Timing Observations of Diffusions

Aurya Javeed; Giles Hooker

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arXiv · 1709.00771

Timing Observations of Diffusions

Aurya Javeed·Giles Hooker

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Abstract

This paper addresses a problem in experimental design: We consider Itô diffusions specified by some $θ\in \mathbb{R}$ and assume that we are allowed to observe their sample paths only $n$ times before a terminal time $τ< \infty$. We propose a policy for timing these observations to optimally estimate $θ$. Our policy is adaptive (meaning it leverages earlier observations), and it maximizes the expected Fisher information for $θ$ carried by the observations. In numerical studies, this design reduces the variation of estimated parameters by as much as 75% relative to observations spaced uniformly in time. The policy depends on the value of the parameter being estimated, so we also discuss strategies for incorporating Bayesian priors over $θ$.

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Aurya Javeed, Giles Hooker. 2017-09-03. Timing Observations of Diffusions. https://arxiv.org/abs/1709.00771

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