There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper proposes a very tractable approach to modeling changes in regime. The parameters of an autoregression are viewed as the outcome of a discrete-state Markov process. For example, the mean growth rate of a nonstationary series may be subject to occasional, discrete shifts. The econometrician is presumed not to observe these shifts directly, but instead must draw probabilistic inference about whether and when they may have occurred based on the observed behavior of the series. The paper presents an algorithm for drawing such probabilistic inference in the form of a nonlinear iterative filter

A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.

Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Forecasting with artificial neural networks: the state of the art

Recurrence plots for the analysis of complex systems

A periodic signal can be perfectly predicted far into the future since it perfectly repeats every period. There is always some variation in the waveform over time for signals which are labeled as periodic but which are not truly deterministic. A formal definition is presented in this paper for such a varying periodic signal and the properties of such a class of signals are exploited. A measure called a signal coherence function of the amount of random variation in each Fourier component of the signal is defined and its statistical properties are developed. This signal coherence function is very different from the coherence function between two stationary signals. The method is applied to a digitized record of an acoustic signal generated by a boat in a bag in the Baltic Sea south of Stockholm, Sweden.

/pdf/a-statistical-theory-of-signal-coherence-moo47qap63.pdf

A statistical theory of signal coherence

An exposition of higher order cumulants is given using the case of M=6. The basic relationship between the cumulant spectrum of a stationary time series and its polyspectrum is presented. Then the variance and covariance of the sample bispectrum is derived using a relationship between cumulant spectra of the finite Fourier transform for M=2 and 4, and the bispectrum and trispectrum of the time series. >

Higher order cumulants and cumulant spectra

EEG and field potential rhythms established in the cortex and thalamus may accommodate the propagation of seizures. This article describes the interaction between thalamus and cortex during pentylenetetrazol (PTZ) seizures in rats with and without prior treatment with ethosuximide (ESM), a well-known antiepileptic drug (AED) that raises the threshold for seizures, was given before PTZ. The AED was given before PTZ convulsant administration. We track this thalamo-cortical association with a novel measure we have called the cross-bicoherence gain, or BISCOH. This quantity allows us to measure the spectral coherence in a purely higher order spectralmethodology. BISCOH is able to track the formation of nonlinearities at specific frequencies in the recorded EEG. BISCOH showed a strong increase in low alpha wave harmonic generationat 10 and 12.5 Hz after ESM treatment (p < 0.02 and p < 0.007, respectively). Conventional coherence failed to show distinctive and significant changes in thalamo-cortical coupling after ESM treatment at those frequencies and instead showed changes at 5 Hz. This rise in cortical rhythms is evidence of harmonic generation or new frequency formation in the thalamo-cortical system withAED therapy. BISCOH could become a powerful tool in unraveling changes in coherence due to neuroelectric modulation resulting from drug treatment or electrical stimulation.

/pdf/detection-of-nonlinear-interactions-of-eeg-alpha-waves-in-4wt0i275g2.pdf

Detection of nonlinear interactions of EEG alpha waves in the brain by a new coherence measure and its application to epilepsy and anti-epileptic drug therapy.

Two American political scientists and a Ukrainian sociologist analyze the results of Ukraine's 1998 parliamentary elections. The purpose is to test propositions about the cognitive organization of voters' attitudes about issues and evaluations of the political parties that seek to mobilize their vote. The article then examines differences on these scores between the East and West of the country. A test is provided of the spatial model of voting that has been found to be a successful predictor of belief organization in other countries and milieux.

Ukraine's 1998 Parliamentary Elections: A Spatial Analysis

This paper presents an empirical analysis of two models of non-voting which Ordeshook and I incorporated into the spatial theory of electoral competition. We called these models abstention from alienation and abstention from indifference since our goal was to formalize established social-psychological hypotheses of non-voting. The data used in this paper is part of the 1968 election survey conducted by the University of Michigan's Survey Research Center.

/pdf/some-evidence-on-non-voting-models-in-the-spatial-theory-of-1w8o7qvt3u.pdf

Melvin J. Hinich

Papers

A statistical theory of signal coherence

Higher order cumulants and cumulant spectra

Detection of nonlinear interactions of EEG alpha waves in the brain by a new coherence measure and its application to epilepsy and anti-epileptic drug therapy.

Ukraine's 1998 Parliamentary Elections: A Spatial Analysis

Some evidence on non-voting models in the spatial theory of electoral competition