A key advantage of beta distributions which I expected to see mentioned is that they are a conjugate prior for the binomial distribution—it’s incredibly easy to update based on additional information. For example, we can look at the question you suggested, “What is the probability of my car being stolen this year, using data from the 10-block radius around my house?” Every day, we get new information about this—so we can update simply by adding the new data to the two parameters of the beta distribution.
I’ll also mention that the beta distribution is used heavily in property reinsurance, since it can be modelled as the percentage of the value of something which is destroyed in an event—it’s bounded, unlike the normal distribution, and can represent secondary uncertainty well—for example, conditional on, say, a category 4 hurricane with a given wind speed and radius following a certain track, we still don’t know how much damage a given house will have, but can use a beta distribution to represent it. (The we convolve the likelihoods with the damage function, but that’s a different discussion.)
A key advantage of beta distributions which I expected to see mentioned is that they are a conjugate prior for the binomial distribution—it’s incredibly easy to update based on additional information. For example, we can look at the question you suggested, “What is the probability of my car being stolen this year, using data from the 10-block radius around my house?” Every day, we get new information about this—so we can update simply by adding the new data to the two parameters of the beta distribution.
I’ll also mention that the beta distribution is used heavily in property reinsurance, since it can be modelled as the percentage of the value of something which is destroyed in an event—it’s bounded, unlike the normal distribution, and can represent secondary uncertainty well—for example, conditional on, say, a category 4 hurricane with a given wind speed and radius following a certain track, we still don’t know how much damage a given house will have, but can use a beta distribution to represent it. (The we convolve the likelihoods with the damage function, but that’s a different discussion.)