[david_draco]

As far as I am aware, there is no symbolic computing tool yet for probability distributions? For example, multiplying two multivariate Gaussian PDFs together and getting the covariance matrix out. Or defining all the ingredients for a Kalman filter (prediction model and observing process) and getting the necessary formulas out (as in sympy's lambdify).

[jampekka]

Sympy can manipulate Gaussian distributions symbolically, but the Gaussian is more or less the only distribution that can be really symbolically manipulated.

Though I'm not sure Sympy can handle the conditional (Bayesian posterior) distribution needed for the Kalman filter.

In any case, you are better off working direcly with the mean and variance (or covariance matrix) if you want to play around with the Kalman filter with Sympy.

[mitthrowaway2]

The posterior is also a Gaussian, is it not?

[jampekka]

Yes.

[jiggawatts]

I'm pretty sure Wolfram Mathematica can do what you're looking for.

See:

https://reference.wolfram.com/language/howto/WorkWithStatist...

and:

https://reference.wolfram.com/language/ref/MultinormalDistri...

[nathansherburn]

Not sure if relevant but I thought this looked very cool.

https://www.squiggle-language.com/docs