Bayesian statistics and biased procedures

A comparison of Neyman's theory of interval estimation with the corresponding subjective Bayesian theory of credible intervals shows that the Bayesian approach to the estimation of statistical parameters allows experimental procedures which, from the orthodox objective viewpoint, are clearly biased and clearly inadmissible. This demonstrated methodological difference focuses attention on the key difference in the two general theories, namely, that the orthodox theory is supposed to provide a known average frequency of successful estimates, whereas the Bayesian account provides only a coherent ordering of degrees of belief and a subsequent maximization of subjective expected utilities. To rebut the charge of allowing biased procedures, the Bayesian must attack the foundations of orthodox, objectivist methods. Two apparently popular avenues of attack are briefly considered and found wanting. The first is that orthodox methods fail to apply to the single case. The second is that orthodox methods are subject to a typical Humean regress. The conclusion is that orthodox objectivist methods remain viable in the face of the subjective Bayesian alternative — at least with respect to the problem of statistical estimation.     

Proactive interference and spontaneous alternation in rats

Two pairs of trials were given to naive rats in a T-maze. The first trial of a pair was forced to one arm, the second was free, and the delay between trials was 25 min. or 10 hr. Rats left in the maze for 15 sec. following the forced choice showed increased alternation on the second pair of trials at the 25-min. delay as compared with the 10-hr. delay. This was interpreted as due to a decline in alternation with delay on this pair of trials, together with an overall increase in alternation between the first and second pairs, and is consistent with the proactive interference theory of forgetting. Rats left in for 2 min. showed a decline in alternation with delay on the first pair of trials, but not on the second; this is inconsistent with the proactive interference theory.     

Discrimination of circles and squares with and without knobs by goldfish

Different groups of goldfish were trained to discriminate between a circle and either a square, a diamond, a square with a knob added at the top or a diamond with a knob. All subjects readily mastered the discrimination, and there was no significant difference between the groups in the number of trials taken to criterion. In transfer tests it was found that: (i) while there was no transfer from square to diamond or vice versa, the presence of knobs on these shapes did mediate transfer from one to the other, provided the knob remained in the top part of the shapes; (ii) all groups learned much more about the tops of the shapes than about the bottom halves; (iii) animals discriminated the square from the circle largely by detecting the presence of a strong horizontal edge at the top of the figure; (iv) two features of the diamond were discriminated--the presence of oblique contours and the existence of a point in the upper half of the shape. The results are discussed in terms of a proposed model of shape recognition.     

Book reviews

Animal Discrimination Learning. Edited by R. M. Gilbert and N. S. Sutherland. London: Academic Press. 1969. Pp. xvi + 501. 1358.

Luce, R. D. and Tukey, J. W. (1964). Simultaneous conjoint measurement: a new type of fundamental measurement. J. math. Psychol. I, 1-27.

Discrimination Learning. By D. A. Riley. Boston: Allyn and Bacon Inc. 1968. Pp. 172. Paperback 21s.

Annual Review of Psychology. Vol. 20. Palo Alto: Annual Reviews Inc. 1969. Pp. ix + 544. $9.00.

Cutaneous Sensation. By David Sinclair. London: Oxford University Press. 1967. Pp. xii + 306. 63s.

Modelling of Thinking and the Mind.. By N. M. Amosov. Translated by L. Finegold. New York: Spartan Books. London: Macmillan. 11967. Pp. xiii + 192.

The Mind of Mnemonist. By A. R. Luria. London: Jonathan Cape. 1969. Pp. xi + 160. 25s.

Determinants of Infant Behaviour IV. Edited by B. M. Foss. London: Methuen. 1969. Pp. 303. £3 10s.

Brain and Behaviour. Volumes 1-4. Edited by Karl Pribram. Harmondsworth: Penguin Books Ltd. 1969. Pp. 496 +573 + 523 + 524. 12s. 6d. per volume.