Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distributionF if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the Savage representation. Examples of scoring rules for probabilistic forecasts in the form of predictive densities include the logarithmic, spherical, pseudospherical, and quadratic scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rules, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring rules for quantile and interval forecasts are also discussed. We relate proper scoring rules to Bayes factors and to cross-validation, and propose a novel form of cross-validation known as random-fold cross-validation. A case study on probabilistic weather forecasts in the North American Pacific Northwest illustrates the importance of propriety. We note optimum score approaches to point and quantile estimation, and propose the intuitively appealing interval score as a utility function in interval estimation that addresses width as well as coverage.
A general method is developed to generate fuzzy rules from numerical data. The method consists of five steps: divide the input and output spaces of the given numerical data into fuzzy regions; generate fuzzy rules from the given data; assign a degree of each of the generated rules for the purpose of resolving conflicts among the generated rules; create a combined fuzzy rule base based on both the generated rules and linguistic rules of human experts; and determine a mapping from input space to output space based on the combined fuzzy rule base using a defuzzifying procedure. The mapping is proved to be capable of approximating any real continuous function on a compact set to arbitrary accuracy. Applications to truck backer-upper control and time series prediction problems are presented.>
This volume presents late-1990s thinking on monetary policy rules and seeks to determine just what types of rules and policy guidelines function best. A co-operative research effort that allowed contributors to evaluate different policy rules using their own specific approaches, this collection presents their findings on the potential response of interest rates to an array of variables, including alterations in the rates of inflation, unemployment, and exchange. This work illustrates that simple policy rules are more robust and more efficient than complex rules with multiple variables. A state-of-the-art appraisal of the fundamental issues facing the Federal Reserve Board and other central banks, the text should be of interest for economic analysts and policymakers alike.
This essay proposes an emotion-management perspective as a lens through which to inspect the self, interaction, and structure. Emotion, it is argued, can be and ofter is subject to acts of management. The individual often works on inducing or inhibiting feelings so as to render them "appropriate" to a situation. The emotion-management perspective draws on an interactive account of emotion. It differs from the dramaturgical perspective on the one hand and the psychoanalytic perspective on the other. It allows us to inspect at closer range than either of those perspectives the relation among emotive experience, emotion management, feeling rules, and ideology. Feeling rules are seen as the side of ideology that deals with emotion and feeling. Emotion management is the type of work it takes to cope with feeling rules. Meaning-making jobs, more common in the middle class, put more premium on the individual's capacity to do emotion work. A reexamination of class differences in child rearing suggest that middle-class families prepare their children for emotion management more and working-class families prepare them less. In this way each prepares its children to psychologically reproduce the class structure.
In this article we study the amortized efficiency of the “move-to-front” and similar rules for dynamically maintaining a linear list. Under the assumption that accessing the ith element from the front of the list takes θ(i) time, we show that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules. Other natural heuristics, such as the transpose and frequency count rules, do not share this property. We generalize our results to show that move-to-front is within a constant factor of optimum as long as the access cost is a convex function. We also study paging, a setting in which the access cost is not convex. The paging rule corresponding to move-to-front is the “least recently used” (LRU) replacement rule. We analyze the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule (Belady's MIN algorithm) by a factor that depends on the size of fast memory. No on-line paging algorithm has better amortized performance.
In the context of the development of prototypic assessment instruments in the areas of cognition, personality, and adaptive functioning, the issues of standardization, norming procedures, and the important psychometrics of test reliability and validity are evaluated critically. Criteria, guidelines, and simple rules of thumb are provided to assist the clinician faced with the challenge of choosing an appropriate test instrument for a given psychological assessment. Clinicians are often faced with the critical challenge of choosing the most appropriate available test instrument for a given psychological assessment of a child, adolescent, or adult of a particular age, gender, and class of disability. It is the purpose of this report to provide some criteria, guidelines, or simple rules of thumb to aid in this complex scientific decision. As such, it draws upon my experience with issues of test development, standardization, norming procedures, and important psychometrics, namely, test reliability and validity. As I and my colleagues noted in an earlier publication, the major areas of psychological functioning, in the normal development of infants, children, adolescents, adults, and elderly people, include cognitive, academic, personality, and adaptive behaviors (Sparrow, Fletcher, & Cicchetti, 1985). As such, the major examples or applications discussed in this article derive primarily, although not exclusively, from these several areas of human functioning.
Goodness-of-fit (GOF) indexes provide "rules of thumb"—recommended cutoff values for assessing fit in structural equation modeling. Hu and Bentler (1999) proposed a more rigorous approach to evaluating decision rules based on GOF indexes and, on this basis, proposed new and more stringent cutoff values for many indexes. This article discusses potential problems underlying the hypothesis-testing rationale of their research, which is more appropriate to testing statistical significance than evaluating GOF. Many of their misspecified models resulted in a fit that should have been deemed acceptable according to even their new, more demanding criteria. Hence, rejection of these acceptable-misspecified models should have constituted a Type 1 error (incorrect rejection of an "acceptable" model), leading to the seemingly paradoxical results whereby the probability of correctly rejecting misspecified models decreased substantially with increasing N. In contrast to the application of cutoff values to evaluate each solution in isolation, all the GOF indexes were more effective at identifying differences in misspecification based on nested models. Whereas Hu and Bentler (1999) offered cautions about the use of GOF indexes, current practice seems to have incorporated their new guidelines without sufficient attention to the limitations noted by Hu and Bentler (1999).
In Information Rules, authors Shapiro and Varian reveal that many classic economic concepts can provide the insight and understanding necessary to succeed in the information age. They argue that if managers seriously want to develop effective strategies for competing in the new economy, they must understand the fundamental economics of information technology. Whether information takes the form of software code or recorded music, is published in a book or magazine, or even posted on a website, managers must know how to evaluate the consequences of pricing, protecting, and planning new versions of information products, services, and systems. The first book to distill the economics of information and networks into practical business strategies, Information Rules is a guide to the winning moves that can help business leaders navigate successfully through the tough decisions of the information economy. Subjects covered include: Competitive advantage, Economic analysis, Game theory, Information age, Information economy, Information technology, Intellectual property, Marketing strategy, New economy, Pricing, Pricing strategy, Value of information
We describe novel computational techniques for constructing induction rules for deductive synthesis proofs. Deductive synthesis holds out the promise of automated construction of correct computer programs from specifications of their desired behaviour. Synthesis of programs with iteration or recursion requires inductive proof, but standard techniques for the construction of appropriate induction rules are restricted to recycling the recursive structure of the specifications. What is needed is induction rule construction techniques that can introduce novel recursive structures. We show that a combination of rippling and the use of meta-variables as a least-commitment device can provide such novelty.
We are given a large database of customer transactions. Each transaction consists of items purchased by a customer in a visit. We present an efficient algorithm that generates all significant association rules between items in the database. The algorithm incorporates buffer management and novel estimation and pruning techniques. We also present results of applying this algorithm to sales data obtained from a large retailing company, which shows the effectiveness of the algorithm.
In the effort to understand the evolution of mammalian brains, we have found that common relationships between brain structure mass and numbers of nonneuronal (glial and vascular) cells apply across eutherian mammals, but brain structure mass scales differently with numbers of neurons across structures and across primate and nonprimate clades. This suggests that the ancestral scaling rules for mammalian brains are those shared by extant nonprimate eutherians - but do these scaling relationships apply to marsupials, a sister group to eutherians that diverged early in mammalian evolution? Here we examine the cellular composition of the brains of 10 species of marsupials. We show that brain structure mass scales with numbers of nonneuronal cells, and numbers of cerebellar neurons scale with numbers of cerebral cortical neurons, comparable to what we have found in eutherians. These shared scaling relationships are therefore indicative of mechanisms that have been conserved since the first therians. In contrast, while marsupials share with nonprimate eutherians the scaling of cerebral cortex mass with number of neurons, their cerebella have more neurons than nonprimate eutherian cerebella of a similar mass, and their rest of brain has fewer neurons than eutherian structures of a similar mass. Moreover, Australasian marsupials exhibit ratios of neurons in the cerebral cortex and cerebellum over the rest of the brain, comparable to artiodactyls and primates. Our results suggest that Australasian marsupials have diverged from the ancestral Theria neuronal scaling rules, and support the suggestion that the scaling of average neuronal cell size with increasing numbers of neurons varies in evolution independently of the allocation of neurons across structures.
Three rules which have been found useful, on an empirical basis, to predict the relative facility of ring forming reactions are presented; the physical bases of such rules are described.
Widely used constitutive laws for engineering materials assume plastic incompressibility, and no effect on yield of the hydrostatic component of stress. However, void nucleation and growth (and thus bulk dilatancy) are commonly observed is some processes which are characterized by large local plastic flow, such as ductile fracture. The purpose of this work is to develop approximate yield criteria and flow rules for porous (dilatant) ductile materials, showing the role of hydrostatic stress in plastic yield and void growth. Other elements of a constitutive theory for porous ductile materials, such as void nucleation, plastic flow and hardening behavior, and a criterion for ductile fracture will be discussed in Part II of this series. The yield criteria are approximated through an upper bound approach. Simplified physical models for ductile porous materials (aggregates of voids and ductile matrix) are employed, with the matrix material idealized as rigid-perfectly plastic and obeying the von Mises yield criterion. Velocity fields are developed for the matrix which conform to the macroscopic flow behavior of the bulk material. Using a distribution of macroscopic flow fields and working through a dissipation integral, upper bounds to the macroscopic stress fields required for yield are calculated. Their locus in stress space forms the yield locus. It is shown that normality holds for this yield locus, so a flow rule results. Approximate functional forms for the yield loci are developed.
We estimate a forward-looking monetary policy reaction function for the postwar United States economy, before and after Volcker's appointment as Fed Chairman in 1979. Our results point to substantial differences in the estimated rule across periods. In particular, interest rate policy in the Volcker-Greenspan period appears to have been much more sensitive to changes in expected inflation than in the pre-Volcker period. We then compare some of the implications of the estimated rules for the equilibrium properties of inflation and output, using a simple macroeconomic model, and show that the Volcker-Greenspan rule is stabilizing.
We live in a dynamic economic and commerical world, surrounded by objects of remarkable complexity and power. In many industries, changes in products and technologies have brought with them new kinds of firms and forms of organization. We are discovering news ways of structuring work, of bringing buyers and sellers together, and of creating and using market information. Although our fast-moving economy often seems to be outside of our influence or control, human beings create the things that create the market forces. Devices, software programs, production processes, contracts, firms, and markets are all the fruit of purposeful action: they are designed. Using the computer industry as an example, Carliss Y. Baldwin and Kim B. Clark develop a powerful theory of design and industrial evolution. They argue that the industry has experienced previously unimaginable levels of innovation and growth because it embraced the concept of modularity, building complex products from smaller subsystems that can be designed independently yet function together as a whole. Modularity freed designers to experiment with different approaches, as long as they obeyed the established design rules. Drawing upon the literatures of industrial organization, real options, and computer architecture, the authors provide insight into the forces of change that drive today's economy.
Recommendations to expand Cohen’s (1988) rules of thumb for interpreting effect sizes are given to include very small, very large, and huge effect sizes. The reasons for the expansion, and implications for designing Monte Carlo studies, are discussed.
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Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Fréchet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.