I have three values ($x_1=2$, $x_2=8$, and $x_3=4$). These are drawn from a Binomial distribution with parameter $k=12$ and unknown parameter $p$. The prior distribution of $p$ is a Beta distribution with parameters $\alpha=3$ and $\beta=1$.

I know that the posterior would be a Beta distribution with parameters $\alpha+\sum x_i$ and $\beta+n-\sum x_i$.

So with that in mind, the answer would be $p \sim Beta(17,-10)$

But I'm confused on if:

1) I should be using the parameter $k$ somewhere or if it is not needed and

2) If a parameter can be negative or if I did something wrong.

I have very minimal knowledge of this subject and am just starting to learn.

  • 1
    $\begingroup$ How do you get the -10 for $\beta$? $\endgroup$ – Lerner Zhang Apr 15 '20 at 0:37
  • $\begingroup$ Prior β=1, n=3 and the sum =14. So 1+3-14=-10 $\endgroup$ – mmd123 Apr 15 '20 at 0:58
  • $\begingroup$ In beta distribution , both parameters must be positive. $\endgroup$ – Masoud Apr 15 '20 at 1:17

If $p\sim Beta(\alpha , \beta) $ so

$$\Pi (p|x)\propto f(x_1,x_2,x_3|p) \Pi(p)=p^{\sum x_i + \alpha -1} (1-p)^{3n-\sum x_i+ \beta -1} $$ so

$$p|x \sim Beta(\alpha +\sum x_i=17 , 3n+\beta-\sum x_i=3*12+1-17=20).$$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.