A primer of multivariate statistic by Richard J. Harris

By Richard J. Harris

As he used to be taking a look over fabrics for his multivariate path, Harris (U. of latest Mexico) discovered that the path had outstripped the present variation of his personal textbook. He determined to revise it instead of use a person else's simply because he unearths them veering an excessive amount of towards math avoidance, and never paying adequate recognition to emergent variables or to structural equation modeling. He has up to date the 1997 moment version with new assurance of structural equation modeling and diverse elements of it, new demonstrations of the homes of a few of the ideas, and desktop purposes built-in into each one bankruptcy instead of appended.

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Now let W be a proposition asserting the occurrence of some typical religious miracle, say, that a man walks unassisted across the surface of a lake. This case can be made to resemble the balls-in-the-urn case by supposing, first, that ¬ W always denotes the outcome, say, of the lake having an empty surface and, second, by decreasing the prior probability of W by increasing the number of ways the surface can be empty while still presenting the same visual stimulus our observer. But the case can be made to resemble the lottery case by supposing that ¬ W is comprised of different possibilities that present different visual stimuli (empty lake surface; man, with imperceptible wires attached to a balloon, walking across the lake).

He therefore concluded, like a just reasoner, that such evidence carried falsehood on the very face of it, and that a miracle supported by any human testimony, was more properly a subject of derision than of argument. 31 And about numerous corroborative witnesses to the Jansenist miracles, he writes: “And what have we to oppose to such clouds of witnesses, but the absolute impossibility or miraculous nature of the events, which they relate? And this surely, in the eyes of all reasonable people, will alone be regarded as a sufficient refutation” (E 125: 149).

So Price was wrong: his conclusion that, when deceit is absent, improbabilities as such do lessen the capacity of testimony to report the truth is not true in general. Case 2. Next suppose that the witness never makes an error of color perception but may lie about what she sees. Then • (13) • where p ℓ ≡ Pr(H ℓ /W&K) and p′ ℓ ≡ Pr(H ℓ /B&K) and H ℓ is the hypothesis that the witness lies. Again the diminution effect sets in. Case 3. I now allow for both error in color perception and for deceit on the part of the witness, but for sake of simplicity, I assume that error and deceit are probabilistically independent.

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A primer of multivariate statistic by Richard J. Harris
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