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By G.G. Brittan

Deservedly so, Jules Vuillemin is generally revered and enormously well known. it's not easily that he has produced a wide physique of exceptional paintings, in lots of diversified components of philosophy. Or that he combines to an strange measure rigorous criteria with a really broad standpoint. or maybe that during his path-breaking money owed of algebra, of !)escartes, of Kant and of Russell, he confirmed in new and profound methods how the histories of technological know-how and philosophy should be used to light up one another. it's also that he has pursued the appliance of formal concepts and the security of liberal associations with an extraordinary singlemindedness and braveness. In a time and position the place the previous have been in most cases overlooked and the latter usually attacked, he carried on, at a few own fee, embodying a conventional and excellent notion of the philosophical existence, bridging nationwide ameliorations. those that be aware of him additionally treasure his friendship. regularly curious, he delights in new evidence and new reports, and continuously heightens the conception of these round him. nearly each year, on the collage de France he brought fresh classes consistently with clean and fruitful inSights. exceedingly solicitous, he follows the lives of the households round him in nice element. The devotion of his scholars is legend. His own strength is usually legend. many people have him bounding up the steps at a time or during the gardens of the Luxembourg, his wit and irony apace.

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W'En Note that our assumptions about nand p preclude the possibilities of the "denominator being zero or infinite. Theorem 1: A statistic T is sufficient if and only if, for x l ,x 2 EX, T(x l ) = T(x 2), implies L(wl x I) - L(wl x 2). In other words, a statistic T : X + J is sufficient if and only if, for every tE::r, it is true that -all points x on the T-surface X t generate equivalent likelihood 25 Information and Likelihood: Principles functions. The following result is then an immediate consequence of the above.

In the other kind of situations, where we have 'invariance and such other things', Barnard says that we can make assertions that are 'far wider and firmer'. But, wider and firmer than what? ciently firm or wide? What does oC assert that is not suffi- We must recognize this basic fact that "c does not assert anything that can be measured in terms of its operating characteristics. e with a set of his favourite likelihood methods of inference (see Section 1 of Chapter 3) and it is this set of likelihood methods that he is now finding to be generally lacking in width and firmness.

25 is 'more informative' than e2' it is equally incontrovert i ble that the particular sample (17, 115) from experi- ment &2 will tell us a great deal more about the parameter than will the sample (17, 20, ••• , 52) from &25" To be more specific, with Inf {e n ,(xl' x2' ••• , xn )} we know without any shadow of doubt that the true value of w must belong to the set where m = 100 - (x n - xl)' In the present case the likelihood function (for the parameter w) is 'ilat' over the set A and is zero outside (a situation that is typical of all survey sampling setups) and this means that the sample (xl' x 2 ' ••• , xn) from experiment en 'supports' each of the points in the set A with equal intensity.

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