Probability Theory: The Logic of ScienceCambridge University Press, 10/04/2003 The standard rules of probability can be interpreted as uniquely valid principles in logic. In this book, E. T. Jaynes dispels the imaginary distinction between 'probability theory' and 'statistical inference', leaving a logical unity and simplicity, which provides greater technical power and flexibility in applications. This book goes beyond the conventional mathematics of probability theory, viewing the subject in a wider context. New results are discussed, along with applications of probability theory to a wide variety of problems in physics, mathematics, economics, chemistry and biology. It contains many exercises and problems, and is suitable for use as a textbook on graduate level courses involving data analysis. The material is aimed at readers who are already familiar with applied mathematics at an advanced undergraduate level or higher. The book will be of interest to scientists working in any area where inference from incomplete information is necessary. |
من داخل الكتاب
النتائج 1-5 من 84
الصفحة 13
... independent variables' A and B can take on only those two values. At this point, a logician might object to our ... independently either of two values {T, F). There are, therefore, exactly 24 = 16 different logic functions f(A, B), and ...
... independent variables' A and B can take on only those two values. At this point, a logician might object to our ... independently either of two values {T, F). There are, therefore, exactly 24 = 16 different logic functions f(A, B), and ...
الصفحة 16
... independent NAND gates on one semiconductor chip. Given a sufficient number of these and no other circuit components, it is possible to generate any required logic function by interconnecting them in various ways. This short excursion ...
... independent NAND gates on one semiconductor chip. Given a sufficient number of these and no other circuit components, it is possible to generate any required logic function by interconnecting them in various ways. This short excursion ...
الصفحة 27
... independent variables, the functional equation to be solved is F(x,v)=F(u,z). (2.15) Differentiating with respect to x and y we obtain, in the notation of (2.10), (2.16) F2(x, v)Fi(y, z) = F,(M, z)F2(x, y). Elimination of F\(u, z) from ...
... independent variables, the functional equation to be solved is F(x,v)=F(u,z). (2.15) Differentiating with respect to x and y we obtain, in the notation of (2.10), (2.16) F2(x, v)Fi(y, z) = F,(M, z)F2(x, y). Elimination of F\(u, z) from ...
الصفحة 28
... independent of z. Now, (2.17) can be written equally well as G(x, v)F2(y, z) = G(x, y)C(y, z), (2.18) and denoting the left-hand sides of (2.17), (2.18) by U, V respectively, we verify that a V/tiy = ftU/dz. Thus, G(x, y)G(y, z) must be ...
... independent of z. Now, (2.17) can be written equally well as G(x, v)F2(y, z) = G(x, y)C(y, z), (2.18) and denoting the left-hand sides of (2.17), (2.18) by U, V respectively, we verify that a V/tiy = ftU/dz. Thus, G(x, y)G(y, z) must be ...
الصفحة 32
... independent variables, we have from (2.48) 5( v) = S\S(x)] + exp{-</}5(.v)5'[5(.v)] + O(exp{-2</}). (2.50) Using (2.46) and its derivative 5'[5(.v)]5'U) = 1, this reduces to — = 1 - exp{-(a + q)} + 0(exp{-2?}), (2.51) x ...
... independent variables, we have from (2.48) 5( v) = S\S(x)] + exp{-</}5(.v)5'[5(.v)] + O(exp{-2</}). (2.50) Using (2.46) and its derivative 5'[5(.v)]5'U) = 1, this reduces to — = 1 - exp{-(a + q)} + 0(exp{-2?}), (2.51) x ...
المحتوى
CLXXI | 341 |
CLXXII | 343 |
CLXXIII | 345 |
CLXXIV | 346 |
CLXXV | 351 |
CLXXVI | 354 |
CLXXVII | 355 |
CLXXVIII | 358 |
21 | |
23 | |
24 | |
30 | |
35 | |
37 | |
43 | |
44 | |
45 | |
47 | |
49 | |
51 | |
52 | |
XXVII | 60 |
XXVIII | 64 |
XXIX | 66 |
XXX | 68 |
XXXII | 69 |
XXXIII | 72 |
XXXIV | 73 |
XXXV | 75 |
XXXVI | 81 |
XXXVII | 82 |
XXXVIII | 84 |
XXXIX | 86 |
XL | 87 |
XLI | 90 |
XLII | 97 |
XLIII | 98 |
XLIV | 101 |
XLV | 107 |
XLVI | 109 |
XLVII | 112 |
XLVIII | 115 |
XLIX | 116 |
L | 117 |
LI | 119 |
LIII | 120 |
LIV | 122 |
LVI | 126 |
LVII | 132 |
LVIII | 133 |
LIX | 135 |
LX | 137 |
LXI | 140 |
LXII | 142 |
LXIII | 143 |
LXIV | 144 |
LXV | 146 |
LXVI | 148 |
LXVII | 149 |
LXVIII | 150 |
LXIX | 152 |
LXX | 154 |
LXXI | 157 |
LXXII | 158 |
LXXIII | 160 |
LXXIV | 163 |
LXXVI | 166 |
LXXVII | 167 |
LXXVIII | 168 |
LXXIX | 172 |
LXXX | 177 |
LXXXI | 178 |
LXXXII | 179 |
LXXXIII | 181 |
LXXXIV | 183 |
LXXXV | 186 |
LXXXVII | 188 |
LXXXVIII | 190 |
LXXXIX | 192 |
XC | 193 |
XCI | 195 |
XCII | 198 |
XCIII | 199 |
XCIV | 200 |
XCV | 202 |
XCVI | 203 |
XCVII | 205 |
XCVIII | 207 |
XCIX | 210 |
C | 211 |
CI | 213 |
CII | 215 |
CIII | 216 |
CIV | 218 |
CV | 219 |
CVI | 220 |
CVII | 221 |
CVIII | 222 |
CIX | 224 |
CX | 227 |
CXI | 229 |
CXII | 231 |
CXIII | 233 |
CXIV | 234 |
CXV | 235 |
CXVI | 236 |
CXVII | 238 |
CXVIII | 239 |
CXIX | 240 |
CXX | 243 |
CXXI | 245 |
CXXII | 246 |
CXXIII | 247 |
CXXIV | 248 |
CXXV | 249 |
CXXVI | 250 |
CXXVII | 253 |
CXXVIII | 254 |
CXXIX | 256 |
CXXX | 257 |
CXXXI | 260 |
CXXXII | 261 |
CXXXIII | 262 |
CXXXIV | 264 |
CXXXVI | 266 |
CXXXVII | 267 |
CXXXIX | 270 |
CXL | 271 |
CXLI | 274 |
CXLII | 276 |
CXLIII | 277 |
CXLIV | 280 |
CXLV | 281 |
CXLVI | 282 |
CXLVII | 285 |
CXLVIII | 289 |
CXLIX | 290 |
CL | 292 |
CLI | 293 |
CLII | 296 |
CLIII | 300 |
CLIV | 302 |
CLV | 304 |
CLVI | 305 |
CLVII | 310 |
CLVIII | 312 |
CLIX | 314 |
CLX | 315 |
CLXI | 317 |
CLXII | 320 |
CLXIII | 321 |
CLXIV | 324 |
CLXV | 326 |
CLXVI | 327 |
CLXVII | 329 |
CLXVIII | 331 |
CLXIX | 335 |
CLXX | 338 |
CLXXIX | 365 |
CLXXX | 370 |
CLXXXI | 372 |
CLXXXII | 374 |
CLXXXIV | 378 |
CLXXXVI | 382 |
CLXXXVIII | 386 |
CLXXXIX | 394 |
CXC | 397 |
CXCI | 398 |
CXCII | 400 |
CXCIII | 402 |
CXCV | 404 |
CXCVI | 406 |
CXCVII | 410 |
CXCVIII | 412 |
CXCIX | 415 |
CC | 417 |
CCI | 418 |
CCII | 421 |
CCIII | 423 |
CCV | 424 |
CCVI | 426 |
CCVII | 428 |
CCVIII | 430 |
CCIX | 432 |
CCX | 437 |
CCXI | 438 |
CCXII | 439 |
CCXIII | 440 |
CCXIV | 443 |
CCXV | 445 |
CCXVI | 449 |
CCXVII | 450 |
CCXVIII | 451 |
CCXIX | 452 |
CCXX | 453 |
CCXXI | 456 |
CCXXII | 459 |
CCXXIII | 464 |
CCXXIV | 467 |
CCXXV | 470 |
CCXXVI | 474 |
CCXXVII | 478 |
CCXXVIII | 480 |
CCXXIX | 483 |
CCXXX | 484 |
CCXXXI | 485 |
CCXXXII | 486 |
CCXXXIII | 490 |
CCXXXIV | 492 |
CCXXXV | 493 |
CCXXXVI | 499 |
CCXXXVII | 500 |
CCXXXVIII | 503 |
CCXXXIX | 505 |
CCXL | 506 |
CCXLI | 507 |
CCXLII | 509 |
CCXLIII | 510 |
CCXLIV | 511 |
CCXLV | 516 |
CCXLVI | 518 |
CCXLVII | 520 |
CCXLVIII | 521 |
CCXLIX | 527 |
CCL | 531 |
CCLI | 532 |
CCLIII | 533 |
CCLIV | 534 |
CCLV | 535 |
CCLVI | 536 |
CCLVII | 540 |
CCLVIII | 541 |
CCLIX | 544 |
CCLX | 545 |
CCLXI | 550 |
CCLXII | 553 |
CCLXIII | 555 |
CCLXIV | 557 |
CCLXV | 559 |
CCLXVI | 561 |
CCLXVII | 563 |
CCLXVIII | 566 |
CCLXIX | 567 |
CCLXX | 568 |
CCLXXII | 571 |
CCLXXIII | 573 |
CCLXXIV | 574 |
CCLXXV | 576 |
CCLXXVII | 579 |
CCLXXIX | 581 |
CCLXXX | 586 |
CCLXXXI | 588 |
CCLXXXII | 589 |
CCLXXXIII | 592 |
CCLXXXV | 594 |
CCLXXXVI | 595 |
CCLXXXVII | 596 |
CCLXXXVIII | 597 |
CCLXXXIX | 599 |
CCXC | 601 |
CCXCI | 602 |
CCXCII | 603 |
CCXCIII | 604 |
CCXCV | 605 |
CCXCVI | 607 |
CCXCVII | 608 |
CCXCVIII | 613 |
CCXCIX | 614 |
CCC | 615 |
CCCI | 617 |
CCCII | 619 |
CCCIII | 620 |
CCCIV | 622 |
CCCV | 624 |
CCCVI | 625 |
CCCVII | 627 |
CCCIX | 628 |
CCCX | 634 |
CCCXI | 636 |
CCCXII | 638 |
CCCXIII | 641 |
CCCXIV | 644 |
CCCXV | 648 |
CCCXVI | 651 |
CCCXVII | 655 |
CCCXVIII | 656 |
CCCXIX | 658 |
CCCXX | 659 |
CCCXXI | 661 |
CCCXXII | 662 |
CCCXXIII | 663 |
CCCXXIV | 665 |
CCCXXV | 666 |
CCCXXVI | 668 |
CCCXXVIII | 669 |
CCCXXIX | 671 |
CCCXXX | 672 |
CCCXXXI | 674 |
CCCXXXII | 675 |
CCCXXXIII | 677 |
CCCXXXIV | 679 |
CCCXXXV | 680 |
CCCXXXVI | 683 |
CCCXXXVII | 705 |
CCCXXXVIII | 721 |
CCCXXXIX | 724 |
عبارات ومصطلحات مألوفة
analysis appears applications argument Bayes binomial calculation Chapter coin common sense conclusions consider Cox's theorems criterion data set decision theory defined density derivation equal equations error estimate evidence example expected fact finite Fisher frequency Gaussian give given Harold Jeffreys hypothesis improper prior independent induction inductive reasoning inference infinite sets integral intuitive Jeffreys knowledge Laplace Laplace's likelihood likelihood function limit loss function mathematical maximum entropy mean measure noise normal notation noted nuisance parameters numerical values observed paradox physical plausible possible posterior distribution posterior pdf posterior probability predictions principle principle of indifference prior information prior probability probability assignment probability distribution probability theory problem product rule propositions random experiment reasoning relevant result robot rules of probability sampling distribution solution specified statement sufficient statistic suppose tell theorem theory as logic toss trials true widgets