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And it's much harder to do with functions, unless you're good with R functional programming, than with discretized values for $p$.
I'm constructing an example similar to what you were doing, but not exactly the same.
Being amazed by the incredible power of machine learning, a lot of us have become unfaithful to statistics.
Our focus has narrowed down to exploring machine learning. We fail to understand that machine learning is not the only way to solve real world problems.
This experiment presents us with a very common flaw found in frequentist approach i.e.
It is the most widely used inferential technique in the statistical world.Similarly, intention to stop may change from fixed number of flips to total duration of flipping.In this case too, we are bound to get different depends heavily on the sample size.Here's some R code that will do the job: And here's the graphical result: As you can see, the posterior distributions do concentrate rather quickly and, despite a poor initial sample, are shifting their peak closer and closer to the true value of 0.5, albeit with some randomness.Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts.
But measured against a sample (fixed size) statistic with some stopping intention changes with change in intention and sample size.