Inverse problems : basics, theory and applications in geophysics / / Mathias Richter

• Record Nr.: UNINA9910483226503321
• Autore: Richter Mathias
• Pubbl/distr/stampa: Cham, Switzerland : , : Birkhäuser, , [2020]; ©2020
• ISBN: 3-030-59317-7
• Edizione: [Second edition.]
• Descrizione fisica: 1 online resource (XIV, 273 p. 57 illus., 43 illus. in color.)
• Collana: Lecture Notes in Geosystems Mathematics and Computing, , 2512-3211
• Disciplina: 515.357
• Soggetti: Inverse problems (Differential equations); Geophysics - Mathematics; Earth sciences
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Characterization of Inverse Problems -- Discretization of Inverse Problems -- Regularization of Linear Inverse Problems -- Regularization of Nonlinear Inverse Problems -- Appendix A. Results from Linear Algebra -- Appendix B. Function Spaces -- Appendix C. The Fourier Transform -- Appendix D. Regularization Property of CGNE -- Appendix E. Existence and Uniqueness Theorems for Waveform Inversion.
• Sommario/riassunto: This textbook is an introduction to the subject of inverse problems with an emphasis on practical solution methods and applications from geophysics. The treatment is mathematically rigorous, relying on calculus and linear algebra only; familiarity with more advanced mathematical theories like functional analysis is not required. Containing up-to-date methods, this book will provide readers with the tools necessary to compute regularized solutions of inverse problems. A variety of practical examples from geophysics are used to motivate the presentation of abstract mathematical ideas, thus assuring an accessible approach. Beginning with four examples of inverse problems, the opening chapter establishes core concepts, such as formalizing these problems as equations in vector spaces and addressing the key issue of ill-posedness. Chapter Two then moves on ; to the discretization of inverse problems, which is a prerequisite for solving them on computers. Readers will be well-prepared for the final chapters that present regularized solutions of inverse problems in finite-dimensional spaces, with Chapter Three covering linear problems and Chapter Four studying nonlinear problems. Model problems reflecting scenarios of practical interest in the geosciences, such as inverse gravimetry and full waveform inversion, are fully worked out throughout the book. They are used as test cases to illustrate all single steps of solving inverse problems, up to numerical computations. Five appendices include the mathematical foundations needed to fully understand the material. This second edition expands upon the first, particularly regarding its up-to-date treatment of nonlinear problems. Following the author’s approach, readers will understand the relevant theory and methodology needed to pursue more complex applications. Inverse Problems is ideal for graduate students and researchers interested in geophysics and geosciences.

Introduction to statistics and SPSS in psychology / / Andrew Mayers

• Record Nr.: UNINA9910150208003321
• Autore: Mayers Andrew
• Pubbl/distr/stampa: Harlow, England : , : Pearson, , [2013]; ©2013
• ISBN: 0-273-73102-5
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (626 pages) : illustrations (some color)
• Collana: Always learning
• Disciplina: 150.15195
• Soggetti: Psychometrics; Psychology - Statistical methods
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover -- Contents -- About the author -- Acknowledgements -- Publisher's acknowledgments -- Guided tour -- 1 Introduction -- Why I wrote this book - what's in it for you? -- Why do psychologists need to know about statistics? -- How this book is laid out - what you can expect -- Online resources -- 2 SPSS - the basics -- Learning ; objectives -- Introduction -- Viewing options in SPSS -- Defining variable parameters -- Entering data -- SPSS menus (and icons) -- Syntax -- Chapter summary -- Extended learning task -- 3 Normal distribution -- Learning objectives -- What is normal distribution? -- Measuring normal distribution -- Statistical assessment of normal distribution -- Adjusting non-normal data -- Homogeneity of between-group variance -- Sphericity of within-group variance -- Chapter summary -- Extended learning task -- 4 Significance, effect size and power -- Learning objectives -- Introduction -- Statistical significance -- Significance and hypotheses -- Measuring statistical significance -- Effect size -- Statistical power -- Measuring effect size and power using G*Power -- Chapter summary -- Extended learning task -- 5 Experimental methods - how to choose the correct statistical test -- Learning objectives -- Introduction -- Conducting 'experiments' in psychology -- Factors that determine the appropriate statistical test -- Exploring differences -- Examining relationships -- Validity and reliability -- Chapter summary -- Extended learning task -- 6 Correlation -- Learning objectives -- What is correlation? -- Theory and rationale -- Pearson's correlation -- Spearman's rank correlation -- Kendall's Tau-b -- Biserial (and point-biserial) correlation -- Partial correlation -- Semi-partial correlation -- Chapter summary -- Research example -- Extended learning task -- 7 Independent t-test -- Learning objectives -- What is a t-test?.; Theory and rationale -- How SPSS performs an independent t-test -- Interpretation of output -- Effect size and power -- Writing up results -- Presenting data graphically -- Chapter summary -- Research example -- Extended learning task -- 8 Related t-test -- Learning objectives -- What is the related t-test? -- Theory and rationale -- How SPSS performs the related t-test -- Interpretation of output -- Effect size and power -- Writing up results -- Presenting data graphically -- Chapter summary -- Research example -- Extended learning task -- 9 Independent one-way ANOVA -- Learning objectives -- Setting the scene: what is ANOVA? -- Theory and rationale -- How SPSS performs independent one-way ANOVA -- Interpretation of output -- Effect size and power -- Writing up results -- Presenting data graphically -- Chapter summary -- Research example -- Extended learning task -- 10 Repeated-measures one-way ANOVA -- Learning objectives -- What is repeated-measures one-way ANOVA? -- Theory and rationale -- How SPSS performs repeated-measures one-way ANOVA -- Interpretation of output -- Effect size and power -- Writing up results -- Presenting data graphically -- Chapter summary -- Research example -- Extended learning task -- 11 Independent multi-factorial ANOVA -- Learning objectives -- What is independent multi-factorial ANOVA? -- Theory and rationale -- How SPSS performs independent multi-factorial ANOVA -- Interpretation of output -- Effect size and power -- Writing up results -- Chapter summary -- Research example -- Extended learning task -- Appendix to Chapter 11: Exploring simple effects -- 12 Repeated-measures multi-factorial ANOVA -- Learning objectives -- What is repeated-measures multi-factorial ANOVA? -- Theory and rationale -- How SPSS performs repeated-measures multi-factorial ANOVA -- Effect size and power -- Writing up results -- Chapter summary.; Research example -- Extended learning task -- 13 Mixed multi-factorial ANOVA -- Learning objectives -- What is mixed multi-factorial ANOVA? -- Theory and rationale -- How SPSS performs mixed multi-factorial ANOVA -- Effect size and power -- Writing up results -- Chapter summary -- Research example -- Extended learning task -- 14 Multivariate analyses -- Learning objectives -- What are multivariate ; analyses? -- What is MANOVA? -- Theory and rationale -- How SPSS performs MANOVA -- Interpretation of output -- Effect size and power -- Writing up results -- Presenting data graphically -- Repeated-measures MANOVA -- Theory and rationale -- How SPSS performs repeated-measures MANOVA -- Interpretation of output -- Effect size and power -- Writing up results -- Chapter summary -- Research example (MANOVA) -- Research example (repeated-measures MANOVA) -- Extended learning tasks -- Appendix to Chapter 14: Manual calculations for MANOVA -- 15 Analyses of covariance -- Learning objectives -- What are analyses of covariance? -- What is ANCOVA? -- Theory and rationale -- How SPSS performs ANCOVA -- Effect size and power -- Writing up results -- MANCOVA: multivariate analysis of covariance -- How SPSS performs MANCOVA -- Effect size and power -- Writing up results -- Chapter summary -- Research examples -- Extended learning tasks -- Appendix to Chapter 15: Mathematics behind (univariate) ANCOVA -- 16 Linear and multiple linear regression -- Learning objectives -- What is linear regression? -- Theory and rationale -- Simple linear regression -- Effect size and power -- Writing up results -- Multiple linear regression -- How SPSS performs multiple linear regression -- Chapter summary -- Research example -- Extended learning task -- Appendix to Chapter 16: Calculating multiple linear regression manually -- 17 Logistic regression -- Learning objectives.; What is (binary) logistic regression? -- Theory and rationale -- How SPSS performs logistic regression -- Writing up results -- Chapter summary -- Research example -- Extended learning task -- 18 Non-parametric tests -- Learning objectives -- Introduction -- Common issues in non-parametric tests -- Mann-Whitney U test -- How SPSS performs the Mann-Whitney U -- Wilcoxon signed-rank test -- How SPSS performs the Wilcoxon signed-rank test -- Kruskal-Wallis test -- How SPSS performs Kruskal-Wallis -- Friedman's ANOVA -- How SPSS performs Friedman's ANOVA -- Chapter summary -- 19 Tests for categorical variables -- Learning objectives -- What are tests for categorical variables? -- Theory and rationale -- Measuring outcomes statistically -- Categorical tests with more than two variables -- Loglinear analysis when saturated model is rejected -- Chapter summary -- Research example -- Extended learning task -- 20 Factor analysis -- Learning objectives -- What is factor analysis? -- Theory and rationale -- How SPSS performs principal components analysis -- Writing up results -- Chapter summary -- Research example -- Extended learning task -- 21 Reliability analysis -- Learning objectives -- What is reliability analysis? -- Theory and rationale -- How SPSS performs reliability analysis -- Writing up results -- Chapter summary -- Research example -- Extended learning task -- Appendix 1: Normal distribution (z-score) table -- Appendix 2: t-distribution table -- Appendix 3: r-distribution table -- Appendix 4: F-distribution table -- Appendix 5: U-distribution table -- Appendix 6: Chi-square ( X[sup(2)]) distribution table -- References -- Glossary -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R.; S -- T -- U -- V -- W -- Y -- Z.
• Sommario/riassunto: Introduction to Statistics and SPSS in Psychology guides the reader carefully and concisely up the statistics staircase to success. Each step is supported by helpful visuals as well as advice on how to overcome problems. Interactive, lively, but never patronising, this is the complete guide to statistics that will take readers through their degree course from beginning to end. Take a step in the right direction and tackle statistics head on with this visual introduction.