In this paper, we derived recurrence relations for joint moment generating functions of nonadjacent generalized order statistics (GOS) of random samples drawn from doubly truncated class of continuous distributions. Recurrence relations for joint moments of nonadjacent GOS (ordinary order statistics (OOS) and k-upper records (k-RVs) as special cases) are obtained. Single and product moment gene...

Most inverse classification algorithms address discrete attributes and can not deal with quantitative attributes. In order to overcome the disadvantage, the discretization algorithms are applied to the inverse classification algorithms, and the main idea is: firstly, a group of feature attributes are selected by using feature selection algorithm; then, the quantitative attributes are discretize...

In recent years, several inverse solutions of magnetoencephalography (MEG) have been proposed. Among them, the multiple signal classification (MUSIC) method utilizes spatiotemporal information obtained from magnetic fields. The conventional MUSIC method is, however, sensitive to Gaussian noise and a sufficiently large signal-to-noise ratio (SNR) is required to estimate the number of sources and...

Probability theory and statistics are two main tools in signal and image processing. Bayesian inference has a privileged place in developing methods for inverse problems arising in signal and image processing which can be applied in real world applications. In this tutorial presentation, first I will breifly present the Bayesian estimation approach in signal and image processing. Then, I will s...

Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints ca...

Glottal inverse filtering is a technique used to derive the glottal waveform during voiced speech. Closed phase inverse filtering (CPIF) is a common approach for achieving this goal. During the closed phase there is no input to the vocal tract and hence the impulse response of the vocal tract can be determined through linear prediction. However, a number of problems are known to exist with the ...

The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses on refining the power posterior approach to improve estimation of the evidence. The power posterior method involves transitioning from the prior to the posterior by powering the likelihood by an inv...

We study the joint distribution of descents and inverse descents over the set of permutations of n letters. Gessel conjectured that the two-variable generating function of this distribution can be expanded in a given basis with nonnegative integer coefficients. We investigate the action of the Eulerian operators that give the recurrence for these generating functions. As a result we devise a re...

"Trajectory Extension Learning" is a new technique for Learning Control in Robots which assumes that there exists some parameter of the desired trajectory that can be smoothly varied from a region of easy solvability of the dynamics to a region of desired behavior which may have more difficult dynamics. By gradually varying the parameter, practice movements remain near the desired path while a ...

Most inverse classification algorithms address discrete attributes and can not deal with quantitative attributes. In order to overcome the disadvantage, the discretization algorithms are applied to the inverse classification algorithms, and the main idea is: firstly, a group of feature attributes are selected by using feature selection algorithm; then, the quantitative attributes are discretize...