Successive nonparametric estimation of conditional distributions

Spatial characterization of non-Gaussian attributes in earth sciences and engineering commonly requires the estimation of their conditional distribution. The indicator and probability kriging approaches of current nonparametric geostatistics provide approximations for estimating conditional distributions. They do not, however, provide results similar to those in the cumbersome implementation of simultaneous cokriging of indicators. This paper presents a new formulation termed successive cokriging of indicators that avoids the classic simultaneous solution and related computational problems, while obtaining equivalent results to the impractical simultaneous solution of cokriging of indicators. A successive minimization of the estimation variance of probability estimates is performed, as additional data are successively included into the estimation process. In addition, the approach leads to an efficient nonparametric simulation algorithm for non-Gaussian random functions based on residual probabilities.

Heavy tails, importance sampling and cross-entropy

We consider the problem of estimating P(Yi + (...) + Y-n > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a toot for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y-1 + (...) + Y-n > x), n - 1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some specific parametric examples (Pareto and Weibull) how this leads to precise answers which, as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/l and GI/G/l queues are also discussed.

Time-Frequency Distribution Moments of Heart Rate Variability for Neonatal Seizure Detection

In this paper, we propose features extracted from the heart rate variability (HRV) based on the first and second conditional moments of time-frequency distribution (TFD) as an additional guide for seizure detection in newborn. The features of HRV in the low frequency band (LF: 0-0.07 Hz), mid frequency band (MF: 0.07-0.15 Hz), and high frequency band (HF: 0.15-0.6 Hz) have been obtained by means of the time-frequency analysis using the modified-B distribution (MBD). Results of ongoing time-frequency research are presented. Based on our preliminary results, the first conditional moment of HRV which is also known as the mean/central frequency in the LF band and the second conditional moment of HRV which is also known as the variance/instantaneous bandwidth (IB) in the HF band can be used as a good feature to discriminate the newborn seizure from the non-seizure