Frequentist vs. Bayesian

Frequentist only takes the given sample. Bayesian takes the given sample (observed evidence) and a prior belief and combine the two for posterior belief.

Example: What’s the failure rate of a factory producing lighbulbs if 5 of the 100 bulbs failed? Frequentist 5% (taking only given dataset), Bayesian, similar factories have a lot lower failure rate, let’s say 1% so than we add this new evidence and we say this factory probably has 2%.

Bayesian is more flexible (prior belief can be constructed with data, but also with subjective judgment or with more speculative knowledge from other disciplines) and more appropriate for cases where the data set is small. Bayesian is consider less objective (bc frequentist only takes statistic on given dataset.)

Bayesian thinking: Is about asking under this theory what I would expect to see?

So when observing any given reality it requiers separating what is from what I would expect to see.

Example

Taking the simulation hypothesis Sean Carroll says he a) wouldn’t expect to see universe that big and b) wouldn’t expect to be rendered in this resolution. It would be too expensive to run simulation that large. That is if we were living in a simulation it would be much smaller.

Sean Carroll 10:03 link