Lemm J.C. — Bayesian field theory :: Электронная библиотека попечительского совета мехмата МГУ

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Lemm J.C. — Bayesian field theory

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Название: Bayesian field theory

Автор: Lemm J.C.

Аннотация:

Lemm, a former teacher of physics and psychology at the University of Munster, Germany, applies Bayesian methods to problems in physics, offering practical examples of Bayesian analysis for physicists working in areas such as neural networks, artificial intelligence, and inverse problems in quantum theory. Nonparametric density estimation problems are also discussed, including, as special cases, nonparametric regression and pattern recognition.

Язык:

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 425

Добавлена в каталог: 04.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Negative binomial likelihood      65 70
Neumann boundary conditions      352
Neural networks      3 4 180 183—186 215 230
Neural networks, multilayer      183—186
Neural networks, one-layer      see "Perceptron"
Newton method      91 268 348—350 358
Noise induced prior      75—84 93
Non-negativity      6 21 27 41—46 78 93 99 112—114 116 161 198 349 358
Non-negativity and monotonicity      41 99 116
Non-quadratic potentials      8 224—227
Nonparametric boosting      198
Normal equation      175
Normalization      6 23 27 29 33 34 40—46 71 74 78 83 86—91 93—97 99 102 106 107 112—116 131 139 141 161 162 168—170 185—192 197 198 202—207 218 220 222—224 232 239 246 262 264 283 310 323—343 345 347 349 358 362
Normalization constraint      see "Normalization"
Normalization energy      207
Normalization in $L_{2}$ -norm      114
Normalization of eigenfunctions      262 264
Normalization of likelihoods      29 89—91 94—95 112 239 246
Normalization of predictive density      139
Normalization of priors      33 187—191 202—207 220 222—224 246 283 310
Null hypothesis      65 69
Observation equations      29
Occam’s razor      67—70
Optical flow field      187 250 310
Outliers      143 224 225
Output averaging      75 78 79
Output noise      17 19 73—75 77 78 81 82 84 116 142 318
Overfitting      67 112 144 185 192 233 237 271 280 292
p-value      65 70
Pairing fields      197
Particle mass      261 273 293—295 305
Partition sum      23 26 324—325 342
Parzen’s kernel      99 352
path integral      39 see
Penalized maximum likelihood approach      66 71
Perceptron      183 184
Piecewise smooth      224
Plug-in estimate      64 66 210
Pointer states      258
Poisson likelihood      14 127 165
Posterior      9—84
Posterior control      313—321
Posterior energy      26 27 130 131 168
Posterior mode      48 49 see
Posterior state of knowledge      13 20
Prediction error      210
Predictive density      9—84
Prior      9—84
Prior energy      26 40 43 100 116 117 121 123 124 126 128 130 170 178 181 189 203 204 208 217—220 222 223 227 230 267 277 278 281—283 300
Prior mode      49
Prior relaxation      103 106 233 348 351 358
Prior, Gaussian      8 85—164 see
Prior, improper      208 317
Prior, non-quadratic potentials      8 224—227
Prior, noninformative      208 317
Prior, normalization      33 187—191 202—207 220 222—224 246 283 310
Product ansatz      181—182
Projection matrix      176
Projection pursuit      3 63 180 182—183 186 269 309
Prospect theory      59
Pseudo Maximum Likelihood Approximation      71
Quadratic $\epsilon$ -insensitive error      142
Quadratic error      66 86 96 266
Quantum Anti-Zeno effect      291
Quantum field theory      5 39

Quantum Zeno effect      291 296
Quasi Maximum Likelihood Approximation      71
Quasi-Newton methods      268 348 349 357
Quenched field      342
Radial Basis Function (RBF) prior      43 143 148 151 152 265 271 291 354
Radial Basis Functions (RBF)      179 182 354
Rational decisions      319
Reference function      43 68 126 215 218—220 222 273 280 281 316 317 see
Regression      60 126—145
Regression function      4 14 16—18 37 43 45 60 76 79—81 102 106—108 110 118 122 123 126 127 130 141—148 151—153 156 158 160 185 199—201 216 233 235 239 249 269 316 318
Regression, projection pursuit      see "Projection pursuit"
Regularized error functional      27 40 64 70 71 85 86 89 92—94 209 231
Relative entropy      see "Kullback — Leibler entropy"
Replica approach      183 343
Replica method      see "Replica approach"
Resolvent      351
Ridge regression      180
Ritz method      172
Robust statistics      142 143 225
Rotation      118 187 197 205 215 250 254 310
Saddle point approximation      see "Maximum A Posteriori Approximation"
Scalar field      99 323
Scaling      122 187 197 208 215 254 310
Schroedinger equation      115
Self energy      338 339
Simulated annealing      24 191 216 282 283 286
Slater determinant      300 302 304
Smoothing splines      3
Smoothness prior      19 93 100—105 108 118 120 141 143 150—152 157 187 203 221 235 265—267 276 279—281 283 319
Sobolev distance      265
Specific prior energy      42 45 112 117 202
Spin glasses      183 190 325
Spin systems      258
Square-root field      114—115
Squared-error loss      60 61 141 185 245
Statistical field theory      5 26 32
Structural prior      12 15 18 72 74 75 319
Student-t distribution      208
Subjective probability elicitation      319
Support vector machine      3 134 142 165 209
Support vector regression      134 142 165
Switching between filtered differences      218 222 281 282
System equations      29
template function      122 124—126 130 168 170 172 195 197—201 203 208 215—217 219 221 223 230 232—235 241 242 247 251 253 265 281 see
Training energy      126 127 167 175
Truncated Radial Basis Function prior      see "Radial Basis Function (RBF) prior"
Unnormalized likelihood      161
Unsupervised learning      4
Vapnik — Chervonenkis-dimension      315
Variable metric methods      268 348
Variables, continuous      5 7 see real"
variables, dependent      9—20
Variables, discrete y      4
Variables, hidden      9—20 28 29 46 47 64 74 75 85 112 167 188 191 194 239 313—315 318—320
Variables, independent      9—20
Variables, infinite number of      4
Variables, latent      see "Variables hidden"
Variables, multidimensional      4
Variables, real      4 8 see continuous"
Variational derivative      87 116 see
Variational method      6 115 167 168 309
Vector field      118
Virtual training examples      186
Von Neumann series      83
Wiener process      144 147 see
Zero mode      74 76 84 91 92 96 120 350 351 354

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