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LS itself does not assume a Normal error distribution, I guess we all agree on that. And the Bayesian viewpoint doesn't actually make any assumptions about the error distribution either, but it does make strong statements about the current state of knowledge which is a probability distribution. The way you summarise data or knowledge should allow anyone (the concept of an agent or robot is often introduced here to warrant objectivity) to reach the same conclusion. The true B-factors should not be negative but that is domain-specific knowledge that by providing only the first two moments is lost. Any unbiased robot would have to state his/her state of knowledge about the B-factor distribution as being Normal if only the mean and average were provided. If we assume - and there are good reasons for this - that the Bayesian approach a la Jaynes (there are many inconsistent flavours that confuse the Bayesian inference approach with traditional statistical concepts and get caught in condradictions from continuous limiting theorems) provides an optimal method for testing hypotheses (optimal in terms of not making conclusions that are neither warranted by the data and/or the specified domain prior knowledge), then one can analyse traditional methods in this framework and see for which cases the results coincide. When the results are the same, I would say that the conditions that led to this equivalence show the hidden assumptions for the optimal use of the method (I'm afraid I can't provide any textbooks or webpages to back this up - it just seems right). In this case, I guess I'm asking for trouble as the terminology is so different. Representing a 'state of knowledge' doesn't make much sense in traditional statistics. Maximum Likelihood is sort of half way between tradtional and Bayesian and can be seen as a limiting case of uninformative (not necessaerily uniform) priors, however it's normal use is closer to tradtional statistics and would indeed aim as modelling an error distribution. Within this framework LS gives the same results as MaxLik for normal errors. All this says is that the results coincide for normal errors (you hardly ever actually know the real distribution of errors). However, from the Bayesian point of view, an unbiased state of knowledge would be the Normal distribution (that says nothing about the errors other than you have so reason to assume that they are not Normal). Now if LS only gives the same results under the conditions of Normal errors or Normal state of knowledge, then this is the case in which LS is the method of choice. Maybe. Maybe not ;o) Richard PS Talking about bias is also... well, biased. Maximum likelihood estimates are often baised but for normally distributed errors superior to unbiased estimates in the mean square error sense.
