On differentiating the probability of error in multipopular feature selection

A method of linear feature selection for n dimensional observation vectors which belong to one of m populations is presented. Each population has a known apriori probability and is described by a known multivariate normal density function. Specifically we consider the problem of finding a k x n matrix B of rank k (k n) for which the transformed probability of misclassification is minimized. Providing that the transformed a posterior probabilities are distinct theoretical results are obtained which, for the case k = l, give rise to a numerically tractable formula for the derivative of the probability of misclassification. It is shown that for the two population problem this condition is also necessary. The dependence of the minimum probability of error on the a priori probabilities is investigated. The minimum probability of error satisfies a uniform Lipschitz condition with respect to the a priori probabilities

Bayesian Cointegrated Vector Autoregression models incorporating Alpha-stable noise for inter-day price movements via Approximate Bayesian Computation

We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level shifts which are not accurately modeled in the standard Gaussian error correction model (ECM) framework. This involves developing a novel matrix variate Bayesian CVAR mixture model comprised of Gaussian errors intra-day and Alpha-stable errors inter-day in the ECM framework. To achieve this we derive a novel conjugate posterior model for the Scaled Mixtures of Normals (SMiN CVAR) representation of Alpha-stable inter-day innovations. These results are generalized to asymmetric models for the innovation noise at inter-day boundaries allowing for skewed Alpha-stable models. Our proposed model and sampling methodology is general, incorporating the current literature on Gaussian models as a special subclass and also allowing for price series level shifts either at random estimated time points or known a priori time points. We focus analysis on regularly observed non-Gaussian level shifts that can have significant effect on estimation performance in statistical models failing to account for such level shifts, such as at the close and open of markets. We compare the estimation accuracy of our model and estimation approach to standard frequentist and Bayesian procedures for CVAR models when non-Gaussian price series level shifts are present in the individual series, such as inter-day boundaries. We fit a bi-variate Alpha-stable model to the inter-day jumps and model the effect of such jumps on estimation of matrix-variate CVAR model parameters using the likelihood based Johansen procedure and a Bayesian estimation. We illustrate our model and the corresponding estimation procedures we develop on both synthetic and actual data.Comment: 30 page

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions

Necessary and sufficient conditions are given for a maximum likelihood estimate of a subset of mixture proportions. From these conditions, likelihood equations are derived satisfied by the maximum-likelihood estimate and a successive-approximations procedure is discussed as suggested by equations for numerically evaluating the maximum-likelihood estimate. It is shown that, with probability one for large samples, this procedure converges locally to the maximum-likelihood estimate whenever a certain step-size lies between zero and two. Furthermore, optimal rates of local convergence are obtained for a step-size which is bounded below by a number between one and two

Rapid Water Reduction to H_2 Catalyzed by a Cobalt Bis(iminopyridine) Complex

A cobalt bis(iminopyridine) complex is a highly active electrocatalyst for water reduction, with an estimated apparent second order rate constant k_(app) ≤ 10^7 M^(–1)s^(–1) over a range of buffer/salt concentrations. Scan rate dependence data are consistent with freely diffusing electroactive species over pH 4–9 at room temperature for each of two catalytic reduction events, one of which is believed to be ligand based. Faradaic H_2 yields up to 87 ± 10% measured in constant potential electrolyses (−1.4 V vs SCE) confirm high reactivity and high fidelity in a catalyst supported by the noninnocent bis(iminopyridine) ligand. A mechanism involving initial reduction of Co^(2+) and subsequent protonation is proposed

Horn antenna with v-shaped corrugated surface

Corrugated shape is easily machined for millimeter wave application and is better suited for folding antenna designs. Measured performance showed ""V'' corrugations and rectangular corrugations have nearly the same pattern beamwidth, gain, and impedance. Also, ""V'' corrugations have higher relative power loss

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions, Addendum

New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence

Design and Construction of the 3.2 Mev High Voltage Column for Darht II

A 3.2 MeV injector has been designed and built for the Darht II Project at Los Alamos Lab. The installation of the complete injector system is nearing completion at this time. The requirements for the injector are to produce a 3.2 MeV, 2000 ampere electron pulse with a flattop width of at least 2-microseconds and emittance of less than 0.15 p cm-rad normalized. A large high voltage column has been built and installed. The column is vertically oriented, is 4.4 meters long, 1.2 meters in diameter, and weights 5700 kilograms. A novel method of construction has been employed which utilizes bonded mycalex insulating rings. This paper will describe the design, construction, and testing completed during construction. Mechanical aspects of the design will be emphasized.Comment: 3 pages, 4 figures, Linac 200

Estimating normal mixture parameters from the distribution of a reduced feature vector

A FORTRAN computer program was written and tested. The measurements consisted of 1000 randomly chosen vectors representing 1, 2, 3, 7, and 10 subclasses in equal portions. In the first experiment, the vectors are computed from the input means and covariances. In the second experiment, the vectors are 16 channel measurements. The starting covariances were constructed as if there were no correlation between separate passes. The biases obtained from each run are listed