technical report available

[Agathe Girard]

Dear All,

The following new technical report

Gaussian Process Priors with Uncertain Inputs: Multiple-Step Ahead
Prediction
A. Girard, C. E. Rasmussen and R. Murray-Smith

is available at
http://www.dcs.gla.ac.uk/~agathe/reports.html
Feedback most appreciated!

Regards,
Agathe Girard

http://www.dcs.gla.ac.uk/~agathe

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Abstract:

We consider the problem of multi-step ahead prediction
in time series analysis using the non-parametric Gaussian process
model. $k$-step ahead forecasting of a discrete-time non-linear
dynamic system can be performed by doing repeated one-step ahead
predictions. For a state-space model of the form $y_t=f(y_{t-1},
\dots, y_{t-L})$, the prediction of $y$ at time $t+k$ is based on
the estimates ${\hat y_{t+k-1}}, \dots, {\hat y_{t+k-L}}$ of the
previous outputs. We show how, using an analytical Gaussian
approximation, we can formally incorporate the uncertainty about
intermediate regressor values, thus updating the uncertainty on
the current prediction. In this framework, the problem is that of
predicting responses at a random input and we compare the Gaussian
approximation to the Monte-Carlo numerical approximation of the
predictive distribution. The approach is illustrated on a
simulated non-linear dynamic example, as well as on a simple
one-dimensional static example.