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Comment by travisjungroth | Hacker News Reader

Frequentist is the default. People don’t promote it. They just teach it as statistics, use p-values, and look funny at anyone who does otherwise.

It’s like how you wouldn’t hear people in the US promote imperial measurements for home baking. When you dominate, you don’t have to advocate.

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I'd identify a larger problem, which is teaching anything as a bunch of recipes.

My college offered stats in two tracks: There was a one-semester course for science majors, which was mostly plugging numbers into formulas. The course was utterly baffling for most of the students who took it.

There was also a two-semester course for math majors. It was mainly about proofs, but also had time to go into more depth. You have to know the assumptions underlying a formula, if you're expected to prove it. ;-) But it was only taken by the math majors.

I’m not sure that teaching mathstats more broadly is the answer to frequentist approaches being used by default, or to the recipe problem. I did the whole mathstats thing as a student and spent a bunch of time doing calculus around things like maximum likelihood estimators or unbiased estimators. I don’t think it’s very useful for the application of statistics in practice. I would recommend Statistical Rethinking by Richard McElreath as a course in Bayesian statistics targeted at scientists who want to extract correct, useful conclusions from their experiments, which doesn’t follow the “recipe book” pattern.

I'm not sure of that either. For one thing, the students would be blown away.

One thing we didn't have when I took stats was computers. I graduated from high school in 1982, and the colleges in my state were just beginning to get computers. I wonder if stats could be approached differently if it could start with nothing but data -- lots of it -- and graphing tools. This could even happen pre-college.

I don’t know if it’s the “answer”, but it followed a pretty simple logistic curve for our curriculum at uni

First course was almost purely frequentist

Second was half and half with several weeks approaching the frequentist bayesian approach from both sides

Our third stats course was mostly bayesian though self directed as to which point of view was “most appropriate” for the formulated problem sets. I remember roughly half the cohort used a frequentist perspective on a fairly obvious (but not explicit) bayesian assignment and were severely punished by the course coordinator (fairly for a late year subject tbh)

But I don't see p-values as connected to frequentist statistics. Rather, p-values are a concept that applies to the problem of hypothesis testing, which both frequentist and bayesian statistics should apply to, right? And in both cases you would use a p-value. The unique thing that Bayesian statistics can do is fit parameters can calculate uncertainty in those parameters, which does not contradict any of the concepts of hypothesis testing.

A p-value is the frequency you’d expect to see a sample with an effect this size or greater, given the null hypothesis. It’s inherently a frequentist approach to inference.

You can squish it into Bayes by considering it a uniform prior on the real number line that you never update, but you’re not really doing things “in the spirit” of Bayes, then.

What is a “prior” in the context of hypothesis testing? That seems to me to be a concept used in parameter estimation, with Bayes rule. But hypothesis testing is not parameter estimation.

As the linked post points out, you can regularize a p-value based on prior experiments.

IMO, null hypothesis testing is way overused. We should be quantifying the comparison of the null versus alternative hypotheses. People already compare them. Might as well bring some math into it.

How is hypothesis testing different from parameter estimation? They seem conceptually the same to me, with one a special case of the other.

In Bayesian terms there is no distinction between hypothesis testing and parameter estimation.

If your hypothesis is that A is greater than B, then you're test boils down to "The probability that A is greater than B", which is arrived at through parameter estimation via Bayes' Theorem.

You can consider the distribution of estimates for a parameter to represent a space of possible hypothesis for the true value of that parameter and their absolutely or relative likelihood based on the information available.

The also has the pleasant consequence that hypothesis testing using Bayesian methods nearly always is closer to the actual question someone wants to answer rather than replying with confusing statements such as "the probability of rejecting the null hypothesis", which contains an implicit double negative.

> If your hypothesis is that A is greater than B, then you're test boils down to "The probability that A is greater than B", which is arrived at through parameter estimation via Bayes' Theorem.

but even in this situation you would need a threshold for decision making, i.e. a p-value.

"p-value" as a term already has a definition -- one that imposes a frequentist perspective -- so you'd have to come up with a new term to define a Bayesian analogue of that concept.

I fail to understand why the terminology matters. If you need to make a decision then there will be a threshold in the probability that will determine it. It doesn’t matter if you call it p values or anything else.

I'm not understanding your confusion. Different concepts require different words to distinguish them in conversation. p-value is a name, not merely a descriptor, of one possible way to define a threshold. Other ways of defining thresholds get different names so that everyone knows what's being discussed.

Bob bob bob'bob bob bob bob bob, bob bob bob bob bob "Bob".

I'm curious how much professional statistical experience you have? In my experience probabilities alone are very rarely used and distributions of beliefs are combined with distributions of value so you can choose optimal risk/reward scenarios.

Bayesian decision making typically involves combining a cost function with your posterior distribution.

It's worth pointing out that this is typically not possible in most frequentist frameworks since they work in double negative style assertions and arbitrary threshold rather than modeling the problem itself.

While you can map Bayesian approaches to frequentists tests, this is usually a misunderstanding of Bayesian methods coming from a purely frequentist background. Bayesian analysis is fundamentally more flexible since it just the application of the sum and product rules (you don't even need Bayes' theorem since it can be trivially derived from these) as well as corresponding cost/value functions.

I know this reply is a bit late, but, at least in my professional experience, Bayesian decision making typically does not involve just a probability of an event (in which thresholds are more or less arbitrary, including p-values) but involves mapping the probably to a cost/value in which the threshold isn't determined by arbitrary probability threshold but died to business value.

In the most common situations this typically means the expected value well exceeds the expected cost and you're comfortable with the risk if you're wrong.

> What is a “prior” in the context of hypothesis testing?

A prior could be any previous knowledge that you have on the subject, or anything about the world.

Let me give you a silly example. Imagine I do an experiment, on if person A can see the future, and predict coin flips.

Now, imagine that I do this experiment, and lo and behold it passes the 5% threshold P value!

Remember what a P value is. It is simply the percent chance that the results that you got were by chance.

So, if I do that experiment, and it actually gets at the "P value" of 5%, which means that there is a 5% chance of it happening by chance, do you know believe that Person A can see the future?

I wouldn't. I would need a much lower P value to start believing that.

Thats all a prior is. It is using the fact that "Person A can see the future!" is an extraordinary claim. And for that, we require extraordinary evidence. Much better evidence than a mere "5% that it happened by chance". P

I think with a Bayesian test one would use credible intervals rather than p values?

> But I don't see p-values as connected to frequentist statistics.

P-values are fundamentally Frequentist because this framework see that observed data as random, whereas Bayesian statistics believe our observations are the only thing that is actually known, and all the other parameters are what is random in our experiments. That is: the data is the only part of an experiment that is real, everything else that we can't directly observe is something we must hypothesize about.

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