# kernel and mean function for series of function

my series for functions are type.

$$f(x) = a \sin(x-b) , a \sim \mathcal{N}(-1,2) , b \sim \mathcal{N}(-0.5,1)$$

Can someone get me started how to model these functions with GP. I am confused about how should one choose mean function and covariance function?

• This process will not be a GP. Look at $f(0) = a sin(-b)$. This random variable has not a normal distribution. But the definition of a GP demands that every $f(x)$ has a normal distribution. Why do you want to model this as a GP in the first place? – g g Jun 5 '20 at 8:44
• because i have complete knowledge of prior on functions . So I thought , GPs will be better – manifold Jun 5 '20 at 9:00