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- Anastasia Papavasiliou, Ioannis G. Kevrekidis
- Multiscale Modeling & Simulation
- 2007

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 in which 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)

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.

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{Xn|Yn, . . . , Y1}, referred to hereafter as the optimal filter. Following a standard Bayesian technique, we… (More)

- Dewi Harjanto, Theodore Papamarkou, Chris J. Oates, Violeta Rayon-Estrada, F. Nina Papavasiliou, Anastasia Papavasiliou
- Nature communications
- 2016

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)

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.

- Silvia Liverani, Anastasia Papavasiliou
- 2006 IEEE Nonlinear Statistical Signal Processing…
- 2006

We propose a particle filter for the estimation of a partially observed Markov chain that has a non dynamic component. Such systems arise when we include unknown parameters or when we decompose non ergodic systems to their ergodic classes. Our main assumption is that the value of the non dynamic component determines the limiting distribution of the… (More)

The solution of a (stochastic) differential equation can be locally approximated by a (stochastic) expansion. If the vector field of the differential equation is a polynomial, the corresponding expansion is a linear combination of iterated integrals of the drivers and can be calculated using Picard Iterations. However, such expansions grow exponentially… (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{Xn|Yn, . . . , Y1}, referred to hereafter as the optimal filter. We rewrite the system, so that the kernel… (More)

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