Société de Calcul Mathématique, SA 

We are glad to introduce the new book by Olga Zeydina and Bernard Beauzamy:
Probabilistic Information Transfer
A book you will be proud to have for yourself and to show to your friends !
ISBN: 9782952145862, ISSN : 17671175. Size 15,3 x 24 cm. Hardcover, 208 pages.
In real life situations, one rarely has desirably detailed information. It is sometimes incomplete, sometimes corrupted, or with missing or erroneous data. Conversely, some pieces of information do exist. Therefore, there is a natural wish: to try to use the existing information in order to reconstruct some missing items. However, this should be done with two constraints:
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I. Introduction  9 
First Part  General Presentation  15 
Chapter I  Presentation of the tool  17 
I. Introduction  17 
II. Construction of the EPH in one dimension  18 
A. Basic construction  18 
B. An example of application of the EPH  21 
III. Construction of the EPH in any dimension  24 
A. Minimal understanding of the situation  24 
B. The distance  25 
C. Changes with respect to the 1dimensional situation  25 
Chapter II  Taking into account the uncertainties  33 
I. Position of the problem  33 
II. A simple example  34 
III. Precautions to be taken  35 
IV. Taking into account many uncertainties  35 
Chapter III  From local to global estimates  37 
I. Introduction  37 
II. Investigation depending on the dimension  37 
A. Low dimension  37 
B. High dimension  38 
III. A simple example in low dimension  40 
Chapter IV  The EPH in nonhomogeneous situations  45 
I. Introduction  45 
II. Notation  45 
III. Construction of the EPH in a onedimensional space  46 
A. Before the first measurement  46 
B. After the first measurement  47 
C. When several measurements have been made  48 
IV. A simple example  50 
V. Construction of the nonhomogeneous EPH in any dimension  51 
VI. A simple example  53 
Chapter V  Putting weights upon the parameters  57 
I. Introduction  57 
II. Taking into account previous information  58 
III. Propagating the information  58 
IV. Constructing a nonisotropic EPH  59 
A. The formulas  59 
B. Practical construction  60 
Chapter VI  How to choose the data ?  63 
I. Introduction  63 
II. Different pasts  65 
III. Trends and randomness  66 
IV. Position and speed  69 
Chapter VII  One source, many sensors  73 
I. Presentation  73 
II. Mathematical description of the problem  73 
A. Transfer function  73 
B. Fusion of data  74 
III. A simple example  75 
IV. Other procedures  76 
 
Second Part  Applications of the EPH  79 
Chapter I  The use of the EPH in Epidemiology  81 
I. Introduction  81 
II. Traditional methods  81 
A. Linear regression  81 
B. Probability law  82 
III. Description of the problem  82 
IV. Building the EPH  83 
A. Specific construction  83 
B. Computing the parameter lambda  84 
C. Fixing the parameters  85 
V. Computation using EPH  85 
VI. Study of increments  87 
Chapter II  Applications to an Industrial Forecast  91 
I. Introduction  91 
II. Difference between statistics and probabilities  91 
III. General comments about the use of statistics by the Industry  92 
A. Regression Method  93 
B. Index Point method  94 
IV. Better methods  96 
A. Variable Weight Method  96 
B. The EPH  97 
Chapter III  Estimating the pollution in a harbour  103 
I. Description of the problem  103 
II. Traditional methods  103 
III. Using the EPH  104 
A. Estimate of the pollution in the first layer  105 
B. Estimates of the pollution for the second layer  107 
C. Where are the risk zones ?  110 
D. Deciding future measurements  112 
Chapter IV  Construction of a proximity index between Industrial Objects  115 
I. Description of the problem  115 
II. A simple example  116 
A. Nonnumerical values  117 
B. Normalization of the parameters  117 
C. Taking into account the importance of each parameter  118 
D. The distance between two objects  118 
E. Construction of the proximity index  119 
F. Propagation of the information using the EPH  120 
Chapter V  The EPH and the safety of nuclear reactors  123 
I. Description of the problem  123 
II. Two dimensional problem  125 
A. Step 1: transfer coefficients  126 
B. Step 2: taking uncertainties into account  128 
C. Step 3: introducing the EPH  130 
D. Recombining the collectrons  133 
E. Estimating the uncertainties  133 
III. Three dimensional problem  134 
 
Third Part  Technical Construction  135 
Chapter I  General construction of the EPH  137 
I. Introduction  137 
II. Notation  138 
III. Building the EPH in the onedimensional case  138 
A. Before the first measurement  138 
B. After the first measurement  139 
C. Two measurements, one dimension  154 
D. Any number of measurements, one dimension  158 
IV. Building the EPH in the multidimensional case  162 
A. Bounds for each parameter  162 
B. Preliminary normalization of the parameters  162 
C. Densities after normalization  163 
D. Case of 2 parameters.  164 
E. General Case: K parameters and N measurements  165 
V. Questions about the model  172 
A. Discrete and continuous entropy  172 
B. Dependence on the discretization  175 
C. Dependence on the min and max values  176 
Chapter II  Looking for dangerous zones  177 
I. Introduction  177 
II. Presentation of the problem  178 
III. Dangerous zones  179 
IV. Search for an extreme point  183 
V. Random search  184 
A. Preliminary warning  184 
B. Uniform distribution on the unit sphere  188 
C. Random search for dangerous zones  190 
Chapter III  Ranking the parameters  193 
I. Introduction  193 
II. Practical approach  194 
Chapter IV  Existing techniques  199 
I. Introduction  199 
II. Deterministic techniques  199 
III. Probabilistic Techniques  200 
A. Kriging Interpolation  200 
B. Use of other information  201 
References  203 
Credits  205 
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