastability of stochastic processes. Metastability is a fundamental concept to understand the timescale separation between the microscopic model and the macroscopic world. Many algorithms which aim at bridging the timescales are built using this timescale separation.

January 2016 to December 2018.

This project is funded by the ERA–NET Initiative ERANETMED (Euro–Mediterranean Cooperation through ERA–NET Joint Activities and Beyond). It is a collaboration with Greece, Tunisia and Marocco, coordinated by Technical University of Crete (TUC). The French staff includes: Pierre Ailliot (Université de Bretagne Occidentale, Brest), Denis Allard (INRA Avignon), Anne Cuzol (Université de Bretagne Sud, Vannes), Christophe Maisondieu (IFREMER Brest) and Valérie Monbet.

The aim of DESIRES is to develop an Internet–based, multi–parametric electronic platform for optimum design of desalination plants, supplied by renewable energy sources (RES). The platform will rely upon (i) a solar, wind and wave energy potential database, (ii) existing statistical algorithms for processing energy-related data, (iii) information regarding the inter-annual water needs, (iv) a database with the technical characteristics of desalination plant units and the RES components, and (v) existing algorithms for cost effective design, optimal sizing and location selection of desalination plants.

This is the subjet of the PhD project of Ramatoulaye Dabo (université Assane Seck de Ziguinchor and université de Rennes 1).

The question here is to develop adaptive multilevel splitting algorithms
for models that are commonly used in epidemiology, such as SIR (susceptible,
infectious, recovered) models , or more complex
compartmental models.
A significant advantage of adaptive multilevel splitting is its robustness,
since it does not require too much knowledge about the behavior of the
system under study.
An interesting challenge would be to understand how to couple the algorithm
with numerically efficient simulation methods such
as

As part of statistics semester of Labex Lebesgue, Valérie Monbet has co–organized the 3rd workshop on Stochastic Weather Generators, held in Vannes in May 2016. This workshop aimed at bringing together a wide range of researchers, practitioners, and graduate students whose work is related to the stochastic modelling of meteorological variables and stochastic weather generators. Stochastic weather generators give us ability to reliably predict climate-related risks by simulating sequences of daily weather and climate consistent with specific aspects of climate variability and change. The simulated sequences of meteorological variables (rainfall, wind, temperature,etc.) are typically used as inputs into complex environmental and ecosystem models. They have a wide range of applications in hydrology, agriculture and environmental management.

Within the programme *École d'été France Excellence*
promoted by the French embassy in China, she has co–organized
a two–weeks Summer School
in Statistics,
held in Rennes in June/July 2016.
This initiative has offered Chinese students the opportunity to attend
graduate courses in statistics, including practical and seminar sessions.

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

Frédéric Cérou has given an invited talk on the convergence of adaptive multilevel splitting at the RESIM 2016 workshop held in Eindhoven in March/April 2016. He has given, jointly with Mathias Rousset, a talk on a central limit theorem for adaptive multilevel splitting at the 2nd meeting on Adaptive Multilevel Splitting and Rare Events, an event of the MSMath ERC project held at CERMICS in Marne–la–Vallée, in June 2016.

Patrick Héas has given a talk on learning geophysical systems from images, at the seminar of ENS Rennes, in April 2016, and a talk on reduced modeling from partial observations, at the SIAM conference on Uncertainty Quantification, held in Lausanne, in April 2016.

François Le Gland has given a talk on marginalization for rare event simulation in switching diffusions at the RESIM 2016 workshop held in Eindhoven in March/April 2016, and at the probability and statistics seminar of LJK (laboratoire Jean Kuntzmann) in Grenoble, in June 2016.

Valérie Monbet has given a talk on
time varying autoregressive models for multisite weather generators
at the 3rd workshop
on Stochastic
Weather Generators,
held in Vannes in May 2016.
She has also given given a series of three lectures (including a lab session)
at the *École d'été France Excellence*
Summer School
in Statistics,
held in Rennes in June/July 2016.

François Le Gland is a member of
the *conseil d'UFR*
of the department of mathematics of université de Rennes 1.
He is also a member of the *conseil scientifique*
for the EDF/Inria scientific partnership.

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

Patrick Héas gives a course on Monte Carlo simulation methods in 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.

François Le Gland gives

a 2nd year course on introduction to stochastic differential equations, at INSA (institut national des sciences appliquées) Rennes, within the GM/AROM (risk analysis, optimization and modeling) major in mathematical engineering,

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

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,

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

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

Alexandre Lepoutre,
title: *Tracking and detection in Track–Before–Detect context using
particle filtering*,
université de Rennes 1,
started in October 2010,
defense held on October 5, 2016,
funding: ONERA grant,
co–direction: Olivier Rabaste (ONERA, Palaiseau).

Frédéric Cérou and François Le Gland are jointly supervising one PhD student

Ramatoulaye Dabo,
provisional title: *Rare event simulation in epidemiology*,
université Assane Seck de Ziguinchor (Senegal)
and université de Rennes 1,
started in September 2015,
expected defense in 2018,
co–direction: Alassane Diedhiou (université Assane Seck de Ziguinchor).

François Le Gland and Valérie Monbet are jointly supervising one PhD student

Thi Tuyet Trang Chau,
provisional title: *Non parametric filtering for Metocean multi–source
data fusion*,
université de Rennes 1,
started in October 2015,
expected defense in October 2018,
funding: Labex Lebesgue grant and Brittany council grant,
co–direction: Pierre Ailliot (université de Bretagne Occidentale, Brest).

François Le Gland is supervising two other PhD students

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),

Audrey Cuillery,
provisional title: *Bayesian tracking from raw data*,
université du Sud Toulon Var,
started in April 2016,
expected defense in 2019,
funding: CIFRE grant with DCNS,
co–direction: Claude Jauffret (université du Sud Toulon Var)
and Dann Laneuville (DCNS, Nantes).

Valérie Monbet is supervising two other PhD students

Audrey Poterie,
provisional title: *Régression d'une variable ordinale par des données
longitudinales de grande dimension : application à la modélisation des
effets secondaires suite à un traitement par radiothérapie*,
université de Rennes 1,
started in October 2015,
expected defense in 2018,
funding: INSA grant,
co–direction: Jean–François Dupuy (INSA Rennes)
and Laurent Rouvière (université de Haute Bretagne, Rennes).

Marie Morvan,
provisional title: *Modèles de régression pour données
fonctionnelles. Application à la modélisation de données de
spectrométrie dans le proche infra rouge*,
université de Rennes 1,
started in October 2016,
expected defense in 2019,
funding: MESR grant,
co–direction: Joyce Giacofci (université de Haute Bretagne, Rennes)
and Olivier Sire (université de Bretagne Sud, Vannes).

Mathias Rousset is supervising one PhD student

Yushun Xu,
provisional title: *Variance reduction of overdamped Langevin dynamics
simulation*,
université Paris-Est,
started in October 2015,
expected defense in 2018,
co–direction: Pierre-André Zitt (université Paris–Est).

François Le Gland has been a reviewer for the PhD theses of Tepmony Sim (Télécom ParisTech, advisors: Randal Douc and François Roueff) and Clément Walter (université Denis Diderot, Paris, advisor: Josselin Garnier).

Valérie Monbet has been a member of the committee for the HDR of Mathieu Emily (université de Haute Bretagne, Rennes).

Mathias Rousset has been a member of the committee for the PhD thesis of Zofia Trstanova (Inria Grenoble, EPI NANO-D, advisor: Stéphane Redon).