I'm working through an introductory Bayesian stats text: Doing Bayesian Analysis. Having been away from stats for a while and having never working from a Bayesian framework it's a bit challenging.

Right now I'm stumbling on a problem about deriving a posterior probability from a small amount of neuroscience frequency data about a part of the brain being active during certain activities. The data and target answer can be found in Poldrack(2006)[PDF]

The exercise asks:

Given the table showing brain activity during certain activities; suppose a new study finds that the ROI (region of interest) is activated. If the prior probability that the task involves language processing is .5, what is the posterior probability, given that the ROI is activated? A study done by Poldrack(2006) reports that the posterior probability is 0.69.

The frequency data:

And I calculated the conjoint probabilities:

But when I apply Bayes' rule to calculate p(LS+|A+) I get .227

from this:

p(A+|LS+)p(LS+=.5) / p(A+)

(.052*.5) / .113

Would someone be so kind as to point out what I'm misunderstanding?

Right now I'm stumbling on a problem about deriving a posterior probability from a small amount of neuroscience frequency data about a part of the brain being active during certain activities. The data and target answer can be found in Poldrack(2006)[PDF]

The exercise asks:

Given the table showing brain activity during certain activities; suppose a new study finds that the ROI (region of interest) is activated. If the prior probability that the task involves language processing is .5, what is the posterior probability, given that the ROI is activated? A study done by Poldrack(2006) reports that the posterior probability is 0.69.

The frequency data:

Code:

```
Language Study Not Language Study Total
Activated 166 199 365
Not Activated 703 2154 2857
Total 869 2353 3222
```

Code:

```
LS+ LS- Marginal Activated
Activated+ 0.052 0.062 0.113
Activated- 0.218 0.669 0.887
Marginal LS 0.270 0.730 1
```

from this:

p(A+|LS+)p(LS+=.5) / p(A+)

(.052*.5) / .113

Would someone be so kind as to point out what I'm misunderstanding?

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