I wonder about the meaning of uniform prior of an unknown parameter. Any argumentation with detail explanation would be much appreciated.
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$\begingroup$ See stats.stackexchange.com/search?q=%22uniform+prior%22 for examples and context. $\endgroup$– whuber ♦Apr 13, 2020 at 14:04
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2$\begingroup$ Your question is very general.You have a useful comment from @whuber and potentially useful links in an Answer posted 10 hrs ago. Can you let us know if you are looking for something else? Simple example? Answer to an underlying problem not discussed in your Question? $\endgroup$– BruceETApr 14, 2020 at 1:35
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A uniform function is simply a function that takes the same value for all its arguments. For example, $f(\theta)=1,\,\theta\in[0,1]$ is a uniform function. When you take such function as a prior distribution for an unknown parameter $\theta$, you have a uniform prior, also called a flat prior.
See wiki: Bayesian_inference for basic introduction into prior and posterior distributions for unknown parameters, the likelihood function, and the Bayes' theorem, which implies $$ \text{posterior} \propto \text{likelihood} \times \text{prior}. $$
One property of a uniform prior is that it does not move the mode of the likelihood function. In other words, the maximum likelihood estimate (MLE) for an unknown parameter coincides with its maximum a posteriori probability (MAP) estimate when the uniform prior is used (in MAP).
Another useful property is that many distributions have the uniform distribution as its special case. Thus, starting with a flat prior, one can derive a conjugate prior for a given likelihood function.
