Quantum statistical inference for density estimation
A new penalized likelihood method for non-parametric density estimation is proposed, which is based on a mathematical analogy to quantum statistical physics. The mathematical procedure for density estimation is related to maximum entropy methods for inverse problems; the penalty function is a convex information divergence enforcing global smoothing toward default models, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing may be enforced by constraints on the expectation values of differential operators. Although the hyperparameters, covariance, and linear response to perturbations can be estimated by a variety of statistical methods, we develop the Bayesian interpretation. The linear response of the MAP estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood. The method is demonstrated on standard data sets.
The generation and behavior of the fractal Koch array factor from a Kaiser window generator is studied. The main advantage of using Kaiser windows is that pattern parameters become much more flexible through altering the Kaiser window. The mainlobe width, current distribution, side-lobe ratio are now adjustable. Different reduced array structures can be obtained by using different threshold levels. Higher threshold values result in a highly reduced number of elements but they may highly distort the pattern and, hence, the multiband behavior. Finally, we study the effect of quantization of the feeding values. Quantization is necessary for implementation and simplification purposes. Several configurations of current distributions with the corresponding patterns are illustrated for different quantization levels. It is shown that moderate quantization keeps the same interesting similarity properties at several bands.