Do you mean that you want to find the posterior distribution?

The equation P(theta|D1,D2,D3) = P(theta|D1)*P(theta|D2)*P(theta|D3) is wrong because each P(theta|Di) is probably computed using its own prior.

What you would need is the likelihood function for each 3 models: P(Di|theta).

Then:

P(theta|D1,D2,D3)=P(D1|theta)*P(D2|theta)*P(D3|theta) * Prior(theta)/C

where Prior(theta) is the prior of your choice (could come from one of the models) and C is normalization constant that you determine such that the posterior integrates to 1. Note that this equation is only valid if the data Di are statistically independent.

Thanks for the reply Axel, but No I don't want the posterior.

I have three independent prior information of \theta and all three are gaussian with different mean and s.d. I want to club the three information to get one prior on \theta.

So here, D1,D2,D2 are three priors on same parameter \theta. How do I combine these three priors to get just a single normalized gaussian prior, P(\theta).

Thanks

i think you mean to use a multivariate gaussian distribution using the means and variances that you have provided.