Statistics

In the paper it is demonstrated that Bell's theorem is unproveable.

In a first investigation, a Lacan-motivated template of the Poe story is fitted to the data. A segmentation of the storyline is used in order to map out the diachrony. Based on this, it will be shown how synchronous aspects, potentially related to Lacanian registers, can be sought. This demonstrates the effectiveness of an approach based on a model template of the storyline narrative. In a second and more Comprehensive investigation, we develop an approach for revealing, that is, uncovering, Lacanian (...) register relationships. Objectives of this work include the wide and general application of our methodology. This methodology is strongly based on the “letting the data speak” Correspondence Analysis analytics Platform of Jean-Paul Benzécri, that is also the geometric data analysis, both qualitative and quantitative analytics, developed by Pierre Bourdieu. (shrink)

Abstract: -/- We present a teaching activity, whose aim is to enhance students’ understanding of color perception by introducing them to intersubjective color variations among normal perceivers. The approach can be used in different disciplines, including biology, philosophy, psychology, physics, or statistics, for different purposes and with college students having various levels of sophistication and scientific training.

Całość rozpoczyna teoretyczny rozdział matematyczno-statystyczny. Jego istota i charakter jest odmienny, od pozostałych dziewięciu rozdziałów praktyczno-specjalistycznych. Prezentuje on aparat matematyczno-statystyczny niezbędny do zrozumienia treści kolejnych kierunkowych już rozdziałów monografii. Treści merytoryczne tego rozdziału nie są zaprezentowane w formie systematycznego wykładu, czy prezentacji, ale przedstawiają jedynie sygnalnie i syntetycznie pojęcia, definicje, twierdzenia oraz zasady i metody, które stanowią fundament ich zastosowań w naukach ekonomicznych, finansach oraz informatyce. Rozdziały: od drugiego do dziesiątego są kierunkowymi rozdziałami specjalistycznymi i prezentują różne kierunki praktycznych zastosowań (...) metod matematycznych i statystycznych, czyli ilościowych. Rozdziały: drugi i trzeci dotyczą zarządzania finansami. Przy czym pierwszy z nich dotyczy naliczania odsetek w banku od dyspozytorów kredytów i obligacji. Kolejny zaś traktuje o metodach oceny ekonomicznej efektywności projektów inwestycyjnych i produkcyjnych oraz zawiera analizę wrażliwości wybranych wskaźników finansowych na zmiany czynników je tworzących. Rozdział czwarty prezentuje podstawowe informacje i zasady korzystania z arkusza kalkulacyjnego na przykładzie programu MS Excel wraz z omówieniem wybranych funkcji finansowych. W rozdziale piątym omówione są wybrane narzędzia wspomagające przetwarzanie danych informacji, jakimi są systemy SAS wykorzystywane przede wszystkim w interakcjach gospodarczych oraz w procesie dydaktycznym na uczelniach wyższych. Modele zachowań konsumenta, idea aproksymacji oraz wybrane mikroekonomiczne funkcje popytu zostały – wraz z przykładami – omówione w rozdziale szóstym. W rozdziale siódmym czytelnik znajdzie opis działań podejmowanych przez firmę w celu optymalizacji jej finansowego i gospodarczego funkcjonowania w okresie niepewności rynkowej na przykładzie pandemii COVID 19 i konkretnego przdsiębiorstwa. Dwa kolejne rozdziały: ósmy i dziewiąty są ze sobą ściśle zintegrowane. Oba one dotyczą niedookreślonych układów równań liniowych. Pierwszy z nich – o charakterze teoretycznym – poświęcony jest rozważaniom dotyczącym wykorzystywaniu rachunku macierzowego do rozwiązywania niedookreślonych układów równań liniowych. Kolejny zaś przedstawia praktyczne zastosowanie teoretycznych kwestii rozdziału poprzedniego do określenia wyceny wartości rynkowej nieruchomości. Monografię kończy rozdział dziesiąty dotyczący wybranych narzędzi wspierających proces sprzedaży usług finansowych wraz z prezentacją prognoz służących zminimalizowaniu ryzyka i błędów w procesie planowania sprzedaży w organizacji. W większości rozdziałów zawarte są rozwiązane przykładowo zadania z wyczerpującym komentarzem objaśniającym. Niniejsza monografia składa się z dziesięciu rozdziałów, jednak – zdaniem autorów – tematyka zastosowania metod ilościowych nie została w niej wyczerpana. Toteż planowana jest kolejna część tej publikacji zawierająca kontynuację podjętego i aktualnie rozpoczętego tematu. (shrink)

Previous work has shown that the Complex Conceptual Spaces − Single Observation Mathematical framework is a useful tool for event characterization. This mathematical framework is developed on the basis of Conceptual Spaces and uses integer linear programming to find the needed similarity values. The work of this paper is focused primarily on space event characterization. In particular, the focus is on the ranking of threats for malicious space events such as a kinetic kill. To make the Conceptual Spaces framework work, (...) the similarity values between the contents of observations on the one hand and the properties of the entities observed on the other needs to be found. This paper shows how to exploit Dempster-Shafer theory to implement a statistical approach for finding these similarities values. This approach will allow a user to identify the uncertainty involved in similarity value data, which can later be propagated through the developed mathematical model in order for the user to know the overall uncertainty in the observation-to-concept mappings needed for space event characterization. (shrink)

This marks a remarkable milestone when the serendipity-mindsponge-3D knowledge management theory is directly communicated through a well-known media channel like Politico.

Prior experimental studies of anomalous information reception (AIR) have been touted as strong evidence for postmortem survival of consciousness yet are plagued by several methodological weaknesses that preclude clear evidence of positive results. The present team provides an adversarial collaboration to identify and compensate for the major limitations of these previous approaches. We outline a more rigorous preregistered study design that eliminates or minimizes researcher bias in (a) data cleaning and (b) statistical analysis. Obtaining positive results with our recommended design (...) would arguably yield data that skeptics and sympathetic researchers would agree is more clearly interpretable and offers stronger support for a survivalist interpretation. However, this proposed study is not intended to be definitive but rather only a next step in a research program that aims to improve on earlier published efforts. It would also admittedly be time-consuming and expensive to implement, as well as raise ethical considerations in utilizing vulnerable research populations. However, these costs are required to achieve the rigor necessary to advance scientific knowledge in survival research. 1. Introduction -- 2. Laying a Working Foundation -- 3. Choice of "Survival Effect" -- 4. The Recommended Preregistered Protocol -- 5. Considerations and Caveats -- 5.1. Strengths of Such Protocol -- 6. Concluding Thoughts. (shrink)

In this paper we show that Neutrosophic Statistics is an extension of Interval Statistics, since it deals with all kinds of indeterminacy (with respect to data, inferential procedures, probability distributions, graphical representations, etc.), allows for indeterminacy reduction, and uses neutrosophic probability which is more general than imprecise and classical probabilities, and has more detailed corresponding probability density functions. Whereas Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments of Woodall et al (...) [1]. We show that not all indeterminacies (uncertainties) can be represented by intervals. Moreover, in some applications, we should use hesitant sets (which have less indeterminacy) instead of intervals. We redirect the authors to Plitogenic Probability and Plitogenic Statistics which are the most general forms of Multivariate Probability and Multivariate Statistics respectively (including, of course, Imprecise Probability and Interval Statistics as subclasses). (shrink)

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to (...) the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses). (shrink)

Compared with traditional statistics, only a few social scientists employ Bayesian analyses. The existing software programs for implementing Bayesian analyses such as OpenBUGS, WinBUGS, JAGS, and rstanarm can be daunting given that their complex computer codes involve a steep learning curve. In contrast, this paper introduces a new open software for implementing Bayesian network modelling and analysis: the bayesvl R package. The package aims at providing an intuitive gateway for beginners of Bayesian statistics to construct and analyse mathematical models in (...) social sciences... (shrink)

Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that the proportion of papers using logical methods remained more or less constant over that time period but the proportion of papers (...) using probabilistic methods was approximately three times higher in the late 2010s than it was in the late 2000s. Further analyses explored this change by looking more closely at specific methods, specific levels of technical engagement, and specific subdisciplines within philosophy. These analyses indicate that the increasing proportion of papers using probabilistic methods was pervasive, not confined to particular probabilistic methods, levels of sophistication, or subdisciplines. (shrink)

It has been argued that ethical frameworks for data science often fail to foster ethical behavior, and they can be difficult to implement due to their vague and ambiguous nature. In order to overcome these limitations of current ethical frameworks, we propose to integrate the analysis of the connections between technical choices and sociocultural factors into the data science process, and show how these connections have consequences for what data subjects can do, accomplish, and be. Using healthcare as an example, (...) attention to sociocultural conversion factors relevant to health can help in navigating technical choices that require broader considerations of the sociotechnical system, such as metric tradeoffs in model validation, resulting in better ethical and technical choices. This approach promotes awareness of the ethical dimension of technical choices by data scientists and others, and that can foster the cultivation of 'ethical skills' as integral to data science. (shrink)

Evidence-based medicine frequently uses statistical hypothesis testing. In this paradigm, data can only disconfirm a research hypothesis’ competitors: One tests the negation of a statistical hypothesis that is supposed to correspond to the research hypothesis. In practice, these hypotheses are often misaligned. For instance, directional research hypotheses are often paired with non-directional statistical hypotheses. Prima facie, one cannot gain proper evidence for one’s research hypothesis employing a misaligned statistical hypothesis. This paper sheds lights on the nature of and the reasons (...) for such misalignments and it provides a thorough analysis of whether they pose a threat to evidence-based medicine. The upshots are that the misalignments are often hidden for clinicians and that although some cases of misalignments can be partially counterbalanced, the overall threat is non-negligible. The counterbalances either lead to methodological inadequacy, loss of statistical power, or involve a lack of information that could be crucial for decision making. This result casts doubt on various findings of medical studies in addition to issues associated with under-powered studies or the replication crisis. (shrink)

Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order that they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 [2010]: 793–794), Jake H. O’Connell presents a statistical analysis of this argument, according to which the (...) probability of this correspondence occurring by chance is lower than 1%. O’Connell concludes that it is more than 99% probable that this correspondence is the result of Papias copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence, overstates the correspondence between John and Papias, wrongly assumes that if Papias did not know John he ordered the disciples randomly, and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning. (shrink)

The enduring replication crisis in many scientific disciplines casts doubt on the ability of science to estimate effect sizes accurately, and in a wider sense, to self-correct its findings and to produce reliable knowledge. We investigate the merits of a particular countermeasure—replacing null hypothesis significance testing with Bayesian inference—in the context of the meta-analytic aggregation of effect sizes. In particular, we elaborate on the advantages of this Bayesian reform proposal under conditions of publication bias and other methodological imperfections that are (...) typical of experimental research in the behavioral sciences. Moving to Bayesian statistics would not solve the replication crisis single-handedly. However, the move would eliminate important sources of effect size overestimation for the conditions we study. (shrink)

In 1988, three laboratories performed a radiocarbon analysis of the Turin Shroud. The results, which were centralized by the British Museum and published in Nature in 1989, provided ‘conclusive evidence’ of the medieval origin of the artefact. However, the raw data were never released by the institutions. In 2017, in response to a legal request, all raw data kept by the British Museum were made accessible. A statistical analysis of the Nature article and the raw data strongly suggests that homogeneity (...) is lacking in the data and that the procedure should be reconsidered. (shrink)

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide (...) additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

This study presents a description of an open database on scientific output of Vietnamese researchers in social sciences and humanities, one that corrects for the shortcomings in current research publication databases such as data duplication, slow update, and a substantial cost of doing science. Here, using scientists’ self-reports, open online sources and cross-checking with Scopus database, we introduce a manual system and its semi-automated version of the database on the profiles of 657 Vietnamese researchers in social sciences and humanities who (...) have published in Scopus-indexed journals from 2008 to 2018. The final system also records 973 foreign co-authors, 1,289 papers, and 789 affiliations. The data collection method, highly applicable for other sources, could be replicated in other developing countries while its content be used in cross-section, multivariate, and network data analyses. The open database is expected to help Vietnam revamp its research capacity and meet the public demand for greater transparency in science management. (shrink)

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate (...) the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization. (shrink)

Luc Bovens has recently advanced a novel argument for affirmative action, grounded in the plausible idea that it is hard for an employer to evaluate the qualifications of candidates from underrepresented groups. Bovens claims that this provides a profit-maximizing employer with reason to shortlist prima facie less-qualified candidates from underrepresented groups. In this paper, I illuminate three flaws in Bovens’s argument. First, it suffers from model error: A rational employer does not incur costs to scrutinize candidates when it knows their (...) qualifications with perfect certainty, nor does it refuse to hire better-qualified candidates just because they did not require extra scrutiny. Second, Bovens’s core premise--that there is greater variance in the evaluation of underrepresented candidates than there is the evaluation of other candidates--hurts underrepresented candidates rather than helps them. Third, candidates who are not shortlisted for the reasons Bovens gives have a plausible complaint about unfairness in the hiring process. (shrink)

Utility theories—both Expected Utility (EU) and non-Expected Utility (non-EU) theories—offer numericalized representations of classical principles meant for the regulation of choice under conditions of risk—a type of formal representation that reduces the representation of risk to a single number. I shall refer to these as risk-numericalizing theories of decision. I shall argue that risk-numericalizing theories (referring both to the representations and to the underlying axioms that render numericalization possible) are not satisfactory answers to the question: “How do I take the (...) (best) means to my ends?” In other words, they are inadequate or incomplete as instrumental theories. They are inadequate because they are poor answers to the question of what it is for an option to be instrumental towards an end. To say it another way, they do not offer a sufficiently rich account of what it is for something to be a means (an instrument) toward an end. (shrink)

ABSTRACT This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, (...) independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena. (shrink)

The current rise of neurodevelopmental disorders poses a critical need to detect risk early in order to rapidly intervene. One of the tools pediatricians use to track development is the standard growth chart. The growth charts are somewhat limited in predicting possible neurodevelopmental issues. They rely on linear models and assumptions of normality for physical growth data – obscuring key statistical information about possible neurodevelopmental risk in growth data that actually has accelerated, non-linear rates-of-change and variability encompassing skewed distributions. Here, (...) we use new analytics to profile growth data from 36 newborn babies that were tracked longitudinally for 5 months. By switching to incremental (velocity-based) growth charts and combining these dynamic changes with underlying fluctuations in motor performance – as the transition from spontaneous random noise to a systematic signal – we demonstrate a method to detect very early stunting in the development of voluntary neuromotor control and to flag risk of neurodevelopmental derail. (shrink)

This thesis examines philosophical controversies surrounding the evaluation of medical treatments, with a focus on the evidential roles of randomised trials and mechanisms in Evidence-Based Medicine. Current 'best practice' usually involves excluding non-randomised trial evidence from systematic reviews in cases where randomised trials are available for inclusion in the reviews. The first paper challenges this practice and evaluates whether adding of evidence from non-randomised trials might improve the quality and precision of some systematic reviews. The second paper compares the alleged (...) methodological benefits of randomised trials over observational studies for investigating treatment benefits. It suggests that claims about the superiority of well-conducted randomised controlled trials over well-conducted observational studies are justified, especially when results from the two methods are contradictory. The third paper argues that postulating the unpredictability paradox in systematic reviews when no detectable empirical differences can be found requires further justification. The fourth paper examines the problem of absence causation in the context of explaining causal mechanisms and argues that a recent solution is incomplete and requires further justification. Solving the problem by describing absences as causes of 'mechanism failure' fails to take into account the effects of absences that lead to vacillating levels of mechanism functionality. The fifth paper criticises literature that has emphasised functioning versus 'broken' or 'non-functioning' mechanisms emphasising that many diseases result from increased or decreased mechanism function, rather than complete loss of function. Mechanistic explanations must account for differences in the effectiveness of performed functions, yet current philosophical mechanistic explanations do not achieve this. The last paper argues that the standard of evidence embodied in the ICE theory of technological function is too permissive for evaluating whether the proposed functions of medical technologies have been adequately assessed and correctly ascribed. It argues that high-quality evidence from clinical studies is necessary to justify functional ascriptions to health care technologies. (shrink)

Focusing on the history of prehistoric archaeology in the 20th century, this papers shows (1) that statistical multidimensional analyses were carried out by a new kind of actors who challenged the previous common language shared by prehistorians. This fundamental change was important, considering that (2) language is a fundamental point for the epistemology of archaeology. However, a comparison of multidimensional analyses applications over time shall make clear that (3) the differences are mostly a generational matter: the transmission processes between them (...) will be addressed. (shrink)

The danger of deflation has been rather frequently mentioned recently among nu-merous concerns over the European and partly American economies. Analysts cite the Japanese economy which has been suffering from deflation for the last two decades despite the large investments in economy and the government's efforts to increase inflation. Similarly, notwithstanding many trillions of dollars, euro, pounds and yen that were invested in economies over the past few years, the infla-tion in the Western countries still remains low. On the whole, (...) there are reasons to maintain that European countries suffer from ‘the Japanese disease’, and this disease can progress or even become chron-ic. The USA, although to a lesser extent, has the signs of the disease as well. As a result, the financial infusions can become permanent, as it happened in Japan. The present paper defines the reasons of the problem, explains the irregularity of the inflation-deflation processes in the world and also offers some forecasts. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional independence for discrete datasets. The full Bayesian (...) significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Statistics play a critical role in biological and clinical research. To promote logically consistent representation and classification of statistical entities, we have developed the Ontology of Biological and Clinical Statistics (OBCS). OBCS extends the Ontology of Biomedical Investigations (OBI), an OBO Foundry ontology supported by some 20 communities. Currently, OBCS contains 686 terms, including 381 classes imported from OBI and 147 classes specific to OBCS. The goal of this paper is to present OBCS for community critique and to describe a (...) number of use cases designed to illustrate its potential applications. The OBCS project and source code are available at http://obcs.googlecode.com. (shrink)

We study Compositional Models based on Dirichlet Regression where, given a (vector) covariate x, one considers the response variable, y, to be a positive vector with a conditional Dirichlet distribution, y | X We introduce a new method for estimating the parameters of the Dirichlet Covariate Model given a linear model on X, and also propose a Bayesian model selection approach. We present some numerical results which suggest that our proposals are more stable and robust than traditional approaches.

The concept of non-arbitrage plays an essential role in finance theory. Under certain regularity conditions, the Fundamental Theorem of Asset Pricing states that, in non-arbitrage markets, prices of financial instruments are martingale processes. In this theoretical framework, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender arbitrage conditions. Assuming an underlying Variance Gamma statistical model, this study aims to test, using the FBST - Full (...) Bayesian Significance Test, if there is a relevant price difference between essentially the same financial asset traded at two distinct locations. Specifically, we investigate and compare the behavior of call options on the BOVESPA Index traded at (a) the Equities Segment and (b) the Derivatives Segment of BM&FBovespa. Our results seem to point out significant statistical differences. To what extent this evidence is actually the expression of perennial arbitrage opportunities is still an open question. (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The (...) present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

The Gompertz distribution is commonly used in biology for modeling fatigue and mortality. This paper studies a class of models proposed by Adham and Walker, featuring a Gompertz type distribution where the dependence structure is modeled by a lognormal distribution, and develops a new multivariate formulation that facilitates several numerical and computational aspects. This paper also implements the FBST, the Full Bayesian Significance Test for pertinent sharp (precise) hypotheses on the lognormal covariance structure. The FBST’s e-value, ev(H), gives the epistemic (...) value of hypothesis, H, or the value of evidence in the observed in support of H. (shrink)

In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture many of the interesting aspects that are present in the cases of more than two classes and in the problem of estimation, and many of the results can be (...) extended to these cases. Focusing on two-class pattern classification simplifies our discussion, and yet it is directly applicable to a wide range of practical settings. (shrink)

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the unit root (...) hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods.

Entanglement and non-locality are non-classical global characteristics of quantum states important to the foundations of quantum mechanics. Recent investigations have shown that environmental noise, even when it is entirely local in influence, can destroy both of these properties in finite time despite giving rise to full quantum state decoherence only in the infinite time limit. These investigations, which have been carried out in a range of theoretical and experimental situations, are reviewed here.

Probability and Statistics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in probability and statistics. We hear their views on the fields, aims, scopes, the future direction of research and how their work fits in these respects. Interviews with Nick Bingham, Luc Bovens, Terrence L. Fine, Haim Gaifman, Donald Gillies, James Hawthorne, Carl Hoefer, James M. Joyce, Joseph B. Kadane Isaac Levi, D.H. Mellor, Patrick Suppes, Jan (...) von Plato, Carl Wagner, Sandy Zabell. (shrink)

The Generalized Poisson Distribution (GPD) adds an extra parameter to the usual Poisson distribution. This parameter induces a loss of homogeneity in the stochastic processes modeled by the distribution. Thus, the generalized distribution becomes an useful model for counting processes where the occurrence of events is not homogeneous. This model creates the need for an inferential procedure, to test for the value of this extra parameter. The FBST (Full Bayesian Significance Test) is a Bayesian hypotheses test procedure, capable of providing (...) an evidence measure on sharp hypotheses (where the dimension of the parametric space under the null hypotheses is smaller than that of the full parametric space). The goal of this work is study the empirical properties of the FBST for testing the nullity of extra parameter of the generalized Poisson distribution. Numerical experiments show a better performance of FBST with respect to the classical likelihood ratio test, and suggest that FBST is an efficient and robust tool for this application. (shrink)

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a quadratic rate on (...) the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

This article presents a two level hierarchical forecasting model developed in a consulting project for a Brazilian magazine publishing company. The first level uses a VARMA model and considers econometric variables. The second level takes into account qualitative aspects of each publication issue, and is based on polynomial networks generated by Genetic Programming (GP).

Exploratory factor analysis (EFA) of the Psychopathic Personality Inventory (PPI; S. O. Lilienfeld, 1990; S. O. Lilienfeld & B. P. Andrews, 1996) with a community sample has suggested that the PPI subscales may comprise 2 higher order factors (S. D. Benning, C. J. Patrick, B. M. Hicks, D. M. Blonigen, & R. F. Krueger, 2003). However, substantive and structural evidence raises concerns about the viability of this 2-factor model, particularly in offender populations. The authors attempted to replicate the S. D. (...) Benning et al. 2-factor solution using a large (N= 1,224) incarcerated male sample. Confirmatory factor analysis of this model resulted in poor model fit. Similarly, using the same EFA procedures as did S. D. Benning et al., the authors found little evidence for a 2-factor model. When they followed the recommendations of J.-W. van Prooijen and W. A. van der Kloot (2001) for recovering EFA solutions, model fit results provided some evidence that a 3-factor EFA solution could be recovered via confirmatory factor analysis. (shrink)

Gene clustering is a useful exploratory technique to group together genes with similar expression levels under distinct cell cycle phases or distinct conditions. It helps the biologist to identify potentially meaningful relationships between genes. In this study, we propose a clustering method based on multivariate normal mixture models, where the number of clusters is predicted via sequential hypothesis tests: at each step, the method considers a mixture model of m components (m = 2 in the first step) and tests if (...) in fact it should be m - 1. If the hypothesis is rejected, m is increased and a new test is carried out. The method continues (increasing m) until the hypothesis is accepted. The theoretical core of the method is the full Bayesian significance test, an intuitive Bayesian approach, which needs no model complexity penalization nor positive probabilities for sharp hypotheses. Numerical experiments were based on a cDNA microarray dataset consisting of expression levels of 205 genes belonging to four functional categories, for 10 distinct strains of Saccharomyces cerevisiae. To analyze the method’s sensitivity to data dimension, we performed principal components analysis on the original dataset and predicted the number of classes using 2 to 10 principal components. Compared to Mclust (model-based clustering), our method shows more consistent results. (shrink)

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

The report begins by outlining several case studies with varying levels of data, examining the role for extreme event risk analysis. The case studies include BA’s analysis of fire blight and New Zealand apples, bank operational risk and several technical failures. The report then surveys recent developments in methods relevant to evaluating extreme risks and evaluates their properties. These include methods for fraud detection in banks, formal extreme value theory, Bayesian approaches, qualitative reasoning, and adversary and advocacy models. The document (...) includes a supplementary report as an appendix, providing an overview of the quantification of bank operational risks. (shrink)

This essay describes in simple terms some of the major concepts of categorical data analysis (CDA) that have been and will continue to be useful in the analysis of sociological data, examples of which include data in the area of social stratification and mobility, and in many other areas that make use of survey data and/or panel studies data, and in empirical studies of latent types, latent variables, and latent structures. The exposition does not make use of any mathematical formulas, (...) and the only arithmetic used is very simple multiplication, division, and addition. Simple numerical examples, constructed for expository purposes, are used as an aid in describing the concepts of categorical data analysis that are considered in the essay. These concepts include quasi-independence, quasi-symmetry, symmetric association, uniform association, and other related concepts useful in the analysis of mobility tables, and also other concepts that are useful in other areas of study. (shrink)