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2004

2016

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We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of fast/slow problems for which a closed coarse-grained equation for the slow variables can be rigorously derived, which we… (More)

Particle filters are Monte-Carlo methods that aim to approximate the optimal filter of a partially observed Markov chain. In this paper, we study the case where the transition kernel of the Markov chain depends on unknown parameters: we construct a particle filter for the simultaneous estimation of the parameter and the partially observed Markov chain… (More)

In this paper, we study the problem of estimating a Markov chain X(signal) from its noisy partial information Y , when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional distribution process P{X n |Y n ,. .. , Y 1 }, referred to hereafter as the optimal filter. Following a standard Bayesian… (More)

We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the optimal filter.

We construct an estimator based on " signature matching " for differential equations driven by rough paths and we prove its consistency and asymptotic normality. Note that the the Moment Matching estimator is a special case of this estimator.

RNA editing is a mutational mechanism that specifically alters the nucleotide content in transcribed RNA. However, editing rates vary widely, and could result from equivalent editing amongst individual cells, or represent an average of variable editing within a population. Here we present a hierarchical Bayesian model that quantifies the variance of editing… (More)

The paper is split in two parts: first, we construct the exact likelihood for a discretely observed rough differential equation, driven by a piecewise linear path. In the second part, we use this likelihood in order to construct an approximation to the likelihood for a discretely observed rough differential equation. Finally, We show that the approximation… (More)

In this paper, we study the problem of estimating a Markov chain X(signal) from its noisy partial information Y , when the transition probability kernel depends on some unknown parameters. Our goal is to compute the conditional distribution process P{X n |Y n ,. .. , Y 1 }, referred to hereafter as the optimal filter. We rewrite the system, so that the… (More)

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