Percepied makes some interesting
comments about black ravens,
theories, and
statistics. All in all, a very good discussion. Here I merely add a bit of
information to what is discussed in the last part of his/her write up where there is
analysis of what a respectable scientist would do. Frankly, that is where there is a serious problems.
The problem is that Precepied suggests that a statistician would by definition be using Bayesian statistics to analyze data, or evaluate evidence. Nothing could be further from the truth. At the present time, my guess would be that statistical analyses that employ Bayesian statistics are, as a proportion of, say, journals that publish quantitative work, about 5% of all articles. Maybe less. Most statistical analysis relies on what we might call "classic" statistical analysis, which does not incorprorate Bayesian statistics.
A very quick review is in order, to point out to the reader what the major difference is between the two types of analyses. I'll keep it very short, as the main thrust belongs in another node. Classic statistical analysis tests the likelihood that a null hypothesis occurs by chance, and conversely, that the alternative hypothesis does not occur by chance. The null hypothesis usually assumes that some parameter is equal to zero. The value of some estimated parameter is compared to zero, and the difference between the two is tested for statistical significance.
Bayesian statistics does fundamemtally the same thing: Evaluating a null versus alternative hypothesis. The difference is in the assumption of what the null hypothesis tells us about the expected value of the parameter to be estimated. Bayesian statistics argues that that value should not be zero, but some other value, to be determined by the analyst. In theory, this makes a lot of sense. The problem is in the determination of those prior values. If not zero, what value then? This is where there are tremendous debates about the value of doing Bayesian analysis. In general though, there is great value in learning about, and possibly incorporating, Bayesian analysis into one's work. As long as the "priors" problem can be resolved somehow, of course.
So, in sum, a respectable scientist does not have to do any Bayesian statistics to be repsected by statisticians.
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A followup given Percepied's comments. Let me note that I didn't intend the write-up to be an attack on Bayesian statistics. In my opinion, the process is fascinating and is likely the appropriate approach for certain problems. The all ravens are black, in my opinion, is not one of those.
Why?
The all ravens are black problem, it seems to me , is the perfect kind of case to use for testing a null hypothesis H0:X=0, with the alternative being H0~=0. Null is all are black, alternative is at least one is not black. Using Bayesian stats, we would start with an assumption ( the prior value) that already suggests that not all ravens are black. That being the case, we wouldn't need to go any furhter... not all ravens are black by assumption, end of story.
In other cases, however, it might be best to use Bayesian stats. Suppose we have knowledge of a relationship between age and voting. As information is updated, we can change the priors, and move forward with the analysis. That would be fine. The all ravens are black problem is not one of this kind.
All said though, let me reiterate: This is not an attack on Bayesian stats, which I believe are fascinating.