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## Some Aspects of the Sequential Design of Experiments

Venue: | Bulletin of the American Mathematical Society |

Citations: | 461 - 0 self |

### Citations

927 |
A stochastic approximation method,” The
- Robbins, Monro
- 1951
(Show Context)
Citation Context ...ntial design. The non-sequential study of Problem I was initiated by Hotelling [7] (see also [8]), but no sequential theory has yet been published. Problem II has been considered by Robbins and Monro =-=[9]-=-; their method is as follows. Let {an} be a sequence of positive constants such that 00 00 (18) Z)«n<00, 2 a n = °°, 1 1 let 0i be arbitrary, and set534 HERBERT ROBBINS [September (19) 0w+i - On + an... |

815 |
Sequential Analysis
- Wald
- 1947
(Show Context)
Citation Context ...e value of n is stochastically dependent on the observations. A logical extension of the idea of double sampling came during World War II with the development, chiefly by Wald, of sequential analysis =-=[2]-=-, in which the observations are made one by one and the decision to terminate sampling and to accept or reject the lot (or, more generally, to accept or reject whatever statistical "null hypothesis" i... |

368 |
Statistical Decision Functions
- Wald
- 1949
(Show Context)
Citation Context ...ign of any experiment as data accumulates. The question, of course, is how best to do this. We are indebted to Wald for the first significant contribution to the theory of sequential design. His book =-=[5]-=- states the problem in full generality and gives the outline of a general inductive method of solution. The probability problems involved are formidable, since dependent probabilities occur in all the... |

33 |
First course in probability and statistics
- NEYMAN
- 1950
(Show Context)
Citation Context ...fi) J T 2 - (a + fi) and hence that (4) lim _" + ff- 2 «ft_ g' where we have set •™ 2-(« + /3) y I-7'i952] SEQUENTIAL DESIGN OF EXPERIMENTS 531 (5) 7- * " ' ' 2 It follows that in using the rule Ri, =-=(6)-=- Hm E ( — ) = lim ( — ) = y + — n-*<» \ n / n->» \ ft / 1 Now, if we knew which of the two numbers ce, /3 is the greater, then by using the corresponding coin exclusively we could achieve the result (... |

13 |
A method of sampling inspection
- Dodge, Romig
- 1929
(Show Context)
Citation Context ...agraph that the answer is yes, not only in the case of the coins but for any two populations. Returning to the general case in which A and B are arbitrary statistical populations for which the values =-=(1)-=- exist, consider the sampling rule R defined as follows: let 1 = ai < a2 < • • • < an < • • • , 2 = 6i < b2 < • • • < bn < • • • be two fixed, disjoint, increasing sequences of positive integers of de... |

11 |
Statistical aspects of ESP
- Feller
- 1940
(Show Context)
Citation Context ...any such rule R let (9) Ln(A, B, R) == max (a, 0) - E ® where E denotes expectation computed on the basis of a1 fi> and R, and let (10) Mn(R) = max [Ln(A, B, R)], («.0)532 HERBERT ROBBINS [September =-=(11)-=- <t>M = min [Mn(R)]. (R) It would be interesting to know the value of <j>{n) and the explicit description of any "minimax" rule R for which the value <j>(n) is attained. A much simpler problem is : do... |

10 |
A sample survey of the acreage under jute in Bengal
- Mahalanobis
- 1939
(Show Context)
Citation Context ...r could be a random variable dependent on the observations. Despite the total absence of theory, a notable pioneering venture in the spirit of sequential design was carried out in 1938 by Mahalanobis =-=[3]-=- to determine the acreage under jute in Bengal. Preliminary sur-195*1 SEQUENTIAL DESIGN OF EXPERIMENTS 529 veys were made on a small scale to estimate the values of certain parameters, a knowledge of... |

10 |
The experimental determination of the maximum of a function
- Hotelling
- 1941
(Show Context)
Citation Context ... xi, • • • , #i_i at the previous levels 0i, • • • , 0;_i of the treatment, so that we are dealing with problems of sequential design. The non-sequential study of Problem I was initiated by Hotelling =-=[7]-=- (see also [8]), but no sequential theory has yet been published. Problem II has been considered by Robbins and Monro [9]; their method is as follows. Let {an} be a sequence of positive constants such... |

1 |
large-scale sample surveys
- On
- 1944
(Show Context)
Citation Context ...eys were made on a small scale to estimate the values of certain parameters, a knowledge of which was essential to the efficient design of a subsequent large scale census. In a subsequent publication =-=[4]-=- Mahalanobis called attention to the desirability of revising the design of any experiment as data accumulates. The question, of course, is how best to do this. We are indebted to Wald for the first s... |

1 |
Planning experiments seeking maxima, Chap. 3 of Selected techniques of statistical analysis
- Friedman, Savage
- 1947
(Show Context)
Citation Context ...i_i at the previous levels 0i, • • • , 0;_i of the treatment, so that we are dealing with problems of sequential design. The non-sequential study of Problem I was initiated by Hotelling [7] (see also =-=[8]-=-), but no sequential theory has yet been published. Problem II has been considered by Robbins and Monro [9]; their method is as follows. Let {an} be a sequence of positive constants such that 00 00 (1... |