# Calculate posterior from normal prior and some observations [duplicate]

I know Bayes Theorem in a basic way. If I was given prior and likelihood in the form of probabilities I can fill in the formula. When watching this video the following graph was discussed (2:50): The light gray curve is the prior, probably something like $\mathcal{N}(55,10)$. How can I calculate the posterior distribution (dark gray) shown in the figure? It would need to be something along

$p(f|y)=\dfrac{p(f)\cdot p(y|f)}{p(y)}=\dfrac{\mathcal{N}(55,10) \cdot p(y|f)}{p(y)}$.

How do I find the likelihood $p(y|f)$ for "a few given observations" like those 4 points (58, 61, 64, 69) bps and what is the probability $p(y)$ of these observations?

• Possible duplicate of Bayesian updating with new data See also stats.stackexchange.com/questions/232824/… for another example.
– Tim
Jan 12, 2017 at 15:38
• Thanks for the references. I can't quite infer the solution to my problem from them though. I would appreciate a numerical example.
– ste
Jan 12, 2017 at 15:49
• But the numerical example is given in the linked answers... What exactly is unclear for you?
– Tim
Jan 12, 2017 at 16:00
• Bishop's Pattern Recognition p97f and your posts helped me to figure it out, thanks!
– ste
Jan 14, 2017 at 10:29