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Analysis of Neural Data [[electronic resource] /] / by Robert E. Kass, Uri T. Eden, Emery N. Brown
| Analysis of Neural Data [[electronic resource] /] / by Robert E. Kass, Uri T. Eden, Emery N. Brown |
| Autore | Kass Robert E |
| Edizione | [1st ed. 2014.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 |
| Descrizione fisica | 1 online resource (663 p.) |
| Disciplina | 612.8 |
| Collana | Springer Series in Statistics |
| Soggetto topico |
Statistics
Neurosciences Neuropsychology Statistics for Life Sciences, Medicine, Health Sciences Statistical Theory and Methods |
| ISBN | 1-4614-9602-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Exploring Data -- Probability and Random Variables -- Random Vectors -- Important Probability Distributions -- Sequences of Random Variables -- Estimation and Uncertainty -- Estimation in Theory and Practice -- Uncertainty and the Bootstrap -- Statistical Significance -- General Methods for Testing Hypotheses -- Linear Regression -- Analysis of Variance -- Generalized Regression -- Nonparametric Regression -- Bayesian Methods -- Multivariate Analysis -- Time Series -- Point Processes -- Appendix: Mathematical Background -- Example Index -- Index -- Bibliography. |
| Record Nr. | UNINA-9910299963003321 |
Kass Robert E
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 2014 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos
| Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos |
| Autore | Kass Robert E |
| Pubbl/distr/stampa | New York, : Wiley, 1997 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 519.54 |
| Altri autori (Persone) | VosPaul W. <1961-> |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Mathematical statistics - Asymptotic theory
Geometry, Differential |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-27403-5
9786613274038 1-118-16598-5 1-118-16597-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Geometrical Foundations of Asymptotic Inference; Contents; Preface; 1 Overview and Preliminaries; 1.1 Overview; 1.1.1 Part I; 1.1.2 Part II; 1.1.3 Part III; 1.2 Notation; 1.2.1 Parameter Spaces; 1.2.2 Differentiation; 1.2.3 Tensor Notation; 1.2.4 Connection Notation; PART I ONE-PARAMETER CURVED EXPONENTIAL FAMILIES; 2 First-Order Asymptotics; 2.1 Introduction; 2.2 Exponential Families; 2.2.1 Basic Properties; 2.2.2 Asymptotics; 2.3 Curved Exponential Families: Definition and Examples; 2.3.1 Definition and Basic Properties; 2.3.2 Examples; 2.4 Estimators; 2.4.1 Estimating Equations
2.4.2 Auxiliary Spaces2.5 Fisher Information; 2.5.1 Information and Sufficiency; 2.5.2 The Information Inner Product; 2.5.3 Observed Information; 2.5.4 The Kullback-Leibler Divergence; 2.6 Consistency, Asymptotic Normality, and Efficiency; 2.6.1 Consistency and Asymptotic Normality; 2.6.2 Efficiency; 2.7 Bibliographical Remarks; 3 Second-Order Asymptotics; 3.1 Introduction; 3.2 Statistical Curvature; 3.2.1 Definition and Calculation; 3.2.2 Examples; 3.3 Information Loss and Local Sufficiency; 3.3.1 Information Loss; 3.3.2 Information Recovery; 3.3.3 Local Sufficiency 3.4 Other Applications of Statistical Curvature3.4.1 Second-Order Efficiency; 3.4.2 Deficiency; 3.4.3 Large Deviations; 3.4.4 The Fisher Scoring Algorithm; 3.5 Edgeworth Expansions; 3.6 Posterior Expansions; 3.7 Extensions; 3.7.1 Efron's General Formula; 3.7.2 Small-Dispersion Asymptotics; 3.8 Bibliographical Remarks; PART II MULTIPARAMETER CURVED EXPONENTIAL FAMILIES; 4 Extensions of Results from the One-Parameter Case; 4.1 Introduction; 4.2 Multiparameter Curved Exponential Families; 4.3 Curvature; 4.3.1 Curvature and Information Loss; 4.3.2 Asymptotic Risk and Bias 4.3.3 Interpretation in Nonlinear Regression4.3.4 Statistical Curvature in General Families; 4.4 Information Loss and Sufficiency; 4.5 Multivariate Edgeworth Series; 4.6 Posterior Expansions; 4.7 Bibliographical Remarks; 5 Exponential Family Regression and Diagnostics; 5.1 Introduction; 5.2 Normal Regression; 5.2.1 Normal Regression Model; 5.2.2 Maximum Likelihood Estimate; 5.2.3 Tangent Bundle; 5.3 Exponential Family Regression; 5.3.1 Preliminary Concepts; 5.3.2 A Vector Space Structure; 5.3.3 The Fisher Information Inner Product; 5.3.4 Estimation Algorithms; 5.4 Measures of Influence 5.4.1 Normal Linear Regression5.4.2 Exponential Family Regression; 5.5 Sensitivity Analysis of the Moment Structure; 5.5.1 Quasi-Likelihood Functions; 5.5.2 The Measures DL and LDLa; 5.5.3 Perturbations of the Moment Structure; 5.6 Bibliographical Remarks; 6 Curvature in Exponential Family Regression; 6.1 Introduction; 6.2 Background on Nonlinear Regression; 6.2.1 Asymptotic Normality; 6.2.2 Curvature Measures of Nonlinearity; 6.3 Curvature in Exponential Family Nonlinear Regression; 6.3.1 Generalizing the Standardized Second-Derivative Array; 6.3.2 Curvature Measures 6.4 Summaries of the Observed Third-Derivative Array |
| Record Nr. | UNINA-9910139590303321 |
|
Kass Robert E
|
||
| New York, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos
| Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos |
| Autore | Kass Robert E |
| Pubbl/distr/stampa | New York, : Wiley, 1997 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 519.54 |
| Altri autori (Persone) | VosPaul W. <1961-> |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Mathematical statistics - Asymptotic theory
Geometry, Differential |
| ISBN |
1-283-27403-5
9786613274038 1-118-16598-5 1-118-16597-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Geometrical Foundations of Asymptotic Inference; Contents; Preface; 1 Overview and Preliminaries; 1.1 Overview; 1.1.1 Part I; 1.1.2 Part II; 1.1.3 Part III; 1.2 Notation; 1.2.1 Parameter Spaces; 1.2.2 Differentiation; 1.2.3 Tensor Notation; 1.2.4 Connection Notation; PART I ONE-PARAMETER CURVED EXPONENTIAL FAMILIES; 2 First-Order Asymptotics; 2.1 Introduction; 2.2 Exponential Families; 2.2.1 Basic Properties; 2.2.2 Asymptotics; 2.3 Curved Exponential Families: Definition and Examples; 2.3.1 Definition and Basic Properties; 2.3.2 Examples; 2.4 Estimators; 2.4.1 Estimating Equations
2.4.2 Auxiliary Spaces2.5 Fisher Information; 2.5.1 Information and Sufficiency; 2.5.2 The Information Inner Product; 2.5.3 Observed Information; 2.5.4 The Kullback-Leibler Divergence; 2.6 Consistency, Asymptotic Normality, and Efficiency; 2.6.1 Consistency and Asymptotic Normality; 2.6.2 Efficiency; 2.7 Bibliographical Remarks; 3 Second-Order Asymptotics; 3.1 Introduction; 3.2 Statistical Curvature; 3.2.1 Definition and Calculation; 3.2.2 Examples; 3.3 Information Loss and Local Sufficiency; 3.3.1 Information Loss; 3.3.2 Information Recovery; 3.3.3 Local Sufficiency 3.4 Other Applications of Statistical Curvature3.4.1 Second-Order Efficiency; 3.4.2 Deficiency; 3.4.3 Large Deviations; 3.4.4 The Fisher Scoring Algorithm; 3.5 Edgeworth Expansions; 3.6 Posterior Expansions; 3.7 Extensions; 3.7.1 Efron's General Formula; 3.7.2 Small-Dispersion Asymptotics; 3.8 Bibliographical Remarks; PART II MULTIPARAMETER CURVED EXPONENTIAL FAMILIES; 4 Extensions of Results from the One-Parameter Case; 4.1 Introduction; 4.2 Multiparameter Curved Exponential Families; 4.3 Curvature; 4.3.1 Curvature and Information Loss; 4.3.2 Asymptotic Risk and Bias 4.3.3 Interpretation in Nonlinear Regression4.3.4 Statistical Curvature in General Families; 4.4 Information Loss and Sufficiency; 4.5 Multivariate Edgeworth Series; 4.6 Posterior Expansions; 4.7 Bibliographical Remarks; 5 Exponential Family Regression and Diagnostics; 5.1 Introduction; 5.2 Normal Regression; 5.2.1 Normal Regression Model; 5.2.2 Maximum Likelihood Estimate; 5.2.3 Tangent Bundle; 5.3 Exponential Family Regression; 5.3.1 Preliminary Concepts; 5.3.2 A Vector Space Structure; 5.3.3 The Fisher Information Inner Product; 5.3.4 Estimation Algorithms; 5.4 Measures of Influence 5.4.1 Normal Linear Regression5.4.2 Exponential Family Regression; 5.5 Sensitivity Analysis of the Moment Structure; 5.5.1 Quasi-Likelihood Functions; 5.5.2 The Measures DL and LDLa; 5.5.3 Perturbations of the Moment Structure; 5.6 Bibliographical Remarks; 6 Curvature in Exponential Family Regression; 6.1 Introduction; 6.2 Background on Nonlinear Regression; 6.2.1 Asymptotic Normality; 6.2.2 Curvature Measures of Nonlinearity; 6.3 Curvature in Exponential Family Nonlinear Regression; 6.3.1 Generalizing the Standardized Second-Derivative Array; 6.3.2 Curvature Measures 6.4 Summaries of the Observed Third-Derivative Array |
| Record Nr. | UNINA-9910678281303321 |
|
Kass Robert E
|
||
| New York, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos
| Geometrical foundations of asymptotic inference [[electronic resource] /] / Robert E. Kass, Paul W. Vos |
| Autore | Kass Robert E |
| Pubbl/distr/stampa | New York, : Wiley, 1997 |
| Descrizione fisica | 1 online resource (378 p.) |
| Disciplina | 519.54 |
| Altri autori (Persone) | VosPaul W. <1961-> |
| Collana | Wiley series in probability and statistics. Probability and statistics |
| Soggetto topico |
Mathematical statistics - Asymptotic theory
Geometry, Differential |
| ISBN |
1-283-27403-5
9786613274038 1-118-16598-5 1-118-16597-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Geometrical Foundations of Asymptotic Inference; Contents; Preface; 1 Overview and Preliminaries; 1.1 Overview; 1.1.1 Part I; 1.1.2 Part II; 1.1.3 Part III; 1.2 Notation; 1.2.1 Parameter Spaces; 1.2.2 Differentiation; 1.2.3 Tensor Notation; 1.2.4 Connection Notation; PART I ONE-PARAMETER CURVED EXPONENTIAL FAMILIES; 2 First-Order Asymptotics; 2.1 Introduction; 2.2 Exponential Families; 2.2.1 Basic Properties; 2.2.2 Asymptotics; 2.3 Curved Exponential Families: Definition and Examples; 2.3.1 Definition and Basic Properties; 2.3.2 Examples; 2.4 Estimators; 2.4.1 Estimating Equations
2.4.2 Auxiliary Spaces2.5 Fisher Information; 2.5.1 Information and Sufficiency; 2.5.2 The Information Inner Product; 2.5.3 Observed Information; 2.5.4 The Kullback-Leibler Divergence; 2.6 Consistency, Asymptotic Normality, and Efficiency; 2.6.1 Consistency and Asymptotic Normality; 2.6.2 Efficiency; 2.7 Bibliographical Remarks; 3 Second-Order Asymptotics; 3.1 Introduction; 3.2 Statistical Curvature; 3.2.1 Definition and Calculation; 3.2.2 Examples; 3.3 Information Loss and Local Sufficiency; 3.3.1 Information Loss; 3.3.2 Information Recovery; 3.3.3 Local Sufficiency 3.4 Other Applications of Statistical Curvature3.4.1 Second-Order Efficiency; 3.4.2 Deficiency; 3.4.3 Large Deviations; 3.4.4 The Fisher Scoring Algorithm; 3.5 Edgeworth Expansions; 3.6 Posterior Expansions; 3.7 Extensions; 3.7.1 Efron's General Formula; 3.7.2 Small-Dispersion Asymptotics; 3.8 Bibliographical Remarks; PART II MULTIPARAMETER CURVED EXPONENTIAL FAMILIES; 4 Extensions of Results from the One-Parameter Case; 4.1 Introduction; 4.2 Multiparameter Curved Exponential Families; 4.3 Curvature; 4.3.1 Curvature and Information Loss; 4.3.2 Asymptotic Risk and Bias 4.3.3 Interpretation in Nonlinear Regression4.3.4 Statistical Curvature in General Families; 4.4 Information Loss and Sufficiency; 4.5 Multivariate Edgeworth Series; 4.6 Posterior Expansions; 4.7 Bibliographical Remarks; 5 Exponential Family Regression and Diagnostics; 5.1 Introduction; 5.2 Normal Regression; 5.2.1 Normal Regression Model; 5.2.2 Maximum Likelihood Estimate; 5.2.3 Tangent Bundle; 5.3 Exponential Family Regression; 5.3.1 Preliminary Concepts; 5.3.2 A Vector Space Structure; 5.3.3 The Fisher Information Inner Product; 5.3.4 Estimation Algorithms; 5.4 Measures of Influence 5.4.1 Normal Linear Regression5.4.2 Exponential Family Regression; 5.5 Sensitivity Analysis of the Moment Structure; 5.5.1 Quasi-Likelihood Functions; 5.5.2 The Measures DL and LDLa; 5.5.3 Perturbations of the Moment Structure; 5.6 Bibliographical Remarks; 6 Curvature in Exponential Family Regression; 6.1 Introduction; 6.2 Background on Nonlinear Regression; 6.2.1 Asymptotic Normality; 6.2.2 Curvature Measures of Nonlinearity; 6.3 Curvature in Exponential Family Nonlinear Regression; 6.3.1 Generalizing the Standardized Second-Derivative Array; 6.3.2 Curvature Measures 6.4 Summaries of the Observed Third-Derivative Array |
| Record Nr. | UNISA-996209056103316 |
|
Kass Robert E
|
||
| New York, : Wiley, 1997 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||