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| Wallace C.S. — Statistical and Inductive Inference by Minimum Message Length |
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| Предметный указатель |
Quantizing lattices 178 285
quantum mechanics 340
Quinlan, T.R. 315
Raman. A. 314
Random coding of estimates 210
Random variables 19—21
RANGE 20
Range, known, uniform distribution of, mean of 183—187
reality 2
Records 355—356
Redundant code 79
Regression in categories 320
Regular expressions 127
Regular grammars, inferences of 305—314
Regular grammars, probabilistic 308
Retrace equality 348—349
Reversible laws 340—341
Rissanen, J.J. 4—5 73 99—100 401 408—415
Rivest, R.L. 315
Ron, D 321—325
Rounding-off quantum 168
Roundoff error 224
Roundoff vector 241
Rumantir, G.W. 272
Sample mean 260
Sample variance 260
Schemes, R. 327
Schou estimate 268
Schou, G. 268
Schwarz, G. 35
science 1
Science, Grand Theories of 386—387
Science, philosophy of 1—2
Scientific languages 391
Second law of thermodynamics 88
Set X of possible data 144—145
Set(s), discrete hypothesis 156
Set(s), of possible inferences 147 148
Shannon Fano code 70
Shannon information 57—100
Shannon information, algorithmic complexity versus 107—110
Shannon measure 104
Shannon, C.E. 4 57—100 103—110 118 121 225
simplicity 12
Singularities in priors 237
Sloane. N.J.A. 178 257
Small-sample message length, MML 235—236
Smith, A.F.M. 47
Smith. B. 125
SMML see “Strict minimum message length estimators”
Solomonoff prediction 396 404 405
Solomonoff, R.J. 3 5 401—408
SPACING 170—171
Spacing functions 223—226
Spacing functions, family of 242
Speech 59
Spherical von Mises — Fisher distribution 268—269
Spirtes, P. 327
SRM (Structural Risk Minimization) 274 321 322
Standard deviation 201
State space 340
state variables 134
Statistical critique, summary of 54—55
Statistical inference 3
Statistics, sufficient see “Sufficient statistics”
Stick collision model 352
Stirling's approximation 86 179
Stochastic complexity 409
Stop and start conditions, Turing machines 102—103
Strict minimum message length (SMML) estimators 143—196
Strict minimum message length (SMML) estimators, approximation to sequence problem 325—326
Strict minimum message length (SMML) estimators, approximations to, summary 218—219
Strict minimum message length (SMML) estimators, binomial example 157—160
Strict minimum message length (SMML) estimators, defined 143
Strict minimum message length (SMML) estimators, discrimination of 192—195
Strict minimum message length (SMML) estimators, efficiency of 189—192
Strict minimum message length (SMML) estimators, explanation for continuous data 166—187
Strict minimum message length (SMML) estimators, explanation for discrete data 153 166
Strict minimum message length (SMML) estimators, general properties of 187—195
Strict minimum message length (SMML) estimators, generality of 189
Strict minimum message length (SMML) estimators, minimizing relations for 156—157
Strict minimum message length (SMML) estimators, problem definition 144—153
Strict minimum message length (SMML) estimators, quadratic approximations to 221—255
String length, expected 64
Strings, non-random 109
| Structural equivalence 330—331
Structural models 305 336
Structural risk minimization (SRM) 274 321—322
Subjective nature of information 79—81
Success count ranges 159
Sufficient statistics 29 161—163
Sufficient statistics, binomial example using 163 164
Sufficient statistics, minimal 163
Surrogate class label estimate 288—289
symbols 58
Symmetry 50
Target functions 274
Teleological explanation 367
Test statistic 33
TETRAD II 327 335—336
Theories 10
Theories, approximate 14
Theories, demise of 11 14
Theories, Grand, of Science 386 387
Theory description codes 124
Theory description codes, as priors 114—115
Theory descriptions, universal codes in 1 15—116
Thorn, A. 275
Time reversal 350
Time reversibility 337 340 341
Time, Thermodynamic Arrow of 337—384
TM see “Turing machines”
TOM (Totally ordered model) 328 333
Totally ordered model (TOM) 328—333
Transformed parameter 241
Transition arcs 305
Tree, coding class distributions at leaves 317—318
Tree, coding structure 316—318
Tree, leaves 61
Tree, levels 64
Trinomial distribution, solution for 165—166
Turing machines (TM) 101—102
Turing machines (TM), choice of 103
Turing machines (TM), Educated (ETM) 130—131
Turing machines (TM), Universal see “Universal Turing Machines”
Turing probability distributions 103—104
Two-chamber simulations 379 382
Unary code 92
Uncertainty regions, in hypothesis space 214—215
Uncertainty regions, meaning of 215—218
Uncertainty regions, via Dowe's construction 216
Uncertainty regions, via limited precision 216
Unclassified models, classified models versus 295—297
Uniform distribution of known range, mean of 183—187
Uniform prior 182
Uniform problem 186
Uninformative priors 49—51
Universal codes 98 100
Universal codes, in theory descriptions 115 116
Universal Turing Machines (UTM) 3 105—107 125 127 388 389 392
Universal Turing Machines (UTM), as priors 124—130
Universal Turing Machines (UTM), differences among 130—133
Universal Turing Machines (UTM), primitive (UTM0) 135 140
UTM see “Universal Turing Machines”
UTM0, (Primitive Universal Turing Machines) 135—140
V'yugin. V.V. 414
V-C method 274
Vapnik. V.N. 274
Variance 31
Variance, sample 260
Vector-valued continuous random variables 20—21
Verb 389
Viswanathan, M. 274 323—326
Vitanyi, P.M.B. 392
von Mises-Fisher distribution 266 269
von Mises-Fisher distribution, circular 267 268
von Mises-Fisher distribution, spherical 268—269
Voronoi regions 178 179
Voronoi regions, hexagonal 181
Vovk, V. 405
Wishart distribution 262
Within-instance variance 203
Witten, I.H. 73
Woodroofe, M. 35
Word 60
Work tape, Turing machines 101
Worst case excess length 410
Zador's bound 178 257
Zador. P. 178 257
Zero bias 188
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