I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following:

I have a matrix of temperatures, depending on two parameters (Alpha and Beta). We can plot this matrix with matplotlib, and we get :

[]

I would like to build a model that estimate the probability distribution of the alpha and beta given a temperature. An example will be : what are the alpha and beta that most likely produce a temperature of 33 degrees ?

I know that it deals with Bayesian issues, maybe a Mixture of Gaussians(but in infinite dimension), but i have no idea what type of algorithm i have to use...

Any idea ?

Thank you so much !

I'm currently facing a new type of problem, and i have no idea how to solve it, so any suggestion will be really appreciated ! The problem is the following:

I have a matrix of temperatures, depending on two parameters (Alpha and Beta). We can plot this matrix with matplotlib, and we get :

[]

Because we can only observe the temperature in practice, I would like to build a model that estimate the probability distribution of the alpha and beta given a temperature. An example will be : what are the alpha and beta that most likely produce a temperature of 33 degrees ?

Now suppose, we have many measurements of temperature, is it possible to get the probability distribution of alpha and beta given the observed temperatures.

Example : we observed a lot of 28 degrees, we can induce that alpha is probably around 0.8 and alpha around 525. (we can suppose that we can approximate this distribution with a Gaussian for example)

I know that it deals with Bayesian issues, propagation of uncertainty, but i have no idea what type of algorithm i have to use... and how to do in practice.

Any idea ? (it seems to be a quite complicated problem no ? )

Thank you so much !