Facts are true claims, in contrast with mere opinions, or normative claims. John Cook supplies this “stat fact”: scientist do and do not want subjective posterior probabilities. Which is it? And are these descriptions of the different methods widely accepted “facts”? I’ve placed this in my “rejected posts” (under msc kvetching” simply because I don’t take this seriously enough to place on my regular blog.
Putting the methods you use into context
It may come as a surprise, but the way you were probably taught statistics during your undergraduate years is not the way statistics is done. …It might be disconcerting to learn that there is no consensus amongst statisticians about what a probability is for example (a subjective degree of belief, or an objective long-run frequency?). …..
Bayesian methods are arguably the oldest; the Rev. Thomas Bayes published his theorem (posthumously) in 1764. …The controversial part of Bayesian methodology is the prior information (which is expressed as a distribution and often just referred to as “a prior”), because two people may have different prior knowledge or information and thus end up with a different result. In other words, individual knowledge (or subjective belief) can be combined with experimental data to produce the final result. Probabilities are therefore viewed as personal beliefs, which naturally differ between individuals. This doesn’t sit well with many scientists because they want the data “to speak for themselves”, and the data should give only one answer, not as many answers as there are people analysing it! It should be noted that there are also methods where the prior information is taken from the data itself, and are referred to as empirical Bayesian methods, which do not have the problem of subjectivity. ….The advantage of Bayesian methods is that they can include other relevant information and are therefore useful for integrating the results of many experiments. In addition, the results of a Bayesian analysis are usually what scientists want, in terms of what p-values and confidence intervals represent.
Note that the references include only critics of standard statistical methods; not even Cox is included. Stat fact: this is not a statistically representative list?
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