A uniform prior is a type of prior distribution used in Bayesian statistics that assumes all outcomes are equally likely before any data is observed. This concept is particularly important in the …

To specify the prior parameters $\alpha$ and $\beta$, it is useful to know the mean and variance of the beta distribution (for example, if you want your prior to have a certain mean and …

the distribution is called a “uniform prior”, if its density or mass is constant over $\Theta$; the distribution is called a “non-uniform prior”, if its density or mass is not constant over $\Theta$.

Jan 22, 2015 · I would expect a uniform prior to be a good example of an uninformed prior and get the same result as the frequentist approach. However, this is not the case. As an example, …

The appropriate prior distribution for the parameter θ of a Bernoulli or Binomial distribution is one of the oldest problems in statistics 1. Bayes and Laplace suggesting a uniform prior, which is …

Prior probability is a probability distribution that expresses established beliefs about an event before (i.e. prior to) new evidence is taken into account. When the new evidence is used to …

A prior distribution where the probability of every outcome is the same. For discrete data , this is a probability of 1/N for each value, where N is the number of values. If the data is unbounded …

First note that the prior density, which is uniform on \((0, 1)\), is the beta \((1, 1)\) density. The posterior density is another beta, whose first parameter is obtained by adding the number of …

In Section 2 and Section 4, we provide an explicit formula and some potentially useful approx-imations for the posterior mean of μ when μ has a uniform prior in the solid ball Bn(0, c).

We used uniform priors, and no, the posteriors will not necessarily be uniform. Even if the parameters are uniformly distributed, parameter values closer to the "true" value have a higher …

Mar 18, 2021 · What you can say is that the posterior has the same form as the likelihood, up to a proportionality constant. Specifically, applying Bayes formula using a uniform prior on $\mu$ …

Jan 21, 2018 · Assuming that given a mean $\mu$, the data are normally distributed with variance $10$ and assuming a uniformly distributed prior density on the interval $(90, 110)$, we are …

My question is this: using the Uniform distribution works fine for the likelihood since we are holding $D$ constant and distributing across $a$, but what distribution should we use for the prior …

In many models it is possible to set an "uninformative" set of priors that allows some moments (e.g., the prior mean) to vary over the entire possible range of values, and this nonetheless …

Jul 23, 2019 · I came across this paper ($\textit{Prior distributions for variance parameters in hierarchical models}$ - $\textit{Andrew Gelman}$) that advocates uniform prior though it is for …

Jul 27, 2021 · One way to describe the situation in informal betting (“operational”) Bayesian terms is that the claim about an improper uniform prior overlooks how the information content of the …

Jul 11, 2020 · Prior is a belief you have on some quantity, typically on a set of parameters, without having any look at the data. If data is involved, the belief you have is updated and is called as …

If you use a uniform prior on a set that contains the MLE, then MAP=MLE always. The reason for this is that under this prior structure, the posterior distribution and the likelihood are proportional.