Estimation in Discretely Observed Diffusions Killed at a Threshold

Enrico  Bibbona; Susanne Ditlevsen

doi:10.1111/j.1467-9469.2012.00810.x

Estimation in Discretely Observed Diffusions Killed at a Threshold

Enrico Bibbona, Susanne Ditlevsen

Institut for Matematiske Fag

10 Citationer (Scopus)

Abstract

Parameter estimation in diffusion processes from discrete observations up to a first-passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein–Uhlenbeck model for biological relevant parameters can be up to 25–100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analysed.

Originalsprog	Engelsk
Tidsskrift	Scandinavian Journal of Statistics
Vol/bind	40
Udgave nummer	2
Sider (fra-til)	274-293
ISSN	0303-6898
DOI	https://doi.org/10.1111/j.1467-9469.2012.00810.x
Status	Udgivet - jun. 2013

Adgang til dokumentet

10.1111/j.1467-9469.2012.00810.x

Citationsformater

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abstract = "Parameter estimation in diffusion processes from discrete observations up to a first-passage time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modelled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on a misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein–Uhlenbeck model for biological relevant parameters can be up to 25–100 per cent. We compute or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analysed.",

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