Timeline for What is the intuition behind beta distribution?
Current License: CC BY-SA 4.0
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| Feb 23, 2023 at 4:07 | history | edited | aerin | CC BY-SA 4.0 |
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| Oct 16, 2022 at 2:35 | comment | added | Galen | Here is a Python gist of aerin's Beta distribution plots. | |
| Jun 10, 2021 at 13:26 | comment | added | Neil G | ...the Jeffreys prior, which corresponds to the arcsine distribution. Equivalently, this is the uniform distribution if you had chosen the odd-seeming parametrization using the sine of the angle I described above. | |
| Jun 10, 2021 at 13:24 | comment | added | Neil G | Although your reasoning about the maximum likelihood estimate is correct, the part of your answer that's misleading is when you say "you got zero for the head and zero for the tail. Then, your guess about the probability of success should be the same throughout [0,1]." This assumes a uniform prior, and that the uniform distribution on [0, 1] is minimally assumptive. There's no reason to believe that. If you had arbitrarily chosen a different parametrization, your uniform distribution would correspond to a different $\alpha, \beta$. Incidentally, an invariant prior distribution would be | |
| Jun 10, 2021 at 13:21 | comment | added | Neil G | This answer seems intuitive, but it's a bit misleading. I agree that the beta distribution can model a density over probabilities $p \in [0, 1]$. However, there is no reason to prefer that parametrization. For example, you could just as easily model a density over the odds $\frac{p}{1-p}$, which is called the beta-prime distribution. You could model the log-odds, or you scale the probability $p$ [0, 1] to $[0, \frac{\pi}{2}]$, and model a density over the sin of that number. In each case, the shape of the density is different. | |
| Jun 11, 2020 at 14:32 | history | edited | CommunityBot |
Commonmark migration
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| Apr 12, 2020 at 19:01 | history | edited | Alexis | CC BY-SA 4.0 |
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| Jan 8, 2020 at 21:27 | comment | added | jkm | I really like this approach, they two are naturally related. The binomial coefficient is defined as a product of three factorials. The p.d.f.'s normalizing Beta function can be defined by a product of three Gamma functions. A Gamma function is literally a hack (okay, 'analytic continuation', whatever) for extending factorials from positive integers to all numbers. In fact, a Beta where the Gammas' parameters are integers gives you the same value as a binomial coefficient with k+1 and vice versa. | |
| Jan 8, 2020 at 21:16 | comment | added | Sextus Empiricus | What do you mean by 'models the probability'? And what do you mean by 'the probability is a random variable' outside the Bayesian context? | |
| Jan 8, 2020 at 20:49 | history | answered | aerin | CC BY-SA 4.0 |