Differential geometry in statistical inference

Cover of: Differential geometry in statistical inference |

Published by Institute of Mathematical Statistics in Hayward, Calif .

Written in English

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  • Mathematical statistics.,
  • Geometry, Differential.

Edition Notes

Includes bibliographies.

Book details

StatementS.-I. Amari ... [et al.].
SeriesLecture notes-monograph series ;, v. 10
ContributionsAmari, Shunʼichi.
LC ClassificationsQA276 .D53 1987
The Physical Object
Paginationiii, 240 p. :
Number of Pages240
ID Numbers
Open LibraryOL2416451M
ISBN 100940600129
LC Control Number87082603

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Buy Differential Geometry in Statistical Inference (IMS Lecture Notes--Monograph Series, Volume 10) on FREE SHIPPING on qualified orders Differential Geometry in Statistical Inference (IMS Lecture Notes--Monograph Series, Volume 10): Shun-ichi Amari, O. Barndorff-Nielsen, Robert E. Kass, Steffen L.

Lauritzen, C. Rao, Shanti S Cited by: : Differential Geometry in Statistical Inference (IMS Lecture Notes--Monograph Series, Volume 10) () by Shun-ichi Amari; O. Barndorff-Nielsen; Robert E. Kass; Steffen L.

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Barndorff-Nielsen, Robert E. Kass, Steffen L. Lauritzen, C. Rao. Get this from a library. Differential geometry in statistical inference. [Shun'ichi Amari;]. Abstract. A higher-order asymptotic theory of statistical inference is presented in a unified manner in the differential-geometrical framework.

The first- second- and third-order efficiencies of estimators are obtained in terms of the curvatures and connections of submanifolds related to both the model and by: 6.

#Metrika#1 "More than hundred references are given showing the growing interest in differential geometry with respect to statistics.

The book can only strongly be recommended to a geodesist since it offers many new insights into statistics on a familiar ground." #Manuscripta Geodaetica#2. Differential Geometry in Statistical Inference (IMS Lecture Notes--Monograph Series, Volume 10) 作者: Shun-ichi Amari / O. Barndorff-Nielsen / Robert E.

Kass / Steffen L. Lauritzen / C. Rao 出版社: Institute of Mathematical Statistics 出版年: 定价: USD 装帧:. A brief survey is given of three different strands of theoretical developments which relate to the area of interplay between differential geometry and statistical inference: (i) an adjusted profile likelihood for which the adjustment factor turns out to be expressible in terms of the embedding curvature, (ii) yokes and geometry, in particular symplectic geometry, (iii) orthogeodesic models and.

Differential geometry provides an aesthetically appealing and often revealing view of statistical inference. Beginning with an elementary treatment of one-parameter statistical models and ending with an overview of recent developments, this is the first book Differential geometry in statistical inference book provide an introduction to the subject that is largely accessible to readers not already familiar with differential geometry.

Differential Geometry and Statistics | Michael K. Murray, John W. Rice (auth.) | download | B–OK. Download books for free.

Find books. Differential geometry in statistical inference. JSTOR, Hayward, California Cafaro C () The information geometry of chaos. Pro Differential geometry in statistical inference book, New York, USA. Kass RE, Vos PW () Geometrical foundations of asymptotic inference. John Wiley & Sons, New York, USA.

Marriot P, Salmon M () Applications of differential geometry in. Institute of Mathematical Statistics Lecture Notes - Monograph Series. Info; Contents; Search ← Previous book Next book → IMS Lecture Notes Monogr. Ser. Vol ; Differential geometry in statistical inference.

Geometrical foundations of asymptotic inference are described in simple cases, without the machinery of differential geometry. A primary statistical goal is to provide a deeper understanding of. Try the new Google Books Get print book.

No eBook available. ; Barnes& Springer-Verlag, - Geometry, Differential - pages. 0 Reviews. From inside the book - Write a review.

We haven't found any reviews in the usual places. Contents. Chapter. 1: HIGHERORDER ASYMPTOTIC THEORY OF STATISTICAL INFERENCE. Differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the issues that can be hidden in an algebraic development of a problem.

This volume is the first to apply these techniques to s: 1. Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem.

Originally published inthis volume was an early example. Statistical Inference from Stochastic Processes Proceedings of a Summer Research Conference held 49 Complex differential geometry and nonlinear differential equations, Yum-Tong Siu, Editor The paper used in this book is acid-free and falls within the guidelines established to.

Author: M.K. Murray Publisher: Routledge ISBN: Size: MB Format: PDF, ePub, Mobi View: Get Books. Differential Geometry And Statistics Differential Geometry And Statistics by M.K.

Murray, Differential Geometry And Statistics Books available in PDF, EPUB, Mobi Format. Download Differential Geometry And Statistics books, Several years ago our statistical friends and. The second half of the text provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry.

The book can serve as a suitable text for a topics course for advanced undergraduates and graduate students. Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points.

It has connections to manifold learning and provides the mathematical and algorithmic foundations of. Chapter Geometric 2-Manifolds David W.

Henderson, Daina Taimiņa, Experiencing Geometry, Fourth Edition (), ; Chapter III: Extensive manifolds and elliptic geometry Alfred North Whitehead, A treatise on universal algebra: with applications (Cambridge: The University Press, ), ; Chapter 2.

Historically, information geometry can be traced back to the work of C. Rao, who was the first to treat the Fisher matrix as a Riemannian metric. The modern theory is largely due to Shun'ichi Amari, whose work has been greatly influential on the development of the field.

[citation needed]Classically, information geometry considered a parametrized statistical model as a Riemannian manifold. Books shelved as differential-geometry: Differential Geometry of Curves and Surfaces by Manfredo P.

Do Carmo, Elementary Differential Geometry by Andrew. Many of the key concepts and results of statistical inference (cf. also Statistics) can be expressed efficiently in terms of differential re-expressions have been helpful both in illuminating classical statistical procedures and in developing new methodology.

Differential Geometry in Statistical Inference S.-I. Amari, O. Barndorff-Nielsen, R. Kass, S. Lauritzen and C. Rao Lecture Notes-Monograph Series. Vol. 10, Differential Geometry in Statistical Inference (), pp.

i-iii++19+++++ ( pages) Published By: Institute of Mathematical Statistics. Lauritzen, S.L. () Chapter 4: Statistical Manifolds. Differential Geometry in Statistical Inference. Vol. 10, Institute of Mathematical Statistics, Lecture Notes Monograph Series, Hayward, has been cited by the following article: TITLE: A Note on Finding Geodesic Equation of Two Parameters Gamma Distribution.

AUTHORS: William W. We present here a brief review of papers and monographs on the differential geometry of statistical manifolds. In this introductory chapter we seek to cover sufficient differential geo-metry in order to understand its application to econometrics. It is not intended to be a comprehensive review either of differential geometric theory, or of all the applications that geometry has found in statistics.

Buy Bayesian Inference Statistical AnalysIS: 40 (Wiley Classics Library) 1 by E. Box, George (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible s: 3. Two canonical books on the subject, with reviews, then two other references: Differential Geometry and Statistics, M.K.

Murray, J.W. Rice. Ever since the introduction by Rao in of the Fisher information metric on a family of probability distributions there has been interest among statisticians in the application of differential geometry to statistics.

differential geometry, followed by a sketch of some of the early statistical applications. Then a summary is given of more recent work applying differential geometry to the asymptotic theory of statistical inference.

Finally, current work and possible directions for the future are discussed. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry.

Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman-Scott problem), is demonstrated concisely in Part III.

Statistical inference is the process by which properties of a population are deduced based on a sample of data drawn from that population. Working across a variety of research areas and with a range of collaborators, Andrews incorporates ideas from differential geometry and decision theory to build technically rigorous statistical inference.

Depending on your feelings about math, information geometry is either a sort of sublime union of differential geometry and statistics, or a Frankenstein’s Monster of two other monsters. Information geometry lets us do statistics on manifolds, which seems arbitrary (especially if you don’t know what a manifold is), but might be useful, and.

Statistics and Data Science This is the start of a book for a graduate-level course at NYU Physics titled Statistics and Data Science. Here are some of the objectives of this course: Learn essential concepts of probability. Become familiar with how intuitive notions of probability are connected to formal foundations.

Browse Book Reviews. Algebraic Geometry. Interdisciplinary Design of Game-based Learning Platforms. Fengfeng Ke, Valerie Shute, Kathleen M. Clark, and Gordon Erlebacher Novem Mathematics Education.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python. Ed Bueler. Novem Textbooks. Stochastic Calculus: A Practical Introduction This compact yet thorough text zeros in on the parts of the theory that are particularly relevant to applications.

It begins with a description of Brownian motion and the associated stochastic calculu. Models of Randomness and Statistical Inference Statistics is a discipline that provides with a methodology allowing to make an infer-ence from real random data on parameters of probabilistic models that are believed to generate such data.

The position of statistics. Some books on Likelihood Estimation * Amari, Barndorff-Nielsen, Kass, Lauritzen and Rao, Differential geometry in statistical inference. $-\small{\text{Geometrical approach for proving existence, uniqueness and other properties of MLE.}}$ * Butler, Saddlepoint Approximations with Applications.

$-\small{\text{Saddlepoint approximations to the MLE on complicated models.}}$. 2 days ago  Topology (with the goal of understanding differential geometry) Does anyone have textbook recommendations that cover these topics while making connections to physics + computation explicit throughout.

(My work up to this point has been in scalable Bayesian inference with an emphasis on pretending measure theory doesn't exist. Statistical Physics, Information Geometry and Inference for Learning (SPIGL'20) Thank you for your participation: The event was held both onsite and online.

We are looking forward to welcoming you at Geometric Science of Information (GSI) in Paris! Well, that depends a lot on what kind of statistics you are wanting to learn. I have to comment first that measure theory is not what most people consider “a bit of math”; many statisticians, if they learn that well at all, don’t encounter it unti.

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