HIGH RESOLUTION 2-DIMENSIONAL POWER SPECTRAL ESTIMATION

A neural net algorithm for multidimensional maximum entropy spectrum estimation

Maximum entropy canonical correlations

A method for finding an approximate solution of the maximum entropy (ME) method for bearing estimation is presented. It is especially suitable for the coherent source problem. This solution shows that the ME spectrum is an all-pole spectrum and the coefficients of its denominator polynomial can be found from the estimation error for the signals. Since no spatial smoothing is required, it is possible to find a solution for two closely spaced sources with a three-element array, based on single snapshot data. Depending on how the signal is estimated, it is possible to find a superresolution spectrum with the discrete Fourier transform (DFT) only.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

: This tutorial paper describes the maximum entropy spectrum and the Burg technique for computing the prediction error power and prediction error filter coefficients in the associated spectral estimation formula. The maximum entropy spectrum is identical to the autoregressive spectral estimator. Also included in this paper is a discussion of the K-line spectrum, which is the wavenumber analogue of the frequency-domain maximum entropy spectrum, and the Burg technique modifications necessary for its implementation. The purpose of this paper is to provide a complete and self-contained account of the main features of the maximum entropy spectrum. Since many of the relevant mathematical derivations are not found in the formal published literature, they are incorporated in this paper. Supporting material and various sidelights of the maximum entropy spectrum appear in the appendices.

Multicollinearity hampers empirical econometrics. The remedies proposed to date suffer from pitfalls of their own. The ridge estimator is not generally accepted as a vital alternative to the ordinary least-squares (OLS) estimator because it depends upon unknown parameters. The generalized maximum entropy (GME) estimator of Golan, Judge and Miller depends upon subjective exogenous information that affects the estimated parameters in an unpredictable way. This paper presents novel maximum entropy estimators inspired by the theory of light that do not depend upon any additional information. Monte Carlo experiments show that they are not affected by any level of multicollinearity and dominate OLS uniformly. The Leuven estimators are consistent and asymptotically normal.

We propose a new learning method for discrete space statistical classifiers. Similar to Chow and Liu (1968) and Cheeseman (1983), we cast classification/inference within the more general framework of estimating the joint probability mass function (p.m.f.) for the (feature vector, class label) pair. Cheeseman's proposal to build the maximum entropy (ME) joint p.m.f. consistent with general lower-order probability constraints is in principle powerful, allowing general dependencies between features. However, enormous learning complexity has severely limited the use of this approach. Alternative models such as Bayesian networks (BNs) require explicit determination of conditional independencies. These may be difficult to assess given limited data. Here we propose an approximate ME method, which, like previous methods, incorporates general constraints while retaining quite tractable learning. The new method restricts joint p.m.f. support during learning to a small subset of the full feature space. Classification gains are realized over dependence trees, tree-augmented naive Bayes networks, BNs trained by the Kutato algorithm, and multilayer perceptrons. Extensions to more general inference problems are indicated. We also propose a novel exact inference method when there are several missing features.

Power spectral analysis normal and pathological brainstem auditory evoked potentials

The spectral resolution and statistical significance of a harmonic analysis obtained by low‐order maximum entropy methods (MEM) can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA‐MEM method is applied both to a synthetic time series and a time series of atmospheric angular momentum (AAM) data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, we detect reliable evidence for intraseasonal and interannual oscillations in AAM. The interannual periods include a quasi‐biennial one and a low‐frequency one, of 5 years, both related to the El Niño/Southern Oscillation. In the intraseasonal band, separate oscillations of about 48.5 and 51 days are ascertained.

Inversion of emissivity spectrum and temperature in the TIR waveband based on the Maximum Entropy

주행중인 차량의 동적 거동에 대한 응답을 해석하기 위하여 시간영역에서 뿐만 아니라 주파수 영역에서의 해석이 필요하다. 주파수 영역에서의 해석을 위하여 시간영역에서의 값을 FFT를 이용하여 주파수 영역으로 변화하는 방법이 일반적으로 사용되어 왔다. 본 연구에서는 최대 엔트로피 방법을 이용하여 기존의 FFT 방법보다 차량의 과도응답특성을 시간영역 및 주파수 영역에서 편리하게 해석할 수 있는 방법을 제시하고 있다. In this paper the nonstationary response of accelerating vehicle is firstly obtained by using nonstationary road roughness model in time domain. To get the result of nonstationary response in frequency domain, the maximum entropy method is used for Processing nonstationary response of vehicle in frequency domain. The three-dimensional transient maximum entropy spectrum (MES) of response is given.

Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

Price responsiveness of herbicide demand in corn for farmers in Indiana's White River Basin using cross-section data from individual farms is estimated. Particular attention is paid to appropriate treatment of binding nonnegativity constraints. Estimation was first attempted using an approach to demand systems estimation suggested by Lee and Pitt. However, analytical and computational difficulties effectively preclude estimation by the Lee and Pitt approach. As an alternative, a maximum entropy (ME) approach is presented and discussed. Results from the ME estimator tentatively indicate limited response of herbicide demand to changes in own prices. The maximum entropy approach to demand systems estimation appears to have merit and warrants further attention.

An ME-based approximation for multi-server queues with preemptive priority

A method for determining the maximum entropy (ME) estimate of the full joint transmit/receive MIMO channel covariance matrix is presented, where only knowledge of the separate transmit and receive covariances is assumed. The resulting ME covariance is similar to, but distinct from, the Kronecker modelling strategy, warranting a direct comparison of the two techniques. Application of the method to wideband indoor multiple-input multiple-output (MIMO) measurements taken at 2.4 GHz indicates a slight improvement in the modelling accuracy of the dominant covariance eigenvalues compared to the Kronecker model. On the other hand, the double-directional joint transmit/receive Bartlett spectra are nearly identical, indicating that the ME technique does not significantly improve modelling of the channel multipath structure. This fact suggests that accurate multipath modelling for MIMO systems may not be possible without detailed joint transmit/receive channel knowledge.

We present a computationally efficient method of calculating confidence intervals for the maximum entropy (ME) or autoregressive (AR) spectrum, based on new theoretical considerations. The method is consistent with the well-known asymptotic results, and it can be incorporated under certain assumptions into the Levinson-Durbin recursion. The method is also extended to ME wavenumber estimation.