1,627 research outputs found
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
Inference for reaction networks using the Linear Noise Approximation
We consider inference for the reaction rates in discretely observed networks
such as those found in models for systems biology, population ecology and
epidemics. Most such networks are neither slow enough nor small enough for
inference via the true state-dependent Markov jump process to be feasible.
Typically, inference is conducted by approximating the dynamics through an
ordinary differential equation (ODE), or a stochastic differential equation
(SDE). The former ignores the stochasticity in the true model, and can lead to
inaccurate inferences. The latter is more accurate but is harder to implement
as the transition density of the SDE model is generally unknown. The Linear
Noise Approximation (LNA) is a first order Taylor expansion of the
approximating SDE about a deterministic solution and can be viewed as a
compromise between the ODE and SDE models. It is a stochastic model, but
discrete time transition probabilities for the LNA are available through the
solution of a series of ordinary differential equations. We describe how a
restarting LNA can be efficiently used to perform inference for a general class
of reaction networks; evaluate the accuracy of such an approach; and show how
and when this approach is either statistically or computationally more
efficient than ODE or SDE methods. We apply the LNA to analyse Google Flu
Trends data from the North and South Islands of New Zealand, and are able to
obtain more accurate short-term forecasts of new flu cases than another
recently proposed method, although at a greater computational cost
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