For example, the standard deviation of a normal distribution is a constant? Why is that?
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What's your own background on the problem? When I asked a similar question in my undergraduate stats class, my professor accused me of being an "improperly trained Bayesian". – AdamO Jul 19 '23 at 15:18
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Briefly a random variable can be a constant - it takes one value with probability 1. Parameters of a distribution are equivalently defined according to the SLLN: the mean of the distribution is what you get when $n \rightarrow \infty$, you can for instance defined $\mu = E[\bar{X}]$, which is a useful consideration for Bayesian asymptotics. – AdamO Jul 19 '23 at 15:20
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If I understand correctly, from the Bayesian point of view, the parameter we are trying to estimate is a random variable and has its distribution, right? We have usually a prior about its distribution and a posterior after observation. So I always assume the parameter is a random variable. But today, I read from a finance textbook that the standard deviation from a distribution is a constant, but not a variable (note that they didn't say random variable), which makes me quite confused. – symphony001 Jul 19 '23 at 16:00
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See this site search. (This is a highly refined search because thousands of posts here on CV refer to model parameters.) – whuber Jul 19 '23 at 16:15