Steps towards a unified basis for scientific models and methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2010
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 245-253) and index 1. Basic elements. 1.1. Introduction : complementarity and its implications. 1.2. Conceptually defined variables. 1.3. Inaccessible c-variables. 1.4. On decisions from a statistical point of view. 1.5. Contexts for experiments. 1.6. Experiments and selected parameters. 1.7. Hidden variables and c-variables. 1.8. Causality, counterfactuals. 1.9. Probability theory. 1.10. Probability models for experiments. 1.11. Elements of group theory -- - 2. Statistical theory and practice. 2.1. Historical development of statistics as a science. 2.2. The starting point of statistical theory. 2.3. Estimation theory. 2.4. Confidence intervals, testing and measures of significance. 2.5. Simple situations where statistics is useful. 2.6. Bayes' formula and Bayesian inference. 2.7. Regression and analysis of variance. 2.8. Model checking in regression. 2.9. Factorial models. 2.10. Contrasts in ANOVA models. 2.11. Reduction of data in experiments : sufficiency. 2.12. Fisher information and the Cramér-Rao inequality. 2.13. The conditionality principle. 2.14. A few design of experiment issues. 2.15. Model reduction. 2.16. Perfect experiments -- - 3. Statistical inference under symmetry. 3.1. Introduction. 3.2. Group actions and statistical models. 3.3. Invariant measures on the parameter space. 3.4. Subparameters, inference and orbits. 3.5. Estimation under symmetry. 3.6. Estimation under symmetry. 3.6. Credibility sets and confidence sets. 3.7. Examples. Orbits and model reduction. 3.8. Model reduction for subparameter estimation and prediction. 3.9. Estimation of the maximally invariant parameter : REML. 3.10. Design of experiments situations. 3.11. Group actions defined on a c-variable space. 3.12. Some concluding remarks -- - 4. The transition from statistics to quantum theory. 4.1. Theoretical statistics and applied statistics. 4.2. The Gödel theorem analogy. 4.3. Wave mechanics. 4.4. The formal axioms of quantum theory. 4.5. The historical development of formal quantum mechanics. 4.6. A large scale model. 4.7. A general definition; a c-system. 4.8. Quantum theory axioms under symmetry and complementarity. 4.9. The electron spin example -- 5. Quantum mechanics from a statistical basis. 5.1. Introduction. 5.2. The Hilbert spaces of a given experiment. 5.3. The common Hilbert space. 5.4. States and state variables. 5.5. The Born formula. 5.6. The electron spin revisited. 5.7. Statistical inference in a quantum setting. 5.8. Proof of the quantum rules from our axioms. 5.9. The case of continuous parameters. 5.10. On the context of a system, and on the measurement process -- - 6. Further development of quantum mechanics. 6.1. Introduction. 6.2. Entanglement. 6.3. The Bell inequality issue. 6.4. Statistical models in connection to Bell's inequality. 6.5. Groups connected to position and momentum. Planck's constant. 6.6. The Schrödinger equation. 6.7. Classical information and information in quantum mechanics. 6.8. Some themes and 'paradoxes' in quantum mechanics. 6.9. Histories. 6.10. The many worlds and many minds -- 7. Decisions in statistics. 7.1. Focusing in statistics. 7.2. Linear models. 7.3. Focusing in decision theory. 7.4. Briefly on schools in statistical inference. 7.5. Experimental design. 7.6. Quantum mechanics and testing of hypotheses. 7.7. Complementarity in statistics -- - 8. Multivariate data analysis and statistics. 8.1. Introduction. 8.2. The partial least squares data algorithms. 8.3. The partial least squares population model. 8.4. Theoretical aspects of partial least squares. 8.5. The best equivariant predictor. 8.6. The case of a multivariate dependent variable. 8.7. The two cultures in statistical modelling. 8.8. Model reduction and PLS. 8.9. A multivariate example resembling quantum mechanics -- 9. Quantum mechanics and the diversity of concepts. 9.1. Introduction. 9.2. Daily life complementarity. 9.3. From learning parameter values to learning to make other decisions. 9.4. Basic learning : with and without a teacher. 9.5. On psychology. 9.6. On social sciences Culture, in fact, also plays an important role in science which is, per se, a multitude of different cultures. The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods. Of course, these three domains should not be taken as equals in any sense. But the book holds the important claim that it is possible to develop a common language which, at least to a certain extent, can create direct links and build bridges. From this point of departure, the book will be of interest to the following three types of scientists - statisticians, quantum physicists and chemometricians - and in particular, statisticians and physicists who are interested in interdisciplinary research. Written at a level that is accessible to general readers, not only the academics, the book will appeal to graduate students and mathematically educated persons of all disciplines as well as philosophers, pure and applied mathematicians, and the general public |
| Beschreibung: | 1 Online-Ressource (xviii, 257 p.) |
| ISBN: | 9789814280853 9789814280860 9814280852 9814280860 |
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| 245 | 1 | 0 | |a Steps towards a unified basis for scientific models and methods |c Inge S. Helland |
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| 500 | |a Includes bibliographical references (p. 245-253) and index | ||
| 500 | |a 1. Basic elements. 1.1. Introduction : complementarity and its implications. 1.2. Conceptually defined variables. 1.3. Inaccessible c-variables. 1.4. On decisions from a statistical point of view. 1.5. Contexts for experiments. 1.6. Experiments and selected parameters. 1.7. Hidden variables and c-variables. 1.8. Causality, counterfactuals. 1.9. Probability theory. 1.10. Probability models for experiments. 1.11. Elements of group theory -- | ||
| 500 | |a - 2. Statistical theory and practice. 2.1. Historical development of statistics as a science. 2.2. The starting point of statistical theory. 2.3. Estimation theory. 2.4. Confidence intervals, testing and measures of significance. 2.5. Simple situations where statistics is useful. 2.6. Bayes' formula and Bayesian inference. 2.7. Regression and analysis of variance. 2.8. Model checking in regression. 2.9. Factorial models. 2.10. Contrasts in ANOVA models. 2.11. Reduction of data in experiments : sufficiency. 2.12. Fisher information and the Cramér-Rao inequality. 2.13. The conditionality principle. 2.14. A few design of experiment issues. 2.15. Model reduction. 2.16. Perfect experiments -- | ||
| 500 | |a - 3. Statistical inference under symmetry. 3.1. Introduction. 3.2. Group actions and statistical models. 3.3. Invariant measures on the parameter space. 3.4. Subparameters, inference and orbits. 3.5. Estimation under symmetry. 3.6. Estimation under symmetry. 3.6. Credibility sets and confidence sets. 3.7. Examples. Orbits and model reduction. 3.8. Model reduction for subparameter estimation and prediction. 3.9. Estimation of the maximally invariant parameter : REML. 3.10. Design of experiments situations. 3.11. Group actions defined on a c-variable space. 3.12. Some concluding remarks -- | ||
| 500 | |a - 4. The transition from statistics to quantum theory. 4.1. Theoretical statistics and applied statistics. 4.2. The Gödel theorem analogy. 4.3. Wave mechanics. 4.4. The formal axioms of quantum theory. 4.5. The historical development of formal quantum mechanics. 4.6. A large scale model. 4.7. A general definition; a c-system. 4.8. Quantum theory axioms under symmetry and complementarity. 4.9. The electron spin example -- 5. Quantum mechanics from a statistical basis. 5.1. Introduction. 5.2. The Hilbert spaces of a given experiment. 5.3. The common Hilbert space. 5.4. States and state variables. 5.5. The Born formula. 5.6. The electron spin revisited. 5.7. Statistical inference in a quantum setting. 5.8. Proof of the quantum rules from our axioms. 5.9. The case of continuous parameters. 5.10. On the context of a system, and on the measurement process -- | ||
| 500 | |a - 6. Further development of quantum mechanics. 6.1. Introduction. 6.2. Entanglement. 6.3. The Bell inequality issue. 6.4. Statistical models in connection to Bell's inequality. 6.5. Groups connected to position and momentum. Planck's constant. 6.6. The Schrödinger equation. 6.7. Classical information and information in quantum mechanics. 6.8. Some themes and 'paradoxes' in quantum mechanics. 6.9. Histories. 6.10. The many worlds and many minds -- 7. Decisions in statistics. 7.1. Focusing in statistics. 7.2. Linear models. 7.3. Focusing in decision theory. 7.4. Briefly on schools in statistical inference. 7.5. Experimental design. 7.6. Quantum mechanics and testing of hypotheses. 7.7. Complementarity in statistics -- | ||
| 500 | |a - 8. Multivariate data analysis and statistics. 8.1. Introduction. 8.2. The partial least squares data algorithms. 8.3. The partial least squares population model. 8.4. Theoretical aspects of partial least squares. 8.5. The best equivariant predictor. 8.6. The case of a multivariate dependent variable. 8.7. The two cultures in statistical modelling. 8.8. Model reduction and PLS. 8.9. A multivariate example resembling quantum mechanics -- 9. Quantum mechanics and the diversity of concepts. 9.1. Introduction. 9.2. Daily life complementarity. 9.3. From learning parameter values to learning to make other decisions. 9.4. Basic learning : with and without a teacher. 9.5. On psychology. 9.6. On social sciences | ||
| 500 | |a Culture, in fact, also plays an important role in science which is, per se, a multitude of different cultures. The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods. Of course, these three domains should not be taken as equals in any sense. But the book holds the important claim that it is possible to develop a common language which, at least to a certain extent, can create direct links and build bridges. From this point of departure, the book will be of interest to the following three types of scientists - statisticians, quantum physicists and chemometricians - and in particular, statisticians and physicists who are interested in interdisciplinary research. Written at a level that is accessible to general readers, not only the academics, the book will appeal to graduate students and mathematically educated persons of all disciplines as well as philosophers, pure and applied mathematicians, and the general public | ||
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Datensatz im Suchindex
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| author | Helland, Inge S. |
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| id | DE-604.BV043062393 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:17Z |
| institution | BVB |
| isbn | 9789814280853 9789814280860 9814280852 9814280860 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028486585 |
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| spelling | Helland, Inge S. Verfasser aut Steps towards a unified basis for scientific models and methods Inge S. Helland Singapore World Scientific Pub. Co. c2010 1 Online-Ressource (xviii, 257 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 245-253) and index 1. Basic elements. 1.1. Introduction : complementarity and its implications. 1.2. Conceptually defined variables. 1.3. Inaccessible c-variables. 1.4. On decisions from a statistical point of view. 1.5. Contexts for experiments. 1.6. Experiments and selected parameters. 1.7. Hidden variables and c-variables. 1.8. Causality, counterfactuals. 1.9. Probability theory. 1.10. Probability models for experiments. 1.11. Elements of group theory -- - 2. Statistical theory and practice. 2.1. Historical development of statistics as a science. 2.2. The starting point of statistical theory. 2.3. Estimation theory. 2.4. Confidence intervals, testing and measures of significance. 2.5. Simple situations where statistics is useful. 2.6. Bayes' formula and Bayesian inference. 2.7. Regression and analysis of variance. 2.8. Model checking in regression. 2.9. Factorial models. 2.10. Contrasts in ANOVA models. 2.11. Reduction of data in experiments : sufficiency. 2.12. Fisher information and the Cramér-Rao inequality. 2.13. The conditionality principle. 2.14. A few design of experiment issues. 2.15. Model reduction. 2.16. Perfect experiments -- - 3. Statistical inference under symmetry. 3.1. Introduction. 3.2. Group actions and statistical models. 3.3. Invariant measures on the parameter space. 3.4. Subparameters, inference and orbits. 3.5. Estimation under symmetry. 3.6. Estimation under symmetry. 3.6. Credibility sets and confidence sets. 3.7. Examples. Orbits and model reduction. 3.8. Model reduction for subparameter estimation and prediction. 3.9. Estimation of the maximally invariant parameter : REML. 3.10. Design of experiments situations. 3.11. Group actions defined on a c-variable space. 3.12. Some concluding remarks -- - 4. The transition from statistics to quantum theory. 4.1. Theoretical statistics and applied statistics. 4.2. The Gödel theorem analogy. 4.3. Wave mechanics. 4.4. The formal axioms of quantum theory. 4.5. The historical development of formal quantum mechanics. 4.6. A large scale model. 4.7. A general definition; a c-system. 4.8. Quantum theory axioms under symmetry and complementarity. 4.9. The electron spin example -- 5. Quantum mechanics from a statistical basis. 5.1. Introduction. 5.2. The Hilbert spaces of a given experiment. 5.3. The common Hilbert space. 5.4. States and state variables. 5.5. The Born formula. 5.6. The electron spin revisited. 5.7. Statistical inference in a quantum setting. 5.8. Proof of the quantum rules from our axioms. 5.9. The case of continuous parameters. 5.10. On the context of a system, and on the measurement process -- - 6. Further development of quantum mechanics. 6.1. Introduction. 6.2. Entanglement. 6.3. The Bell inequality issue. 6.4. Statistical models in connection to Bell's inequality. 6.5. Groups connected to position and momentum. Planck's constant. 6.6. The Schrödinger equation. 6.7. Classical information and information in quantum mechanics. 6.8. Some themes and 'paradoxes' in quantum mechanics. 6.9. Histories. 6.10. The many worlds and many minds -- 7. Decisions in statistics. 7.1. Focusing in statistics. 7.2. Linear models. 7.3. Focusing in decision theory. 7.4. Briefly on schools in statistical inference. 7.5. Experimental design. 7.6. Quantum mechanics and testing of hypotheses. 7.7. Complementarity in statistics -- - 8. Multivariate data analysis and statistics. 8.1. Introduction. 8.2. The partial least squares data algorithms. 8.3. The partial least squares population model. 8.4. Theoretical aspects of partial least squares. 8.5. The best equivariant predictor. 8.6. The case of a multivariate dependent variable. 8.7. The two cultures in statistical modelling. 8.8. Model reduction and PLS. 8.9. A multivariate example resembling quantum mechanics -- 9. Quantum mechanics and the diversity of concepts. 9.1. Introduction. 9.2. Daily life complementarity. 9.3. From learning parameter values to learning to make other decisions. 9.4. Basic learning : with and without a teacher. 9.5. On psychology. 9.6. On social sciences Culture, in fact, also plays an important role in science which is, per se, a multitude of different cultures. The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods. Of course, these three domains should not be taken as equals in any sense. But the book holds the important claim that it is possible to develop a common language which, at least to a certain extent, can create direct links and build bridges. From this point of departure, the book will be of interest to the following three types of scientists - statisticians, quantum physicists and chemometricians - and in particular, statisticians and physicists who are interested in interdisciplinary research. Written at a level that is accessible to general readers, not only the academics, the book will appeal to graduate students and mathematically educated persons of all disciplines as well as philosophers, pure and applied mathematicians, and the general public SCIENCE / Philosophy & Social Aspects bisacsh Naturwissenschaft Philosophie Science Philosophy Science Methodology World Scientific (Firm) Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340633 Aggregator Volltext |
| spellingShingle | Helland, Inge S. Steps towards a unified basis for scientific models and methods SCIENCE / Philosophy & Social Aspects bisacsh Naturwissenschaft Philosophie Science Philosophy Science Methodology |
| title | Steps towards a unified basis for scientific models and methods |
| title_auth | Steps towards a unified basis for scientific models and methods |
| title_exact_search | Steps towards a unified basis for scientific models and methods |
| title_full | Steps towards a unified basis for scientific models and methods Inge S. Helland |
| title_fullStr | Steps towards a unified basis for scientific models and methods Inge S. Helland |
| title_full_unstemmed | Steps towards a unified basis for scientific models and methods Inge S. Helland |
| title_short | Steps towards a unified basis for scientific models and methods |
| title_sort | steps towards a unified basis for scientific models and methods |
| topic | SCIENCE / Philosophy & Social Aspects bisacsh Naturwissenschaft Philosophie Science Philosophy Science Methodology |
| topic_facet | SCIENCE / Philosophy & Social Aspects Naturwissenschaft Philosophie Science Philosophy Science Methodology |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=340633 |
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