Small-sample estimation of the error of the optimal binary filter

Precise small-sample estimation of the error of an optimal filter is theoretically limited. This paper shows the possibility of obtaining better estimation in a Bayesian context by postulating prior knowledge regarding the probability distribution of the model. Prior knowledge is employed to estimate the estimation error, and thereby obtain a better estimate of filter error. Error estimation is done in a conservative manner in order not to obtain a low-biased estimate of filter error. This key condition is achieved by finding a majorant of the bias in the estimation of estimation error. The quality of our estimate of the error depends upon the precision of the prior knowledge.