Estimation of probability of events from imperfect Bernoulli trials

Petar M. Djuric; Yufei S. Huang

doi:10.1117/12.351301

25 June 1999 Estimation of probability of events from imperfect Bernoulli trials

Petar M. Djuric, Yufei S. Huang

Proceedings Volume 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems; (1999) https://doi.org/10.1117/12.351301
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

In many experiments, Bernoulli trials are conducted to estimate the probability of an event of interest. The outcomes of the trials are usually known without error, that is, we known with certainty that an event occurred or not. Estimation of the probability of the even then proceeds along lines that can be found in standard textbooks on probability. The problem gets a bit more complicated if the data obtained in a Bernoulli experiment carry uncertainty about the event of interest. We call such trials imperfect Bernoulli trials as opposed to perfect trials when the outcomes of the experiment are known without error. The probability estimation in the case of imperfect trials must be modified to take into account the uncertainties. A complete Bayesian procedure is developed for this purpose. It provides an update formula for the posterior density of the probability of interest as data from new trials are obtained. The work on this program has been motivated by studies in neurophysiology where large sets of patch-clamp recordings of synaptic currents are processed to estimate the probability of a synaptic event. As example, we present application of the methodology to simulated synaptic currents.

Citation Download Citation

Petar M. Djuric and Yufei S. Huang "Estimation of probability of events from imperfect Bernoulli trials", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); https://doi.org/10.1117/12.351301

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