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Bayesian regret

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This term has been used to compare a random buy-and-hold strategy to professional traders' records. This same concept has received numerous different names, as the New York Times notes:
135:, who called his theorem Controlled Random Walks. Other, later papers had titles like 'On Pseudo Games', 'How to Play an Unknown Game', 'Universal Coding' and 'Universal Portfolios'". 284: 43: 400: 191: 65: 112:, who provided the first mathematical treatment of a non-trivial problem of statistical data analysis using what is now known as 463: 458: 443: 169: 162: 36: 30: 127:"In 1957, for example, a statistician named James Hanna called his theorem Bayesian Regret. He had been preceded by 448: 453: 47: 90: 212:
Controlled random walks, D Blackwell, Proceedings of the International Congress of Mathematicians 3, 336-338
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of a Bayesian strategy and that of the optimal strategy (the one with the highest expected payoff).
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The references used may be made clearer with a different or consistent style of
82: 306: 240: 223: 412: 377: 330: 322: 249: 94: 145: 15: 108:(1702–1761), who proved a special case of what is now called 307:"Universal coding, information, prediction, and estimation" 271:, Dordrecht: Springer Netherlands, pp. 115–138, 401:"Pity the Scientist Who Discovers the Discovered" 8: 239: 192:Learn how and when to remove this message 66:Learn how and when to remove this message 29:This article includes a list of general 311:IEEE Transactions on Information Theory 205: 228:The Annals of Mathematical Statistics 7: 370:10.1111/j.1467-9965.1991.tb00002.x 35:it lacks sufficient corresponding 14: 352:Cover, Thomas M. (January 1991). 222:Banos, Alfredo (December 1968). 150: 20: 1: 89:is the expected difference (" 399:Kolata, Gina (2006-02-05). 277:10.1007/978-94-017-2527-9_6 480: 305:Rissanen, J. (July 1984). 263:Harsanyi, John C. (1982), 323:10.1109/TIT.1984.1056936 241:10.1214/aoms/1177698023 50:more precise citations. 354:"Universal Portfolios" 269:Papers in Game Theory 464:Social choice theory 358:Mathematical Finance 459:Bayesian statistics 444:Bayesian estimation 405:The New York Times 114:Bayesian inference 449:Economic theories 286:978-90-481-8369-2 224:"On Pseudo-Games" 202: 201: 194: 76: 75: 68: 471: 454:Machine learning 423: 422: 420: 419: 396: 390: 389: 349: 343: 342: 302: 296: 295: 294: 293: 260: 254: 253: 243: 234:(6): 1932–1945. 219: 213: 210: 197: 190: 186: 183: 177: 154: 153: 146: 71: 64: 60: 57: 51: 46:this article by 37:inline citations 24: 23: 16: 479: 478: 474: 473: 472: 470: 469: 468: 429: 428: 427: 426: 417: 415: 398: 397: 393: 351: 350: 346: 304: 303: 299: 291: 289: 287: 262: 261: 257: 221: 220: 216: 211: 207: 198: 187: 181: 178: 167: 161:has an unclear 155: 151: 144: 138: 129:David Blackwell 122: 93:") between the 87:Bayesian regret 72: 61: 55: 52: 42:Please help to 41: 25: 21: 12: 11: 5: 477: 475: 467: 466: 461: 456: 451: 446: 441: 431: 430: 425: 424: 391: 344: 317:(4): 629–636. 297: 285: 255: 214: 204: 203: 200: 199: 182:September 2018 163:citation style 158: 156: 149: 143: 140: 121: 118: 110:Bayes' theorem 74: 73: 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 476: 465: 462: 460: 457: 455: 452: 450: 447: 445: 442: 440: 437: 436: 434: 414: 410: 406: 402: 395: 392: 387: 383: 379: 375: 371: 367: 363: 359: 355: 348: 345: 340: 336: 332: 328: 324: 320: 316: 312: 308: 301: 298: 288: 282: 278: 274: 270: 266: 259: 256: 251: 247: 242: 237: 233: 229: 225: 218: 215: 209: 206: 196: 193: 185: 175: 171: 165: 164: 159:This article 157: 148: 147: 141: 139: 136: 134: 130: 125: 119: 117: 115: 111: 107: 103: 98: 96: 92: 88: 84: 81: 70: 67: 59: 49: 45: 39: 38: 32: 27: 18: 17: 416:. Retrieved 404: 394: 361: 357: 347: 314: 310: 300: 290:, retrieved 268: 258: 231: 227: 217: 208: 188: 179: 160: 137: 133:statistician 126: 123: 106:Thomas Bayes 101: 99: 86: 77: 62: 53: 34: 439:Game theory 364:(1): 1–29. 83:game theory 48:introducing 433:Categories 418:2017-02-27 292:2023-06-13 174:footnoting 142:References 104:refers to 80:stochastic 31:references 413:0362-4331 386:219967240 378:0960-1627 339:206735464 331:1557-9654 250:0003-4851 131:, also a 120:Economics 100:The term 170:citation 102:Bayesian 56:May 2021 95:utility 44:improve 411:  384:  376:  337:  329:  283:  248:  91:regret 33:, but 382:S2CID 335:S2CID 409:ISSN 374:ISSN 327:ISSN 281:ISBN 246:ISSN 172:and 366:doi 319:doi 273:doi 236:doi 78:In 435:: 407:. 403:. 380:. 372:. 360:. 356:. 333:. 325:. 315:30 313:. 309:. 279:, 267:, 244:. 232:39 230:. 226:. 116:. 85:, 421:. 388:. 368:: 362:1 341:. 321:: 275:: 252:. 238:: 195:) 189:( 184:) 180:( 176:. 166:. 69:) 63:( 58:) 54:( 40:.

Index

references
inline citations
improve
introducing
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stochastic
game theory
regret
utility
Thomas Bayes
Bayes' theorem
Bayesian inference
David Blackwell
statistician
citation style
citation
footnoting
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"On Pseudo-Games"
doi
10.1214/aoms/1177698023
ISSN
0003-4851
"Games with Incomplete Information Played by "Bayesian" Players, I–III Part I. The Basic Model"
doi
10.1007/978-94-017-2527-9_6
ISBN
978-90-481-8369-2
"Universal coding, information, prediction, and estimation"
doi

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