I am trying to better understand how Bayesian Inference can be used.
Let's assume I am measuring a given property, $\theta$, of some material. I have done 100 measurements. These had a Gaussian distribution with some mean $u$ and std. dev. $s$. This represents my 'prior' information, $P(D)$. Now I have done 10 more measurements. To get the posterior, $P(\theta|D)$, I need first to find the likelihood, $P(D|\theta)$ (the normalization is, at least numerically, easy).
So, practically, how can I obtain the likelihood?
P.S. let's keep it general and not assume that the likelihood is also Gaussian, i.e. conjugate to the prior.