week 10 -- Bayes Factor

Question 1

Bayes Factor

a Bayesian alternative to classical hypothesis testing:

also, the p-Factor is hard to interpret

• low means that we decrease belief in null hypothesis and increase belief in alternative
• but high means….? data inconclusive

Answer 1

compares closeness of two hypotheses with the observed data. Which is better?

One way of answering this question is to ask about the relative weight of the evidence: that is, how convincing is the observation with respect to the two hypothesis in question?
We need a way of understanding what it means for evidence to change what we believe. We start with the idea of prior odds, which describe the degree to which we favor one hypothesis over another before we see the data.
P(H0) / P(H1)
where P here represents plausibility and Hc and Hp are hypotheses of Carole and Paul. We can also describe the posterior odds, which describe the degree to which we favor one hypothesis over another after observing the data.
P(H0 ∣ y) / P(H1 ∣ y)

Question 2

p- value vs Bayes factor

P(D ∣ H-zero) vs (D ∣ H-zero) / (D ∣ H-one)

Answer 2

asymmetrical vs symmetrical
hard to interpret vs intutiive to interpret
requires no alternative hypothesis
vs requires specific alternative hypothesis

Question 3

how to specify an alternative hypothesis?

Answer 3

• previous research
• physiological considerations
• minimum therapeutic effect
• comparable manipulation
  …

Question 4

Bayes Factor short and sweet

Answer 4

The Bayes factor is the relative evidence in the data. The evidence in the data favors one hypothesis, relative to another, exactly to the degree that the hypothesis predicts the observed data better than the other.