First-order Statistical Model Research Articles

Scale-Invariant Subspace Detectors Based on First- and Second-Order Statistical Models

The problem is to detect a multi-dimensional source transmitting an unknown sequence of complex-valued symbols to a multi-sensor array. In some cases the channel subspace is known, and in others only its dimension is known. Should the unknown transmissions be treated as unknowns in a first-order statistical model, or should they be assigned a prior distribution that is then used to marginalize a first-order model for a second-order statistical model? This question motivates the derivation of subspace detectors for cases where the subspace is known, and for cases where only the dimension of the subspace is known. For three of these four models the GLR detectors are known, and they have been reported in the literature. But the GLR detector for the case of a known subspace and a second-order model for the measurements is derived for the first time in this paper. When the subspace is known, second-order generalized likelihood ratio (GLR) tests outperform first-order GLR tests when the spread of subspace eigenvalues is large, while first-order GLR tests outperform second-order GLR tests when the spread is small. When only the dimension of the subspace is known, second-order GLR tests outperform first-order GLR tests, regardless of the spread of signal subspace eigenvalues. For a dimension-1 source, first-order and second-order statistical models lead to equivalent GLR tests. This is a new finding.

Creative Chord Sequence Generation for Electronic Dance Music

This paper describes the theory and implementation of a digital audio workstation plug-in for chord sequence generation. The plug-in is intended to encourage and inspire a composer of electronic dance music to explore loops through chord sequence pattern definition, position locking and generation into unlocked positions. A basic cyclic first-order statistical model is extended with latent diatonicity variables which permits sequences to depart from a specified key. Degrees of diatonicity of generated sequences can be explored and parameters for voicing the sequences can be manipulated. Feedback on the concepts, interface, and usability was given by a small focus group of musicians and music producers.

Application of Box–Wilson Optimization Technique to the Partially Oriented Yarn Properties

A static model for partially oriented yarn (POY) production was examined in a commercial POY spinning plant. A two-level factorial, industrial experimental design was used to identify a statistical model. Three independent variables effecting the elongation at break (a POY property of interest) were selected. Namely, yarn winding speed, spinneret flow rate, and spinneret hole diameter. Elongation at break was chosen as the dependent variable. A first-order statistical model was considered to show the dependence of the elongation at break on the operating parameters: 145%; for elongation at break, the optimum values of yarn winding speed, spinneret flow rate, and spinneret hole diameter were found to be as 2938 m/min, 49.74 g/min, and 205 μm, respectively. The statistical model and Box–Wilson steepest ascent method were used.

Application of a statistical technique to the production of Saccharomyces cerevisiae (baker's yeast).

The identification of a static model for Saccharomyces cerevisiae (baker's yeast) production under aerobic conditions has been realized. Two-level factorial experimental design was used to identify a statistical model. In order to find the optimal operating conditions by using the statistical model, Box-Wilson's steepest-ascent method was used [Box and Wilson (1951) J. R. Stat. Soc. Ser. B 13, 1]. Four independent variables which have an effect on aerobic yeast production were selected. These were temperature, pH, air flow rate and agitation rate. Yeast productivity was selected as the dependent variable. A first-order statistical model was considered to illustrate the dependence of the yeast productivity on the operating parameters. Optimum pH, temperature, air flow rate and agitation rate were determined as 5, 32 degrees C, 1 vol./vol. per min and 600 rev./min respectively.

The thermodynamics of liquid Fe-based ternary solutions containing nitrogen

Ternary Fe-based liquid solutions containing nitrogen have been analyzed in terms of a first-order statistical model. The model enables interaction energies between the dissolved N-atoms and the matrix to be extracted from measured solubility data. Such interaction energies have been deduced from experimental thermodynamic data and shown to correlate well with the Allred-Rochow electronegativities of the atomic species in the ternary liquids.

Statistical-Physical Models of Electromagnetic Interference

Most man-made and natural electromagnetic interference, or "noise," are highly non-Gaussian random processes, whose degrading effects on system performance can be severe, particularly on most conventional systems, which are designed for optimal or near optimal performance against normal noise. In addition, the nature, origins, measurement, and prediction of the general EM interference environment are a major concern of any adequate spectral management program. Accordingly, this study is devoted to the development of analytically tractable, experimentally verifiable, statistical-physical models of such electromagnetic interference. Here, classification into three major types of noise is made: Class A (narrow band vis-á-vis the receiver), Class B (broad band vis-á-vis the receiver), and Class C (= Class A + Class B). First-order statistical models are constructed for the Class A and Class B cases. In particular, the APD (a posteriori probability distribution) or exceedance probability, PD, vis;P1 (ϵ > ϵo)A,B, (and the associated probability densities, pdf's w1(ϵ)A,B,[1]) of the envelope are obtained; (the phase is shown to be uniformly distributed in (0, 2π). These results are canonical, i.e., their analytic forms are invariant of the particular noise source and its quantifying parameter values, levels, etc. Class A interference is described by a 3-parameter model, Class B noise by a 6-parameter model.