In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (shrink)

A modal analysis of luck, due to Duncan Pritchard, has become quite popular in recent years. There are many reasons to like Pritchard’s analysis, but at least two compelling problems have been identified. So I propose an alternative analysis of luck based on the laws of statistical mechanics. The statistical analysis avoids the two problems facing Pritchard’s analysis, and it has many other attractive features.

In the Article of Oksana Shepetyak "Statistical Analysis of the Relationship between the Numbers of Christian Churches of the Middle East"is analyzed the modernity of the Christians communities in their historical regions and tendency in their development. The diversity of Eastern Christianity requires a broad and multifaceted study. Most researchers focus on the history of formation, theological and liturgical aspects, and contemporaneity. This study is devoted to the comparison of only statistics, which, however, reveal an entirely new picture of (...) the Christian East. The comparison of the number of believers in the Eastern Churches shows that the Oriental non-orthodox churches dominate in the Alexandrian tradition, while the Eastern Catholic Churches predominate in the East Syrian and Western-Syrian tradition. Instead, the Churches of the Byzantine tradition in the Middle East turned into small religious communities. (shrink)

The quality of the products coming from different lines of production requires some tests called comparative life tests. For lines having the same facility, the lifetime of the product is distributed by Burr XII, the lifetime distribution, and units are tested under type-I generalized hybrid censoring scheme. The observed censoring data are used under maximum likelihood and the Bayes method to estimate the model parameters. The theoretical results are discussed and assessed through data analysis and Monte Carlo simulation study. (...) Finally, we reported some brief comments obtained from numerical computation. (shrink)

Graphical AbstractThe ACcess to Transparent Statistics (ACTS) call to action assembles four measures that are rapidly achievable by journals and funding agencies to enhance the quality of statistical reporting. The ACTS call to action is an appeal for concrete actions from institutions that should spearhead the battle for reproducibility.

Industry involvement in the machine learning (ML) community seems to be increasing. However, the quantitative scale and ethical implications of this influence are rather unknown. For this purpose, we have not only carried out an informed ethical analysis of the field, but have inspected all papers of the main ML conferences NeurIPS, CVPR, and ICML of the last 5 years—almost 11,000 papers in total. Our statistical approach focuses on conflicts of interest, innovation, and gender equality. We have obtained four (...) main findings. (1) Academic–corporate collaborations are growing in numbers. At the same time, we found that conflicts of interest are rarely disclosed. (2) Industry papers amply mention terms that relate to particular trending machine learning topics earlier than academia does. (3) Industry papers are not lagging behind academic papers with regard to how often they mention keywords that are proxies for social impact considerations. (4) Finally, we demonstrate that industry papers fall short of their academic counterparts with respect to the ratio of gender diversity. We believe that this work is a starting point for an informed debate within and outside of the ML community. (shrink)

Recent philosophical studies of probabilistic causation and statistical explanation have opened up the possibility of unifying philosophical approaches with causal modeling as practiced in the social and biological sciences. This unification rests upon the statistical tools employed, the principle of common cause, the irreducibility of causation to statistics, and the idea of causal process as a suitable framework for understanding causal relationships. These four areas of contact are discussed with emphasis on the relevant aspects of causal modeling.

Recent studies on probabilistic causation and statistical explanation (Cartwright 1979; Salmon 1984), I believe, have opened up the possibility of a genuine unification between philosophical approaches and causal modeling (CM) in the social, behavioral and biological sciences (Wright 1934; Blalock 1964; Asher 1976). This unification rests on the statistical tools employed, the principle of common cause, the irreducibility of causation to probability or statistics, and the idea of causal process as a suitable framework for understanding causal relationships. The aim of (...) this paper is to draw attention to these four areas of contact by focusing on the relevant aspects of CM.Causal analysis in the social sciences is based on two fundamental notions: model and method. A causal model is an idealized picture of the causal relationships in the world. Method, on the other hand, refers to certain statistical techniques that are used to evaluate and test a causal model using data which consist of joint observations on the model variables. (shrink)

Statistics play a critical role in biological and clinical research. However, most reports of scientific results in the published literature make it difficult for the reader to reproduce the statistical analyses performed in achieving those results because they provide inadequate documentation of the statistical tests and algorithms applied. The Ontology of Biological and Clinical Statistics (OBCS) is put forward here as a step towards solving this problem. Terms in OBCS, including ‘data collection’, ‘data transformation in statistics’, ‘data visualization’, ‘statistical data (...) analysis’, and ‘drawing a conclusion based on data’, cover the major types of statistical processes used in basic biological research and clinical outcome studies. OBCS is aligned with the Basic Formal Ontology (BFO) and extends the Ontology of Biomedical Investigations (OBI), an OBO (Open Biological and Biomedical Ontologies) Foundry ontology supported by over 20 research communities. We discuss two examples illustrating how the ontology is being applied. In the first (biological) use case, we describe how OBCS was applied to represent the high throughput microarray data analysis of immunological transcriptional profiles in human subjects vaccinated with an influenza vaccine. In the second (clinical outcomes) use case, we applied OBCS to represent the processing of electronic health care data to determine the associations between hospital staffing levels and patient mortality. Our case studies were designed to show how OBCS can be used for the consistent representation of statistical analysis pipelines under two different research paradigms. By representing statistics-related terms and their relations in a rigorous fashion, OBCS facilitates standard data analysis and integration, and supports reproducible biological and clinical research. (shrink)

Based on the novel data collected through original fieldwork on five syntactic phenomena (the position of the finite verb in embedded clauses, in sentences with a modal verb, negative concord, position of focused light/heavy objects in main clauses with a complex tense, scrambling) in the heritage language Mòcheno, we show that i) there exist two populations – one exhibiting intra-speaker variation between German and Italian word orders, and one lacking it; ii) these two populations are the result of diatopic variation (...) and, to a lesser extent, of diastratic variation. The results reached through quantitative statistical analysis are partially convergent with those arrived at by traditional theoretical syntax on Mòcheno, but our analysis has allowed us to shed new light on a series of so-far neglected or poorly understood phenomena. More specifically, we discovered that there exists micro-variation fed by diastratic (age) variation within the Roveda variety, which represents the only case in Mòcheno in which age is a relevant factor in determining variation. We also showed that the traditional claim that the Palù variety is “more German” than the other Mòcheno variety is surely to be confirmed, but we could refine it by showing that German word orders are also accepted by speakers of other varieties and that the acceptability of these word orders in competition with the Italian syntax is not fed by the age of speakers (no diastratic variation). Finally, we showed that the acceptance of German word orders across speakers varies according to the phenomenon investigated: negation is the phenomenon in which German word orders are more likely to be accepted, whereas embedded clauses are the phenomenon in which German word orders are more likely to be rejected. (shrink)

The aim of the present study was to determine statistical differences in a set of badminton competition matches in five different modalities with regard to competition level (Group Phase versus Eliminatory Phase). Data from 453 sets (125 in men’s singles; 108 sets in women’s singles; 77 sets in men’s doubles; 73 in women’s doubles and 70 in mixed doubles) from the RIO 2016 Olympics Games were recorded and classified in two groups of variables to analyse variables related to match (5) (...) and set (15). A descriptive analysis and univariate test (Mann Whitney U) for non-parametric data were conducted. The results show in men’s and women’s singles all the variables related to match were higher in the Elimination Phase than in the Group Phase (p<0.01). In Sets 1 and 3, the longest set duration, rally and average rally were found in the Elimination Phase than Group Stage (p<0.05). In women’s singles, these differences were also recorded in Set 2. For doubles, the results are more stable among groups. Men’s doubles had a longer duration of the match and set (set 1 and set 2) (p<0.01), and also scored highest for average rally strokes (set 1 and set 3) (p<0.05) and shuttles used in the Elimination Phase versus the Group Phase along the match (p<0.01). In women’s doubles, more shuttles were used in a match in the Elimination than in the Group Phase. Moreover, the same results are established for Set 2, including for average rally. Mixed doubles saw no match going to three sets. However, the greatest differences showed a longer rally and average rally being registered in the Elimination than in the Group Phase. In conclusion, the timing factors of the badminton singles and doubles games were different in the Elimination and Group Phases. This information may help players and coaches prepare and administer different types of workouts or, more specifically, competition schedules adapted to the characteristics of modern badminton. (shrink)

Cognitive Science, Volume 46, Issue 9, September 2022.

This article concerns the problem of assessing selected body compo- sition parameters after completion of antitumor therapy and comparing them with the same parameters of healthy children. A high percentage of overweight and obesity, as well as abnormal fat distribution in convalescents with cancer shows a significant adverse effect of therapy on body composition and suggests the need for early intervention in terms of diet and exercise, which would help patients to quickly achieve the proper parameters of body composition. Two (...) main problems will be mentioned during the presented data analysis. Firstly, in each group there was a small number of observations. Because of this, the real differences between examined subgroups may have been omitted. Secondarily, many variables are correlated and are not normally distributed. Therefore, be- side the standard statistical tests to compare two groups, principal component analysis was applied to reduce the dimensions of the attribute space and to attempt to classify two groups of patients. (shrink)

Are there relationships between consciousness and the material world? Empirical evidence for such a connection was reported in several meta-analyses of mind-matter experiments designed to address this question. In this paper we consider such meta-analyses from a statistical modeling perspective, emphasizing strategies to validate the models and the associated statistical procedures. In particular, we explicitly model increased data variability and selection mechanisms, which permits us to estimate 'selection profiles ' and to reassess the experimental effect in view of potential other (...) effects. An application to the data pool considered in the influential meta-analysis of Radin and Nelson (1989) yields indications for the presence of random and selection effects Adjustment for possible selection is found to render the,without such an adjustment significant, experimental effect non-significant. Somewhat different conclusions apply to a subset of the data deserving separate consideration. The actual origin of the data features that are described as experimental, random, or selection effects within the proposed model cannot be clarified y our approach and remains open. (shrink)

This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the other hand, (...) I assert that Neyman-Pearson's testing theory, as well as Fisher's tests of significance, properly belong to decision theory, not to logic, neither deductive nor inductive. I then also disagree with Costantini's view of Fisher's testing model as a theory of hypothetico-deductive inferences.In Section 5 I disapprove Hacking1's evidentialists criticisms of the Neyman-Pearson's theory of statistics (NPT), as well as Hacking2's interpretation of NPT as a theory of probable inference. In both cases Hacking misses the point. I conclude, by claiming that Mayo's conception of the Neyman-Pearson's testing theory, as a model of learning from experience, does not purport any advantages over Neyman's behavioristic model. (shrink)

It is probable that, increasingly, genome investigations are going to be based on statistical formalization. This review summarizes the state of art and potentiality of using statistics in microbial genome analysis. First, I focus on recent advances in functional genomics, such as finding genes and operons, identifying gene conversion events, detecting DNA replication origins and analysing regulatory sites. Then I describe how to use phylogenetic methods in genome analysis and methods for genome‐wide scanning for positively selected amino acids. (...) I conclude with speculations on the future course of genome statistical modeling. BioEssays 25:266–273, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

Statistical significance is almost universally equated with the attribution to some population of nonchance influences as the source of structure in the data. But statistical significance can be divorced from both parameter estimation and probability as, instead, a statement about the atypicality or lack of exchangeability over some distinction of the data relative to some set. From this perspective, the criticisms of significance tests evaporate.

The paper deals with a method of hierarchization of alternatives in a multicriteria environment by means of statistical nonparametric procedures. For each criterion, alternatives are disposed on an ordinal scale. After that a procedure similar to ANOVA is activated on the data. The differences relating to the average ranks of each action are used to build the hierarchical algorithm. The concept of outranking, in a probabilistic meaning, is reached in this way. Thereafter, we arrive at the concept of dominance using (...) pairwise comparisons. A case study is presented which implements the methodological suggestion. (shrink)