Société de Calcul Mathématique, SA
A probability book for Engineers and Researchers:
Probabilistic Information Transfer
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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: 978-2-9521458-6-2, ISSN : 1767-1175. 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 1-dimensional 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 non-homogeneous situations | 45 |
I. Introduction | 45 |
II. Notation | 45 |
III. Construction of the EPH in a one-dimensional 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 non-homogeneous 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 non-isotropic 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 |
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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. Non-numerical 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 |
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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 one-dimensional 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 multi-dimensional 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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