Prior and Posterior Distributions
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- Опубліковано 12 лис 2020
- Here I discuss the concepts of the prior and posterior distribution. Also, illustrate the idea of a conjugate distribution with 3 theorems.
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very helpful video, thank you!
You're welcome. I love hearing that the videos are helpful. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
thank you sir, now i know how to fix them.
You're welcome. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
When calculating normal distribution as conjugate distribution, in the last step how could we know whether or not drop the constant away, like if we drop the constant it may be a normal distribution with variance 1? Thank you for your video! It made me learn a lot.
Such an interesting question. Many thanks for watching! In the normal example we assume that we know the variance, which means that it's a constant in regards to the variable mu. The constants in front of "e" can be dropped but the exponent of "e" contains a piece that must be the new variance in the normal distribution for it to be a normal distribution. So the variance can't be 1 because of the constants in the exponent of "e". I hope that helped. Don't forget to subscribe and let others know about this channel.
When you drop the constants and say that the simpler form is proportional to the form with constants, is that simpler form without the constants what is referred to as the "kernel" of the distribution?
In Bayesian theory, you are correct. One word of caution, is that context matters since "Kernel" has so many different meaning in different areas of math / stats. Many thanks for watching!
if asked for example 'Suppose that X follows a Poisson distribution with rate 'mew' and that
'mew' has exponential distribution with mean 1/100. We observe a
sample x = (1,5,3,10). What is the posterior distribution of ?" What would be the prior distribution? the poisson or the exponential ?
In a subtle way, this was covered in the video. In one of the Theorems, we proved that the Gamma Distribution was a conjugate prior for a Poisson Distribution. Since the Exponential Distribution is a Gamma Distribution, the Theorem can be used for the example you provide. Many thanks for watching and don't forget to subscribe.
@@statisticsmatt so following that example, the distribution that samples are taken from should be used for the prior distribution? Thanks for your replies, already subscribed! I enjoy your videos!
I remebered that was a little difficult for me change the approach of parameter estimation, from frequentist to bayesian... ☹
Your comment made me smile. I think many share your thoughts. Many thanks for watching!
Hi ; could you please help me, I have a research and iam in need to this answer. I have joint prior distribution and need to get the expectation of one of them, how get it , is it true that I find the marginal prior and thank you alot.
Many thanks for watching. Don't forget to subscribe and let others know about this channel. Without looking at the exact problem, your approach seems correct.
at minute 8:18, why did you substitute 'x' for 'p' in the beta distribution?
That's a good question. In Bayesian analyses, the parameter is a random variable. For the prior distribution we assume the parameter, p, follows a beta distribution. So p is the random variable.
@@statisticsmatt Oh okay thank you!