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Very interesting Ben. :-) Reminds me of an ANN (neural network which again has been described somewhere as multilayered hierarchical logistic regression--perceptron) with its input-output and back propagation algorithms (posterior used as prior). Either way these are feedback learning loops that have been around ever since humans grew multiple layers on their cortices. rakesh PS: The information contained in this email is based partly on the posterior of the last email ( in this multilayered and multithreaded discussion) and partly on the prior associated information collected on the cortical perceptron of this emailer who has after much trepidation and calculation ( based on the likelihood ratio of prior emailing feedback) ventured to share this output. On Tue, Nov 9, 2010 at 12:53 AM, Djulbegovic, Benjamin < [log in to unmask]> wrote: > Hi Stephen, > I found what you wrote very interesting (that "Bayesians cannot use a set > of posterior distributions from various studies as the raw input to a > Bayesian analysis.") I have seen many, many papers that claim that "these > (posteriors) should be used as priors"...and we have certainly been teaching > in clinical medicine for years how posterior results of one diagnostic test > should/can be used as the prior for the second diagnostic test (at least, in > serially applied tests...). > Would you mind explaining or sending a reference where this was discussed > so that I can correct my naïve Bayesian views? > Thanks > ben > > > > > -----Original Message----- > From: Evidence based health (EBH) [mailto: > [log in to unmask]] On Behalf Of Stephen Senn > Sent: Monday, November 08, 2010 6:30 AM > To: [log in to unmask] > Subject: Re: SBM-EBM shouting match > > Richard Royall is a statistician who has had much to say about evidence. He > points out that on having completed a study there are three rather different > questions we might wish to answer. > 1. What do I now believe? > 2. What should I now do? > 3. What is the evidence of this study? > > Bayesians are concerned with 1 and (to the extent that they consider > utilities also) with 2. These are good and laudable concerns. > > However, it as an irony of Bayesian analysis that naive Bayesians are wont > to overlook that as the late George Barnard, the father of the likelihood > principle, pointed out, Bayesians cannot use a set of posterior > distributions from various studies as the raw input to a Bayesian analysis. > They can often make better use of standard frequentist summary statistics > (although P-values are very problematic and stopping rules are not really > relevant). > > So personally, I think that there is room within the statistical menagerie > for people who want to do EBM and those who want to do SBM without their > having to snipe at each other. > > Stephen > > -----Original Message----- > From: Evidence based health (EBH) [mailto: > [log in to unmask]] On Behalf Of Croft Daniel (RBF) NOC > Sent: 08 November 2010 10:54 > To: [log in to unmask] > Subject: Re: SBM-EBM shouting match > > Dear List, > > Would someone mind translating this debate into layman language for people > like me who are new to statistics? > > Am I right in thinking that the people who argue for using Bayesian > statistical methods want to consider what we know already when analysing new > data. They do this by estimating values to represent that prior knowledge > that then affect the analysis of the new data. > > The non-Bayesian people consider each new test with no prior > considerations, so that any result is possible. > > And do these two camps generally split into Science-Based Medicine people > and Evidence-Based Medicine people respectively? > > Regards, > > Daniel > > -----Original Message----- > From: Evidence based health (EBH) [mailto: > [log in to unmask]] On Behalf Of Michael Power > Sent: 08 November 2010 10:25 > To: [log in to unmask] > Subject: SBM-EBM shouting match > > David Gorski at the Science-Based Medicine blog has posted a put-down of > Steve Simon's defence of EBM: http://www.sciencebasedmedicine.org/?p=8151 > > I won't join this shouting match, or comment on the gratuitous ad hominems, > or remark on variation of the "but Brutus is an honourable man" rhetoric, or > draw attention (again) to the reification of EBM into a fantastic strawman. > > But, I do want to ask a serious question, provoked by Gorksi's comment that > EBM ignores prior probabilities. > > There must be a reason why Bayesian methods are so seldom used. Professor > Sir Michael Rawlins suggests five possibilities in his much lauded Harveian > Oration ( > http://bookshop.rcplondon.ac.uk/contents/pub262-9bc950aa-00e6-4266-8e80-e4bc63a25262.pdf > ): > > 1) People "prefer the apparent (but illusory) security of a clear > definition of what constitutes an 'extreme' result when tested against the > null hypothesis, and they are reluctant to accept that either personal > belief or judgement should come into play in decision making." "clinical > investigators are > much more reluctant to accept a subjective approach to the interpretation > of probability than statisticians." > > 2) "there have been substantial controversies about the derivation of the > prior probability" "too much has been made of the alleged difficulties" > > 3) "Bayesian analyses are computationally complex" > > 4) "some statisticians - albeit a dwindling number - are unfamiliar with > the techniques of Bayesian analysis and are unwilling (or unable) to adapt. > Some generously attribute this variation in skill-mix to a statistician's > original choice of university. Others, less kindly, believe it to be > generational. As one Bayesian explained to me: 'Statisticians who were > taught how to use log books and slide rules can't usually do Bayesian > statistics'" > > 5) "regulatory authorities have sometimes been hesitant to concede that > Bayesian approaches may have advantages" > > These reasons, especially the 4th (I was taught a long time ago to use log > books and slide rules), seem to me to be insufficient to explain why > Bayesian methods are not more widely used. > > The question I want to ask is (at the risk of exposing my naiveté wrt > Bayesian methods): do the proponents of Bayesian methods mistakenly assume > that p-values and 95% confidence intervals indicate the true probability and > true range of measurements? > > Well trained EBMers know that p-values and 95% CI-s are indicators of > precision (statistical variation). P-values and 95% CI-s are not indicators > of accuracy (truth). This requires other information, which is provided by > critical appraisal and "triangulation" with other results. > > The way I understand it (or misunderstand it) is that with Bayesian methods > the subjective assessment is done when the prior probability is chosen > (note, it is not measured, even if a measurement is chosen). But, with > frequentist methods, the subjective assessment is done when the risk of bias > and error is assessed with critical appraisal. In other words, both methods > require qualitative assessment of their results. > > I prefer the frequentist method because it makes transparent the essential > role of critical appraisal to assess accuracy (risks of bias and error). Am > I wrong? >