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

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• bapowell
In summary, Bayesian inference is a statistical technique that can be used to make inferences about unknown probabilities. It can be used to make predictions about future events, and can be used to assess the evidence for hypotheses.
bapowell
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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
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 said:
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.

stevendaryl said:
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.

Hornbein said:
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.

stevendaryl said:
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
bapowell said:
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?

M can be thought of as the underlying theory, which in practice is a set of equations relating the observable quantities to a set of parameters (together with constraints on those parameters, like the ranges of permitted values). If an observation is made that is not well-accommodated by the model M, then we will find low posterior probabilities for the parameters of the model, p(H|O). This is a signal that we either need to consider additional parameters within M, or consider a new M altogether.

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## 1. What is scientific inference?

Scientific inference is the process of using evidence and reasoning to draw conclusions about the natural world. It involves making predictions and testing those predictions through experiments and observations.

## 2. What is the importance of balancing predictive success with falsifiability in scientific inference?

Balancing predictive success with falsifiability is important because it ensures that scientific theories are both accurate and testable. Predictive success means that a theory accurately predicts future observations, while falsifiability means that the theory can be proven wrong through experimentation or observation.

## 3. How do scientists balance predictive success with falsifiability?

Scientists balance predictive success with falsifiability by using the scientific method. This involves making observations, forming a hypothesis, conducting experiments, analyzing the results, and drawing conclusions. If the results do not support the hypothesis, it can be rejected or modified. This process helps to ensure that theories are both accurate and testable.

## 4. Why is it important to have a balance between predictive success and falsifiability?

Having a balance between predictive success and falsifiability is important because it allows for the development of reliable and accurate scientific theories. If a theory only focuses on predictive success, it may not be testable and therefore cannot be proven wrong or improved upon. On the other hand, if a theory is only focused on falsifiability, it may not accurately predict future observations.

## 5. Can a theory have both high predictive success and high falsifiability?

Yes, a theory can have both high predictive success and high falsifiability. In fact, this is the ideal balance for a scientific theory. A theory with high predictive success means that it accurately predicts future observations, while high falsifiability means that it is testable and can be proven wrong if new evidence or data arises. This balance allows for the development of reliable and accurate theories that can be continuously tested and improved upon.

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