In this post, I want to give a from-first-principles account of Bayesian and frequentists approaches to statistical analysis. Bayesian and frequentism have been discussed here often, although LessWrong posts on these topics are often focused on Bayesians and frequentists as it comes to probability and rationality, or its use in...
In this post, I am going to write about the practical difficulty of specifying priors that reflect internal beliefs, and about the possibility of performing probabilistic inference with partially specified or imprecise priors. For the most part, I will try to give the general intuition and then link to some...
In this post, I want to give a from-first-principles account of Bayesian and frequentists approaches to statistical analysis. Bayesian and frequentism have been discussed here often, although LessWrong posts on these topics are often focused on Bayesians and frequentists as it comes to probability and rationality, or its use in AI. Here, I am going to focus on statistical analyses that are intended for human readers. This is a somewhat experimental attempt to cobble together a sensible framework from the often confusing and mismatched pieces I have encountered when trying to learn about this topic myself, and to keep things grounded on what statistical analysis is actually trying to accomplish rather than on abstract philosophical... (read 2344 more words →)
I agree with some of the sentiments in this post, but I think the claim in the second paragraph "Unfortunately, the CDC has repeatedly given advice with lots of evidence against it", is poorly supported. It suggests that the CDC has given advice that is not just incomplete or somewhat off-base, but that is ineffective and should be ignored. I don't think the points that deal with advice meet that standard:
Packages: The CDC quote explicitly refers to packages from China, so this more a matter of missing advice about what to do in other cases than bad advice.
Masks: At the end of the day, "don't buy masks" seems like good advice... (read more)
That makes a lot of sense, but it does require you to know your utility function ahead of time. When this is not the case we might still want to propagate whatever you know about the prior forward to the posterior as a kind of caching operation for use in future decisions.
In this post, I am going to write about the practical difficulty of specifying priors that reflect internal beliefs, and about the possibility of performing probabilistic inference with partially specified or imprecise priors. For the most part, I will try to give the general intuition and then link to some relevant scholarship. I will quickly review Bayes rule and probabilistic inference to start, but this post is primarily intended for readers that are already familiar with these concepts (you can read introductions in several places).
Bayes rule specifies how to compute the probability of a hypothesis, , given some data, :
Where is called the posterior, is the prior, and... (read 1243 more words →)