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

http://www.la.utexas.edu/hinich/files/Politics/Spatial%20Analysis%20of%20Turkish%20Politics.pdf

A spatial analysis of Turkish party preferences

Abstentions and equilibrium in the electoral process

Two areas of political science that utilize rigorous deductive formulations are: (1) the paradox of voting, and (2) spatial analysis of election competition. It is not surprising that the analysis of the paradox and the development of spatial theory occur simultaneously because the concerns of both endeavors are parallel: we study the paradox to ascertain conditions under which majority-rule equilibria exist, that is, conditions under which at least one alternative exists that cannot be

A Theory of Electoral Equilibrium: A Spatial Analysis Based on the Theory of Games

/pdf/nonlinear-serial-dependence-and-the-weak-form-efficiency-of-27980cok13.pdf

Nonlinear serial dependence and the weak-form efficiency of Asian emerging stock markets

This essay ascertains some general conditions for equivalence and nonequivalence among six election objectives: 01, maximizing expected plurality; 02, maximizing proportion of expected vote; 02, maximizing expected vote; 04, maximizing probability that plurality exceeds some level; 05, maximizing probability that proportion of vote exceeds some level; 06, maximizing probability that vote exceeds some level. The major findings are these: (1) 01, 02, and 03 are equivalent if the election is zero-sum-like in expected vote; (2) 01 and 02 are equivalent if competition is strongly symmetric. A necessary condition for this equivalence is also presented for 2-candidate elections: (3) 01 and 04 are equivalent, as are 03 and 06, if the candidate's forecasting error is independent of all strategies; (4) 01 and 04 are equivalent for two-candidate elections, and for n-candidate elections 02 and 05 are equivalent, as are 03 and 06, if the distribution of a candidate's forecasting error is multivariate normal, and if the level of plurality, proportion, or vote to be exceeded is the minimax value of the election game under 01, 02, or 03; (5) findings of equivalence and nonequivalence depend upon the definition of equivalence (findings 1 and 2 rely upon an election with all candidates at equilibrium strategies, while findings 3 and 4 do not); (6) equivalence and nonequivalence among election objectives may be sensitive to the candidate's attitude toward risk, i.e., to the functional form of his utility function in pluraliy, vote proportion, or vote; election objectives depend on information, competitive environment, and constitutional arrangements. Hence, statements of preference for alternative election systems, laws, and reforms perforce entail reasonable theoretical expectations about the way in which these systems, laws, and reforms affect the candidates' campaign objectives, as well as about equivalence and nonequivalence among these objectives.

https://www.jstor.org/stable/pdfplus/1959747.pdf

Melvin J. Hinich

Papers

A spatial analysis of Turkish party preferences

Abstentions and equilibrium in the electoral process

A Theory of Electoral Equilibrium: A Spatial Analysis Based on the Theory of Games

Nonlinear serial dependence and the weak-form efficiency of Asian emerging stock markets

Election Goals and Strategies: Equivalent and Nonequivalent Candidate Objectives