In case a. we mentioned the lemma of Neyman & Pearson, and using log ratio statistics. In this case we have to estimate which of the two suggested hypotheses is true (which one is more likely). In case b. we have one hypothesis H0 and we have to estimate if it is true or not. In science, usually the null hypothesis H0 says the dull regular conception that everyone goes by, and the scientist wis...

We also saw how to use the Neyman-Pearson lemma to derive a lower bound when M = 2, which is the simple versus simple hypothesis testing case. This is known as Le Cam’s method At the end of last class, I mentioned how Le Cam’s method doesn’t work well for multi-dimensional estimation problems. To see why, let’s revisit the gaussian mean estimation problem where ρ = ‖ · ‖2 and Φ(t) = t, but now ...

In this paper we consider situations in which model based analytical redundancy is to be used to detect faults via a Neyman-Pearson approach to hypothesis testing. In 3] we examined how the statistical power of the resultant test statistic could be improved via the use of reduced order models. Here we extend the work to cover the eeect of static non-linearities by using the stochastic embedding...

In this article we consider the Two-Way ANOVA model with unequal cell frequencies without the assumption of equal error variances. By taking the generalized approach to finding p-values, classical F-tests for no interaction effects and equal main effects are extended under heteroscedasticity. The generalized Ftests developed in this article can be utilized in significance testing or in fixed le...

| General formulas for entropy, mutual information, and divergence are established. It is revealed that these quantities are actually determined by three decisive sequences of random variables; which are, respectively, the normalized source information density, the normalized channel information density, and the normalized log-likelihood ratio. In terms of the ultimate cumulative distribution f...

Consider a set of sensors that receive observations from the environment and transmit finite-valued messages to a fusion center that makes a final decision on one out of M alternative hypotheses. The problem is to provide rules according to which the sensors should decide what to transmit, in order to optimize a measure of organizational performance. We overview the available theory for the Bay...

It is shown that the global power function of any nonparametric test is flat on balls of alternatives except for alternatives coming from a finite dimensional subspace. The present benchmark is here the upper one-sided (or two-sided) envelope power function. Every choice of a test fixes a priori a finite dimensional region with high power. It turns out that also the level points are far away fr...

This paper addresses the problem of multiplicative jump detection and estimation in the time-scale plane. The signature is derived for a multiplicative jump in the time-scale plane. The signature allows the study of two wavelet based detectors. The first detector computes the Continuous Wavelet Transform (CWT) correlation with 2D signature. The second detector sums k e d scale slices of the CWT...

Expressions for "-entropy rate, "-mutual information rate and "-divergence rate are introduced. These quantities, which consist of the quantiles of the asymptotic information spectra, generalize the inf/sup-entropy/information/divergence rates of Han and Verd u. The algebraic properties of these information measures are rigorously analyzed, and examples illustrating their use in the computation...

We present multivariate statistics to detect intensity changes in longitudinal, multimodal, three-dimensional MRI data from patients with multiple sclerosis (MS). Working on a voxel-by-voxel basis, and considering that there is at most one such change-point in the time series of MR images, two complementary statistics are given, which aim at detecting disease activity. We show how to derive the...