[R] Bayesian constrained regression method?

[Michael Bedward]

Hello Jim,

Please reply to the list - you'll have a much better chance of getting
useful suggestions.

> OK so some addition info. I know each of the X2 is in (0,1). Is there any
> method available?

I don't think that's sufficient to estimate b, at least not in my
experience of fitting Bayesian models with MCMC. To get any sort of
precise posterior for b I think you would need to know that, for
instance, X2 is correlated with X1 in some way, or that it can be
described by a particular Beta distribution etc.

I'd be happy to be corrected by others here who know much more than I
do but if the best prior you can come up with for X2 is uniform in
(0,1) I think you have insufficient information to proceed.

Michael


On 24 October 2010 09:28, Jim Silverton <jim.silverton at gmail.com> wrote:
>  I am trying to estimate the parameter b.
>  I have Y and X1 which I know and they are both random. However, I also have
>  X2 which I don't know and is also random. I want to estimat b from the
>  model:
>
>  Y = b*X1  + ( 1 - b ) * X2
>
>  so my constraints areCan anyone offer some suggestions. The values of Y and
> X1 are both pvalues
>  so they are constrained in (0,1).
>
> OK so some addition info. I know each of the X2 is in (0,1). Is there any
> method available?
> Jim
>
> On Sat, Oct 23, 2010 at 8:31 AM, Michael Bedward <michael.bedward at gmail.com>
> wrote:
>>
>> Hi Jim,
>>
>> You don't mention whether you have any prior information regarding X2
>> that can be used to constrain values imputed for it. I think you will
>> need some because without it values sampled for b and X2 respectively
>> will just "see-saw" against each other.
>>
>> Michael
>>
>>
>> On 22 October 2010 18:37, Jim Silverton <jim.silverton at gmail.com> wrote:
>> > Hello everyone,
>> > I am trying to estimate the parameter b.
>> > I have Y and X1 which I know and they are both random. However, I also
>> > have
>> > X2 which I don't know and is also random. I want to estimat b from the
>> > model:
>> >
>> > Y = b*X1  + ( 1 - b ) * X2
>> >
>> > Can anyone offer some suggestions. The values of Y and X1 are both
>> > pvalues
>> > so they are constrained in (0,1).
>> >
>> > --
>> > Thanks,
>> > Jim.
>> >
>> >        [[alternative HTML version deleted]]
>> >
>> > ______________________________________________
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>> > and provide commented, minimal, self-contained, reproducible code.
>> >
>
>
>
> --
> Thanks,
> Jim.
>