Information Measures : Information and its Description in Science and Engineering (Signals and Communication Technology)

個数:

Information Measures : Information and its Description in Science and Engineering (Signals and Communication Technology)

  • 在庫がございません。海外の書籍取次会社を通じて出版社等からお取り寄せいたします。
    通常6~9週間ほどで発送の見込みですが、商品によってはさらに時間がかかることもございます。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合がございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。

  • 提携先の海外書籍取次会社に在庫がございます。通常3週間で発送いたします。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合が若干ございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • 【入荷遅延について】
    世界情勢の影響により、海外からお取り寄せとなる洋書・洋古書の入荷が、表示している標準的な納期よりも遅延する場合がございます。
    おそれいりますが、あらかじめご了承くださいますようお願い申し上げます。
  • ◆画像の表紙や帯等は実物とは異なる場合があります。
  • ◆ウェブストアでの洋書販売価格は、弊社店舗等での販売価格とは異なります。
    また、洋書販売価格は、ご注文確定時点での日本円価格となります。
    ご注文確定後に、同じ洋書の販売価格が変動しても、それは反映されません。
  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 547 p., 64 illus.
  • 商品コード 9783540408550

基本説明

New in softcover. Hardcover was published in 2001.

Full Description

This book is intended to be an introduction to the mathematical description of information in science. The necessary mathematical theory of this introduction will be treated in a more vivid way than in the usual theorem-proof structure. This, however, enables us to develop an idea of the connections between different information measures and to understand the trains of thought in their derivation, which is a crucial point for correct applications. It is therefore our intention in the mathematical descriptions to evolve the important ideas of the derivations, so that we obtain the resulting functions as well as the main thoughts and the conditions for the validity of the result. This simplifies the handling of the information measures, which are sometimes hard to classify without any additional background information. Though the mathematical descriptions are the exact formulations of the measures examined, we do not restrict ourselves to rigorous mathematical considerations, but we will also integrate the different measures into the structure and context of possible information measures. Nevertheless the mathematical approach is unavoidable when we are looking for an objective description and for possible applications in optimization.

Contents

Abstract.- Structure and Structuring.- 1 Introduction.- Science and information.- Man as control loop.- Information, complexity and typical sequences.- Concepts of information.- Information, its technical dimension and the meaning of a message.- Information as a central concept.- 2 Basic considerations.- 2.1 Formal derivation of information.- 2.2 Application of the information measure (Shannon's information).- 2.3 The law of Weber and Fechner.- 2.4 Information of discrete random variables.- 3 Historic development of information theory.- 3.1 Development of information transmission.- 3.2 Development of information functions.- 4 The concept of entropy in physics.- The laws of thermodynamics:.- 4.1 Macroscopic entropy.- 4.2 Statistical entropy.- 4.3 Dynamic entropy.- 5 Extension of Shannon's information.- 5.1 Rényi's Information 1960.- 5.2 Another generalized entropy (logical expansion).- 5.3 Gain of information via conditional probabilities.- 5.4 Other entropy or information measures.- 6 Generalized entropy measures.- 6.1 The corresponding measures of divergence.- 6.2 Weighted entropies and expectation values of entropies.- 7 Information functions and gaussian distributions.- 7.1 Rényi's information of a gaussian distributed random variable.- 7.2 Shannon's information.- 8 Shannon's information of discrete probability distributions.- 8.1 Continuous and discrete random variables.- 8.2 Shannon's information of a gaussian distribution.- 8.3 Shannon's information as the possible gain of information in an observation.- 8.4 Limits of the information, limitations of the resolution.- 8.5 Maximization of the entropy of a continuous random variable.- 9 Information functions for gaussian distributions part II.- 9.1 Kullback's information.- 9.2 Kullback'sdivergence.- 9.3 Kolmogorov's information.- 9.4 Transformation of the coordinate system and the effects on the information.- 9.5 Transformation, discrete and continuous measures of entropy.- 9.6 Summary of the information functions.- 10 Bounds of the variance.- 10.1 Cramér-Rao bound.- 10.2 Chapman-Robbins bound.- 10.3 Bhattacharrya bound.- 10.4 Barankin bound.- 10.5 Other bounds.- 10.6 Summary.- 10.7 Biased estimator.- 11 Ambiguity function.- 11.1 The ambiguity function and Kullback's information.- 11.2 Connection between ambiguity function and Fisher's information.- 11.3 Maximum likelihood estimation and the ambiguity function.- 11.4 The ML estimation is asymptotically efficient.- 11.5 Transition to the Akaike information criterion.- 12 Akaike's information criterion.- 12.1 Akaike's information criterion and regression.- 12.2 BIC, SC or HQ.- 13 Channel information.- 13.1 Redundancy.- 13.2 Rate of transmission and equivocation.- 13.3 Hadamard's inequality and Gibbs's second theorem.- 13.4 Kolmogorov's information.- 13.5 Kullbacks divergence.- 13.6 An example of a transmission.- 13.7 Communication channel and information processing.- 13.8 Shannon's bound.- 13.9 Example of the channel capacity.- 14 'Deterministic' and stochastic information.- 14.1 Information in state space models.- 14.2 The observation equation.- 14.3 Transmission faster than light.- 14.4 Information about state space variables.- 15 Maximum entropy estimation.- 15.1 The difference between maximum entropy and minimum variance.- 15.2 The difference from bootstrap or resampling methods.- 15.3 A maximum entropy example.- 15.4 Maximum entropy: The method.- 15.5 Maximum entropy and minimum discrimination information.- 15.6 Generation of generalized entropy measures.- 16 Concludingremarks.- 16.1 Information, entropy and self-organization.- 16.2 Complexity theory.- 16.3 Data reduction.- 16.4 Cryptology.- 16.5 Concluding considerations.- 16.6 Information.- A.1 Inequality for Kullback's information.- A.2 The log-sum inequality.- A.3 Generalized entropy, divergence and distance measures.- A.3.1 Entropy measures.- A.3.2 Generalized measures of distance.- A.3.3 Generalized measures of the directed divergence.- A.3.4 Generalized measures of divergence.- A.3.4.1 Information radius and the J-divergence.- A.3.4.2 Generalization of the R-divergence.- A.3.4.3 Generalization of the J-divergence.- A.4 A short introduction to probability theory.- A.4.1 Axiomatic definition of probability.- A.4.1.1 Events, elementary events, sample space.- A.4.1.2 Classes of subsets, fields.- A.4.1.3 Axiomatic definition of probability according to Kolmogorov.- Probability space.- A.4.1.4 Random variables.- A.4.1.5 Probability distribution.- A.4.1.6 Probability space, sample space, realization space.- A.4.1.7 Probability distribution and distribution density function.- A.4.1.8 Probability distribution density function (PDF).- A.5 The regularity conditions.- A.6 State space description.