A statistical procedure for testing social reciprocity at group, dyadic and individual levels

This paper examines statistical analysis of social reciprocity, that is, the balance between addressing and receiving behaviour in social interactions. Specifically, it focuses on the measurement of social reciprocity by means of directionality and skew-symmetry statistics at different levels. Two statistics have been used as overall measures of social reciprocity at group level: the directional consistency and the skew-symmetry statistics. Furthermore, the skew-symmetry statistic allows social researchers to obtain complementary information at dyadic and individual levels. However, having computed these measures, social researchers may be interested in testing statistical hypotheses regarding social reciprocity. For this reason, it has been developed a statistical procedure, based on Monte Carlo sampling, in order to allow social researchers to describe groups and make statistical decisions.

A statistical test vs. a validation experiment in Gene Expression Study

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Social reciprocity measures based on dyadic discrepancies: Methodological review and software development

This paper examines statistical analysis of social reciprocity at group, dyadic, and individual levels. Given that testing statistical hypotheses regarding social reciprocity can be also of interest, a statistical procedure based on Monte Carlo sampling has been developed and implemented in R in order to allow social researchers to describe groups and make statistical decisions.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

An exploratory study of the effect of aspect-oriented programming on maintainability

In this paper we describe an exploratory assessment of the effect of aspect-oriented programming on software maintainability. An experiment was conducted in which 11 software professionals were asked to carry out maintenance tasks on one of two programs. The first program was written in Java and the second in AspectJ. Both programs implement a shopping system according to the same set of requirements. A number of statistical hypotheses were tested. The results did seem to suggest a slight advantage for the subjects using the object-oriented system since in general it took the subjects less time to answer the questions on this system. Also, both systems appeared to be equally difficult to modify. However, the results did not show a statistically significant influence of aspect-oriented programming at the 5% level. We are aware that the results of this single small study cannot be generalized. We conclude that more empirical research is necessary in this area to identify the benefits of aspect-oriented programming and we hope that this paper will encourage such research.

Notes on the theory of statistical estimation and of testing hypotheses : lectures /

"Notes prepared by Ralph J. Brookner."

Synergistic epistasis and alternative hypotheses.

Inbreeding generally results in deleterious shifts in mean fitness. If the fitness response to increasing inbreeding coefficient is non-linear, this suggests a contribution of epistasis to inbreeding depression. In a cross-breeding experiment, Salathe & Ebert (2003. J. Evol. Biol. 16: 976-985) tested and found the presence of this non-linearity in Daphnia magna. They argue that epistatic interactions cause this non-linearity. We argue here that their experimental protocol does not allow disentangling the effect of synergistic epistasis from two alternative hypotheses, namely hybrid vigour and statistical non-independence of data.

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes.Against this background the relevance of perturbations and subcompositions can beclearly seen. Moreover we can identify a number of hypotheses of interest involvingthe specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Comparison and validation of tissue modelization and statistical classification methods in T1-weighted MR brain images.

This paper presents a validation study on statistical nonsupervised brain tissue classification techniques in magnetic resonance (MR) images. Several image models assuming different hypotheses regarding the intensity distribution model, the spatial model and the number of classes are assessed. The methods are tested on simulated data for which the classification ground truth is known. Different noise and intensity nonuniformities are added to simulate real imaging conditions. No enhancement of the image quality is considered either before or during the classification process. This way, the accuracy of the methods and their robustness against image artifacts are tested. Classification is also performed on real data where a quantitative validation compares the methods' results with an estimated ground truth from manual segmentations by experts. Validity of the various classification methods in the labeling of the image as well as in the tissue volume is estimated with different local and global measures. Results demonstrate that methods relying on both intensity and spatial information are more robust to noise and field inhomogeneities. We also demonstrate that partial volume is not perfectly modeled, even though methods that account for mixture classes outperform methods that only consider pure Gaussian classes. Finally, we show that simulated data results can also be extended to real data.

Statistical hypothesis testing and common misinterpretations: should we abandon p-value in forensic science applications?

Many people regard the concept of hypothesis testing as fundamental to inferential statistics. Various schools of thought, in particular frequentist and Bayesian, have promoted radically different solutions for taking a decision about the plausibility of competing hypotheses. Comprehensive philosophical comparisons about their advantages and drawbacks are widely available and continue to span over large debates in the literature. More recently, controversial discussion was initiated by an editorial decision of a scientific journal [1] to refuse any paper submitted for publication containing null hypothesis testing procedures. Since the large majority of papers published in forensic journals propose the evaluation of statistical evidence based on the so called p-values, it is of interest to expose the discussion of this journal's decision within the forensic science community. This paper aims to provide forensic science researchers with a primer on the main concepts and their implications for making informed methodological choices.

Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie

Dans ce texte, nous analysons les développements récents de l’économétrie à la lumière de la théorie des tests statistiques. Nous revoyons d’abord quelques principes fondamentaux de philosophie des sciences et de théorie statistique, en mettant l’accent sur la parcimonie et la falsifiabilité comme critères d’évaluation des modèles, sur le rôle de la théorie des tests comme formalisation du principe de falsification de modèles probabilistes, ainsi que sur la justification logique des notions de base de la théorie des tests (tel le niveau d’un test). Nous montrons ensuite que certaines des méthodes statistiques et économétriques les plus utilisées sont fondamentalement inappropriées pour les problèmes et modèles considérés, tandis que de nombreuses hypothèses, pour lesquelles des procédures de test sont communément proposées, ne sont en fait pas du tout testables. De telles situations conduisent à des problèmes statistiques mal posés. Nous analysons quelques cas particuliers de tels problèmes : (1) la construction d’intervalles de confiance dans le cadre de modèles structurels qui posent des problèmes d’identification; (2) la construction de tests pour des hypothèses non paramétriques, incluant la construction de procédures robustes à l’hétéroscédasticité, à la non-normalité ou à la spécification dynamique. Nous indiquons que ces difficultés proviennent souvent de l’ambition d’affaiblir les conditions de régularité nécessaires à toute analyse statistique ainsi que d’une utilisation inappropriée de résultats de théorie distributionnelle asymptotique. Enfin, nous soulignons l’importance de formuler des hypothèses et modèles testables, et de proposer des techniques économétriques dont les propriétés sont démontrables dans les échantillons finis.

Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.

Statistical Object Recognition

Two formulations of model-based object recognition are described. MAP Model Matching evaluates joint hypotheses of match and pose, while Posterior Marginal Pose Estimation evaluates the pose only. Local search in pose space is carried out with the Expectation--Maximization (EM) algorithm. Recognition experiments are described where the EM algorithm is used to refine and evaluate pose hypotheses in 2D and 3D. Initial hypotheses for the 2D experiments were generated by a simple indexing method: Angle Pair Indexing. The Linear Combination of Views method of Ullman and Basri is employed as the projection model in the 3D experiments.

Compositional hypotheses of subcompositional stability and specific perturbation change and their testing

In standard multivariate statistical analysis common hypotheses of interest concern changes in mean vectors and subvectors. In compositional data analysis it is now well established that compositional change is most readily described in terms of the simplicial operation of perturbation and that subcompositions replace the marginal concept of subvectors. To motivate the statistical developments of this paper we present two challenging compositional problems from food production processes. Against this background the relevance of perturbations and subcompositions can be clearly seen. Moreover we can identify a number of hypotheses of interest involving the specification of particular perturbations or differences between perturbations and also hypotheses of subcompositional stability. We identify the two problems as being the counterpart of the analysis of paired comparison or split plot experiments and of separate sample comparative experiments in the jargon of standard multivariate analysis. We then develop appropriate estimation and testing procedures for a complete lattice of relevant compositional hypotheses

Self-play: statistical significance

Heinz recently completed a comprehensive experiment in self-play using the FRITZ chess engine to establish the ‘decreasing returns’ hypothesis with specific levels of statistical confidence. This note revisits the results and recalculates the confidence levels of this and other hypotheses. These appear to be better than Heinz’ initial analysis suggests.