Thus notice that in this case, not only is the y-axis a probability (or more precisely a probability density), but the x-axis is as well (batting average is just a probability of a hit, after all)! The …

Given a model that uses Binomial distribution for likelihood, and Beta distribution for Prior. The product of the two which generates the Posterior is also a Beta distribution. Since the Prior …

2017年5月5日 · Thomas Bayes (1763) derived the Beta distribution [without using this name] as the very first example of posterior distribution, predating Leonhard Euler (1766) work on the …

2018年8月18日 · Beta distribution with $\alpha=4$ and $\beta=7$ means: some phenomenon with a bimodal response had 3 successes and 6 fails in 9 attempts. (I know this one is a bit …

2017年11月29日 · On Wikipedia for example, you can find the following formulas for mean and variance of a beta distribution given alpha and beta: $$ \mu=\frac{\alpha}{\alpha+\beta} $$ and …

That is one useful interpretation of the Beta distribution when it is used as a conjugate prior distribution to the binomial distribution. It breaks down a bit when you consider the possibility …

2021年7月9日 · If the beta distribution is a prior of a Bernoulli distribution (i.e. a rate of success for a binary outcome), then it is completely counterintuitive to me that the beta distribution should …

2020年11月11日 · The approach I've taken so far is to start with a prior that is an uninformative beta distribution: ...

2020年10月27日 · Not sure exactly what you're asking. Perhaps see Wikipedia on the beta distribution if neither of my guesses below is helpful. If you know that the distribution is …

2021年6月29日 · I understand that with mixed-models it is the distribution of the residuals that is important, not the distribution of the raw data points. A QQ-plot of the model residuals also …