8,463 research outputs found
Consistency of the posterior distribution and MLE for piecewise linear regression
We prove the weak consistency of the posterior distribution and that of the
Bayes estimator for a two-phase piecewise linear regression mdoel where the
break-point is unknown. The non-differentiability of the likelihood of the
model with regard to the break- point parameter induces technical difficulties
that we overcome by creating a regularised version of the problem at hand. We
first recover the strong consistency of the quantities of interest for the
regularised version, using results about the MLE, and we then prove that the
regularised version and the original version of the problem share the same
asymptotic properties
On particle filters applied to electricity load forecasting
We are interested in the online prediction of the electricity load, within
the Bayesian framework of dynamic models. We offer a review of sequential Monte
Carlo methods, and provide the calculations needed for the derivation of
so-called particles filters. We also discuss the practical issues arising from
their use, and some of the variants proposed in the literature to deal with
them, giving detailed algorithms whenever possible for an easy implementation.
We propose an additional step to help make basic particle filters more robust
with regard to outlying observations. Finally we use such a particle filter to
estimate a state-space model that includes exogenous variables in order to
forecast the electricity load for the customers of the French electricity
company \'Electricit\'e de France and discuss the various results obtained
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