Modèles à espace d'états non linéaires/non gaussiens et inférence bayésienne par méthode {MCMC} -- Une application en évaluation des stocks halieutiques

National audienceDifference equations with delay are widely used to model the evolution of the biomass of a fish stock (delay difference models). Represented as a state- space model they allow, starting from the data of the annual catches, a relevant Bayesian analysis. For this purpose we can use an hybrid MCMC method combi- ning a Metropolis-Hastings algorithm within a Gibbs sampler, namely the single- component Metropolis-Hastings algorithm

The freedom to choose: integrating communitybased reproductive health services with locally led marine conservation initiatives in southwest Madagascar

Madagascar’s diverse marine ecosystems serve as critical biodiversity habitats and are also essential to the livelihoods, food security and culture of coastal people, including semi-nomadic Vezo fishers based along the southwest coast. Commercialisation of their traditional fisheries, rapid coastal population growth related to unmet family planning needs, and lack of alternatives to fishing in this arid region are resulting in the unsustainable exploitation of coastal resources. In response to these challenges, marine conservation organisation Blue Ventures has developed an approach to community-based conservation and development that reflects the inextricable links between humans, their health and the environment. We describe how this model has evolved in the Velondriake locally managed marine area, home to approximately 1 0,000 people, over the last decade through strong cross-sector partnerships. It has entailed the integration of community-based reproductive health services with locally led marine conservation initiatives including temporary octopus fishery closures, permanent marine reserves and alternative coastal livelihood activities such as aquaculture. All of these programmes are underpinned by community education that engages men, women, youth and children in both health and conservation topics. The provision of voluntary family planning services in the Velondriake area is estimated to have averted more than 800 unintended pregnancies since 2007, and the temporary octopus fishery closure model has been implemented over 1 50 times along the southwest coast since 2004. Preliminary, anecdotal reports from community members and programme staff indicate that this integrated Population-Health-Environment approach enables couples to plan and better provide for their families, empowers women, improves food security and directly supports the sustainability of local conservation efforts. It is proving to be an easily replicable model for addressing community health needs and advancing biodiversity conservation efforts in some of Madagascar’s most remote and under-served areas. Non seulement les écosystèmes marins de Madagascar abritentils une biodiversité exceptionnelle mais ils sont également intrinsèquement liés au mode de vie et à la sécurité alimentaire des populations côtières, notamment des pêcheurs seminomades qui vivent le long de la côte sud-ouest. La commercialisation des produits de la pêche traditionnelle, la croissance rapide de la population qui est en partie liée à des défauts en matière de planification familiale et l’absence d’alternatives à la pêche dans cette région aride se traduisent par une exploitation non durable des ressources côtières. Pour trouver une solution à cette situation, l'organisation de conservation marine Blue Ventures a élaboré une approche holistique qui considère les liens obligés entre les Hommes, leur santé et l'environnement. L’évolution du modèle élaboré pour l’aire marine de Velondriake est décrite ici; elle concerne environ 10 000 personnes au cours de cette dernière décennie et des partenariats multisectoriels. Le modèle a intégré des services de santé reproductive avec des initiatives de conservation marine gérées localement, comme des fermetures temporaires de la pêche aux poulpes, des réserves marines permanentes et des activités génératrices de revenus telles que l'aquaculture. L’ensemble de ces programmes est soutenu par des actions d’éducation en mobilisant les hommes, femmes, jeunes et enfants sur des thèmes aussi variés que la santé ou la protection de l’environnement. Ainsi, on estime que la prestation des services de planification familiale volontaire dans la région de Velondriake a pu éviter plus de 800 grossesses non désirées depuis 2007, et des fermetures temporaires de la pêche aux poulpes plus de 1 50 fois le long de la côte sud-ouest depuis 2004. Des rapports préliminaires et anecdotiques de membres des communautés et des personnels du programmes indiquent que cette approche intégrée « Santé – Population – Environnement » permet aux couples de planifier et de mieux subvenir aux besoins de leurs familles, aux femmes de s’émanciper et aux familles d’améliorer leur sécurité alimentaire tout en soutenant directement la durabilité des activités de conservation marine gérées localement. Ce modèle s’est révélé être facilement reproductible pour répondre aux besoins de santé communautaire et pour faire avancer les efforts de conservation de la biodiversité dans les régions les plus reculées et les plus isolées de Madagascar

Analyse bayésienne de modèles markoviens d'évolution de ressources naturelles

International audienceOne applies Monte Carlo methods to state sapce models with unknown parameters. The first one is a Monte Carlo Markov Chain algorithm. The second one is the particle filtering. We compare these methods applied to a biomass evolution model for fisheries

Using rewriting techniques to produce code generators and proving them correct

AbstractA major problem in deriving a compiler from a formal definition is the production of correct and efficient object code. In this context, we propose a solution to the problem of code-generator generation.Our approach is based on a target machine description where the basic concepts used (storage classes, access modes, access classes and instructions) are hierarchically described by tree patterns. These tree patterns are terms of an abstract data type. The program intermediate representation (input to the code generator) is a term of the same abstract data type.The code generation process is based on access modes and instruction template-driven rewritings. The result is that each program instruction is reduced to a sequence of elementary machine instructions, each of them representing an instance of an instruction template.The axioms of the abstract data type are used to prove that the rewritings preserve the semantics of the intermediate representation

Bayesian numerical inference for hidden Markov models

International audienceIn many situations it is important to be able to propose N independent real- izations of a given distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains (MCMC) interact in order to get an approximation of an indepen- dent N-sample of a given target law. In this method each individual chain proposes can- didates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through examples that it possesses many advantages. This approach is applied to a biomass evolution model

Bayesian numerical inference for Markovian models -- Application to tropical forest dynamics

International audienceBayesian modelling is fluently employed to assess natural ressources. It is associated with Monte Carlo Markov Chains (MCMC) to get an approximation of the distribution law of interest. Hence in such situations it is important to be able to propose N independent realiza- tions of this distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains interact in order to get an approximation of an independent N -sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through example that it possesses many advantages. This approach will be applied to a forest dynamic model

A Markov model of land use dynamics

The application of the Markov chain to modeling agricultural succession is well known. In most cases, the main problem is the inference of the model, i.e. the estimation of the transition matrix. In this work we present methods to estimate the transition matrix from historical observations. In addition to the estimator of maximum likelihood (MLE), we also consider the Bayes estimator associated with the Jeffreys prior. This Bayes estimator will be approximated by a Markov chain Monte Carlo (MCMC) method. We also propose a method based on the sojourn time to test the adequation of Markov chain model to the dataset

Bayesian numerical inference for Markovian models -- Application to tropical forest dynamics

International audienceBayesian modelling is fluently employed to assess natural ressources. It is associated with Monte Carlo Markov Chains (MCMC) to get an approximation of the distribution law of interest. Hence in such situations it is important to be able to propose N independent realiza- tions of this distribution law. We propose a strategy for making N parallel Monte Carlo Markov Chains interact in order to get an approximation of an independent N -sample of a given target law. In this method each individual chain proposes candidates for all other chains. We prove that the set of interacting chains is itself a MCMC method for the product of N target measures. Compared to independent parallel chains this method is more time consuming, but we show through example that it possesses many advantages. This approach will be applied to a forest dynamic model

Modèle markovien d'octroi de crédit en microfinance

ABSTRACT. Starting from the generalized model of Osman Khodr and Francine Diener [1], we present a new model that meets the expectations of the microfinance institution (MFI) and that of the borrowers and that incorporates all the characteristics of the poor, namely tolerance in case of partial default and the possibility of having a progressive loan automatically. This model will provide microfinance institutions with a decision support tool that is better adapted to the reality of microfinance. Our Markov chain consists of several statements associated with the economic status of the borrower including three types of recipients B 1 (state of being beneficiary at a time t = 0), B 2 (state to be beneficiary at a time t = 1) and I (state of financial inclusion: permanent beneficiary), an applicant state A 1 and A T −1 ((T − 1) excluded states). We modeled a borrower's behavior by a λ parameter that depends on the borrower's α probability of success. At the initial time, λ = 1+α 1−α , this quantity changes as soon as the borrower moves from one state to another with a probability of success different from α. The agency's decision to grant a credit depends entirely on the λ parameter which is compared to the set subjective threshold-values. The chance γ to have a loan (γ: probability of credit request granted) for a borrower depends on the parameter λ, with γ = 1 − 1 λ. keywords: Microfinance, Credit Grant Decision, Markov Chain, Individual Loan, Dynamic Incentive, Updated Expected ProfitEn partant du modèle généralisé de Osman Khodr et Francine Diener [1], nous présentons un nouveau modèle qui répond aux attentes de l'institution de microfinance (IMF) et celle des emprunteurs et qui incorpore toutes les caracté-ristiques des populations pauvres, à savoir la tolérance en cas de défaut partiel et la possibilité d'avoir un prêt progressif de façon automatique. Ce modèle offrira aux institutions de microfinance un outil d'aide à la décision plus adapté à la réalité de la microfinance. Notre chaîne de Markov comprend plusieurs états associés à la situation économique de l'emprunteur dont trois types de bénéficiaires B 1 (état d'être bénéficiaire au temps t = 0), B 2 (état d'être bénéficiaire au temps t = 1) et I (état d'inclusion financière: bénéficiaire permanent), un état de demandeur A 1 et A T −1 ((T − 1) états d'exclus). Nous avons modélisé le comportement d'un emprunteur par un paramètre λ qui dépend de la probabilité α de réussite de l'emprunteur. A l'instant initial, λ = 1+α 1−α , cette quantité change dès que l'emprunteur passe d'un état à un autre avec une probabilité de réussite différente de α. La décision de l'agence d'accorder un crédit dépend entièrement du paramètre λ qui est comparé aux valeurs-seuils subjectives fixées. La chance γ d'avoir un prêt (γ: probabilité de demande de crédit accordée) pour un emprunteur est fonction du paramètre λ, avec γ = 1 − 1 λ. MOTS-CLÉS : Microfinance, Décision d'octroi de crédit, chaîne de Markov, Prêt individuel, Incitation dynamique, Profit espéré actualis