LibBi package: OrnsteinUhlenbeckBridge

Synopsis

./init.sh

This simulates a number of data sets for testing. GNU Octave is required. Running it is optional, as a number of simulated data sets are already included.

./run.sh

This runs a particle filter as well as samples from the posterior distribution for a data set of a single observation at time 1.

./test.sh

This runs tests on the bootstrap and bridge particle filters on the simulated data sets. Alternatively, these tests may be run as an array job on a cluster:

qsub -t 0-15 qsub_test_bridge.sh
qsub -t 0-15 qsub_test_bootstrap.sh

Finally, results may be plot with:

octave --path oct/ --eval "plot_and_print"

GNU Octave and OctBi are required.

Note that, as of version 1.1.0 of LibBi, running any of these gives the warnings:

Warning (line 29): 'obs' variables should not appear on the right side of actions in the 'transition' block.
Warning (line 42): 'obs' variables should not appear on the right side of actions in the 'lookahead_transition' block.

This is normal.

Description

This package includes an Ornstein--Uhlenbeck model that is observed directly. The task is to simulate diffusion bridges between the observed values. The form of the model is as studied in Aït-Sahalia (1999):

$$dx=(\theta_{1}-\theta_{2}x), dt+\theta_{3}, dW,$$

with fixed parameters $\theta_1 = 0.0187$, $\theta_2 = 0.2610$ and $\theta_3 = 0.0224$.

It was used as a test case in Del Moral & Murray (2014). The package may be used to reproduce the results in that paper.

References

Aït-Sahalia, Y. Transition Densities for Interest Rate and Other Nonlinear Diffusions. The Journal of Finance, 1999, 54, 1361--1395.

Del Moral, P. & Murray, L. M. Sequential Monte Carlo with Highly Informative Observations, 2014. [arXiv]