# Scientific Inference P3: Balancing predictive success with falsifiability - Comments

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Scientific Inference P3: Balancing predictive success with falsifiability

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Pepper Mint and Greg Bernhardt

This series really is phenomenal!

bapowell
stevendaryl
Staff Emeritus
I second Greg's comment.

But it occurred to me that we really have no basis at all for assigning $P(H)$, the a priori probability of a hypothesis. I suppose that at any given time, there are only a handful of hypotheses that have actually been developed to the extent of making testable predictions, so maybe you can just weight them all equally?

stevendaryl
Staff Emeritus
I second Greg's comment.

But it occurred to me that we really have no basis at all for assigning $P(H)$, the a priori probability of a hypothesis. I suppose that at any given time, there are only a handful of hypotheses that have actually been developed to the extent of making testable predictions, so maybe you can just weight them all equally?

In the article, it's not $P(H)$ but $P(H | \mathcal{M})$, but I'm not sure that I understand the role of $\mathcal{M}$ here.

I second Greg's comment.

But it occurred to me that we really have no basis at all for assigning $P(H)$, the a priori probability of a hypothesis. I suppose that at any given time, there are only a handful of hypotheses that have actually been developed to the extent of making testable predictions, so maybe you can just weight them all equally?

There should be a basis for assigning the prior. It's just not part of the math.

You could collect data that 1% of the population has AIDS. That would be your prior for an individual having the condition.

stevendaryl
Staff Emeritus
There should be a basis for assigning the prior. It's just not part of the math.

You could collect data that 1% of the population has AIDS. That would be your prior for an individual having the condition.

Okay, I was thinking of a different type of "hypothesis": a law-like hypothesis such as Newton's law of gravity, or the hypothesis that AIDS is caused by HIV. I don't know how you would assign a prior to such things.

In the article, it's not $P(H)$ but $P(H | \mathcal{M})$, but I'm not sure that I understand the role of $\mathcal{M}$ here.
You can think of the hypothesis as being the value of a certain parameter, like the curvature of the universe. The model is the underlying theory relating that parameter to the observation, and should include prior information like the range of the parameter.

stevendaryl
anorlunda
Staff Emeritus
You can think of the hypothesis as being the value of a certain parameter, like the curvature of the universe. The model is the underlying theory relating that parameter to the observation, and should include prior information like the range of the parameter.

Suppose we observe something that is totally unrelated to the underlying theory. What is M in that case? What is P(H|M) in that case?

Edit: I should have asked what is P(O|M) in that case?