tag:blogger.com,1999:blog-1812431336777691886.post2362968108950627164..comments2022-05-12T12:41:40.084-04:00Comments on The Mermaid's Tale: Probability does not exist! Part IV. Here's to your health!Anne Buchananhttp://www.blogger.com/profile/09212151396672651221noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1812431336777691886.post-22971725802348560142012-01-24T05:56:00.003-05:002012-01-24T05:56:00.003-05:00If religion or philosophy tries to understand a pe...If religion or philosophy tries to understand a perplexing world using various kinds of approaches, science is trying to understand other aspects of the world,also perplexing. Philosophers and religious scholars recognize the challenges--even when dealing with received texts, as you of course know very well. <br /><br />We should acknowledge our similar problems and conundrums,and where matters of 'faith'--agreement to accept uncertainties--are appropriate.<br /><br />We can't know everything, apparently, and statistical methods are an eerily insubstantial but effective way of dealing with real-world problems. But we should acknowledge what such methods are, and aren't.Ken Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-63747148157569907202012-01-24T00:57:07.521-05:002012-01-24T00:57:07.521-05:00Ken, I agree with your focus in this series. In my...Ken, I agree with your focus in this series. In my comment in the beginning of this series, I only looked at the <i>theory</i> of probability. For example, in some cases, I will refer to a fair coin toss while I know that I could never prove that any give coin toss was absolutely fair, but I need such a theory to make any sense of science. And in your cases, you are criticizing variables in say GWAS that are incredibly complex and often impossibly to quantify in a statistical study.James Goetzhttps://www.blogger.com/profile/02412501436355228925noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-26235477585124388232012-01-19T11:13:17.769-05:002012-01-19T11:13:17.769-05:00I think that's right so long as we keep in min...I think that's right so long as we keep in mind what doubt and uncertainty, and our various assumptions, in mind.Ken Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-72163508420906190462012-01-19T10:55:18.698-05:002012-01-19T10:55:18.698-05:00Yes, I agree that one of the greatest challenges i...Yes, I agree that one of the greatest challenges is to convey the subjective nature of probability to the general public, even when there is a well established technical interpretation as such. Your efforts in this regard are appreciated.<br /><br />Interestingly, influence can work backwards. For example, as Bayesian methods have become more accepted (and perhaps in order that it can have become accepted), it has increasingly been the case that "prior" probabilities are set according to "objective" criteria, either by mathematical formulations, or by referring strictly to historical data (thus lessening the subjective influence of the analyst). Rather than the Bayesian viewpoint opening science to subjectivity, science seems to have constrained Bayesian ideas to become more "objective."Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-61992668707740540492012-01-19T10:10:41.643-05:002012-01-19T10:10:41.643-05:00Absolutely. And thanks for your thoughtful commen...Absolutely. And thanks for your thoughtful comment!<br /><br />We use Bayesian approaches informally and in our own research are developing more formal ways to take multiple sorts of mapping data into account to evaluate candidate regions.<br /><br />Bayesian methods provide a mechanical way, so to speak, of adjusting our strength of confidence in some explanation.<br /><br />Genetics and evolutionary biology use such methods all the time, as you say. I think that investigators may take their 'Bayesian' posterior probabilities more seriously than is legitimate relative to actual truth, as if it removed the subjective component. Then the conclusions are advertised to or get picked up by the gullible public media, grant system, etc. as if they were truths.<br /><br />I would also argue informally at least (I'm not qualified to say whether this is formal or not), that confidence limits are sometimes applied to posteriors, which is a kind of lapse back to frequentism (I think that MCMC methods in biology do that, by examining parametric surface shapes around chosen maxima).<br /><br />Likewise, as I'm sure you know, but many don't, likelihood methods are designed in a way to get the most out of existing data without assumptions of replicability. But then support intervals are constructed, which basically invoke frequentism, I think.<br /><br />These are technical points, and hopefully my perception isn't too far off. In any way, there is still the element of subjectivity that (I think) needs much more serious awareness.Ken Weisshttps://www.blogger.com/profile/02049713123559138421noreply@blogger.comtag:blogger.com,1999:blog-1812431336777691886.post-84401363489435493942012-01-19T10:01:03.948-05:002012-01-19T10:01:03.948-05:00Great series of posts on the nature of probability...Great series of posts on the nature of probability and statistics! I suspect you are aware of a relatively small but very active school of statistical thinking that wholly embraces the notion that probability is subjective, entirely in our heads, and not necessarily derived from repeatable events, but from the beliefs of the statistical analyst (wherever they may derive). This is known as Bayesian statistics. Its ideas are three-hundred years old (originating in a paper published by Thomas Bayes in 1763); since the mid-twentieth century it has maintained a steady voice against the more dominant mode of "frequentist" statistics (which derives from thinking about repeated events); in recent years has become appreciated especially in genetics, evolution, epidemiology, and other computationally intense disciplines.Anonymousnoreply@blogger.com