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Q&A How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule?

0 answers · posted 3y ago by DNB‭ · edited 3y ago by DNB‭

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#2: Post edited by $user avatar$ DNB‭ · 2021-08-05T01:46:23Z (over 3 years ago)

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I learn best visually, and I found these [graph](https://www.thebottomline.org.uk/blog/ebm/bayesian-statistics/). 1. Does it furnish intuition on Theorem 2.3.5 below?
2. E.g. Is the Likelihood Ratio always graphically left of Posterior and Prior? If so, why?
>This can also be pictorially represented – the graph below shows the new posterior belief for a certain treatment has a reduced relative risk when the prior belief is combined with the data collected.
![Image alt text](https://math.codidact.com/uploads/5q3KLQQSKVffwScNR7Swsm89)
![Image alt text](https://math.codidact.com/uploads/ULoTXdroswWCZtQrBeyGcdom)
~~Blitzstein. *Introduction to Probability* (2019 2 ed). p 53.~~

I learn best visually, and I found these [graph](https://www.thebottomline.org.uk/blog/ebm/bayesian-statistics/). 1. Does it furnish intuition on Theorem 2.3.5 below?
2. E.g. Is the Likelihood Ratio always graphically left of Posterior and Prior? If so, why?
>This can also be pictorially represented – the graph below shows the new posterior belief for a certain treatment has a reduced relative risk when the prior belief is combined with the data collected.
![Image alt text](https://math.codidact.com/uploads/5q3KLQQSKVffwScNR7Swsm89)
![Image alt text](https://math.codidact.com/uploads/ULoTXdroswWCZtQrBeyGcdom)
Blitzstein. *Introduction to Probability* (2019 2 ed). p 53.
[Here](https://arbital.com/p/bayes_rule/?l=693) are more details and better pictures of Theorem 2.3.5.

#1: Initial revision by $user avatar$ DNB‭ · 2021-08-05T01:45:09Z (over 3 years ago)

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How do these 3 bell curves of Likelihood, Posterior, Prior pictorialize the Odds form of Bayes' rule?

I learn best visually, and I found these [graph](https://www.thebottomline.org.uk/blog/ebm/bayesian-statistics/). 1. Does it furnish intuition on Theorem 2.3.5 below?

2. E.g. Is the Likelihood Ratio always graphically  left of Posterior and Prior? If so, why? 

>This can also be pictorially represented – the graph below shows the new posterior belief for a certain treatment has a reduced relative risk when the prior belief is combined with the data collected.

![Image alt text](https://math.codidact.com/uploads/5q3KLQQSKVffwScNR7Swsm89)



![Image alt text](https://math.codidact.com/uploads/ULoTXdroswWCZtQrBeyGcdom)

Blitzstein. *Introduction to Probability* (2019 2 ed). p 53.

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