Thread: Bayesian Statistics

Hello,

I have a small question which I find hard to handle:

X~U(0,a)
a is unknown and his prior distribution is:

p c
g(a)=
1-p 2c

find the posterior distribution of a. for which range of x, the posterior distribution of a=c is bigger ? show your calculations.

I found the posterior:

p/c a=c
f(a|x)=
(1-p)/2c a=2c

how can I found the second part ?
cheers !

Originally Posted by WeeG

Hello,

I have a small question which I find hard to handle:

X~U(0,a)
a is unknown and his prior distribution is:

p c
g(a)=
1-p 2c

find the posterior distribution of a. for which range of x, the posterior distribution of a=c is bigger ? show your calculations.

I found the posterior:

p/c a=c
f(a|x)=
(1-p)/2c a=2c

how can I found the second part ?
cheers !

Because spaces are not preserved in posts I find your expressions for g(a) and f(a|x) dificult to understand.

Could you either post them in [code]..[/code] block or as an image file of some kind.

example of use of [code]..[/code] block:

Code:

        a+b
f(x) =  ----
         c

(you may have to addjust the number of spaces to get correct allighment due to vatriable width charaters)

RonL

another try:
( if it doesn't work I'll try the image idea )

Code:

I have a small question which I find hard to handle:

X~U(0,a)
a is unknown and his prior distribution is:

          p    c 
g(a)= 
         1-p  2c

find the posterior distribution of a. for which range of x, the posterior distribution of a=c is bigger ? show your calculations.

I found the posterior:

            p/c        a=c
f(a|x)=
           (1-p)/2c  a=2c

the functions are defined in two different regions.

how can I found the second part ?
cheers !

Originally Posted by WeeG

another try:
( if it doesn't work I'll try the image idea )

Code:

I have a small question which I find hard to handle:

X~U(0,a)
a is unknown and his prior distribution is:

          p    c 
g(a)= 
         1-p  2c

find the posterior distribution of a. for which range of x, the posterior distribution of a=c is bigger ? show your calculations.

I found the posterior:

            p/c        a=c
f(a|x)=
           (1-p)/2c  a=2c

the functions are defined in two different regions.

how can I found the second part ?
cheers !

Is this what you mean?





If so, there is a problem: the definition of does not include ! If it is a posterior distribution, it has to.

Actually, the joint density is



The marginal density of is



And the posterior density is

you are right, the quesion is taken from an old exam I was trying to solve.
there is something wrong with it...I don't know