Conditional Sampling with Distinct Distributions Based on Sampled Values

Python usage
1

Hello :slight_smile:

I am currently working on a problem where the distribution applied to a variable depends on the value sampled from another variable. Specifically, I need to sample from one distribution and then, based on that sampled value, choose from among several other distributions for the next sampling step.

For example:

  • If X falls within a specific range, say [a, b], then Y should be sampled from distribution D_Y1.
  • If X is outside the range [a, b], then Y should be sampled from a completely different distribution D_Y2.

Is there a feature in OpenTURNS that allows this?

Thank you!

2

You may be looking for the Mixture distribution, the probability of each range will have to be normalized into relative weights for each pdf:
https://openturns.github.io/openturns/latest/user_manual/_generated/openturns.Mixture.html

3

Thank you! That looks interesting!

Do you know if it is possible to define the weights based on a distribution without implementing a custom distribution?

I was thinking about a using a JointByConditioningDistribution (BayesDistribution in v1.23) something like this:

uniform_distribution = ot.Uniform(0, 1.0)

collDist = [ot.Triangular(1.0, 2.0, 4.0), ot.Normal(-1.0, 1.0)]
myMixture = ot.Mixture()

parameter_weights = ot.SymbolicFunction(["uniform_sample"], ["[ot.Triangular(1.0, 2.0, 4.0), ot.Normal(-1.0, 1.0)]","[uniform_sample, 1-uniform_sample]"])
combined_2d_velocity_distribution = ot.BayesDistribution(
    myMixture, uniform_distribution, parameter_weights
)

However, I am getting an error saying

expected a link function with output dimension equal to the number of parameters of the conditioned distribution.

I guess this is not what the two distribution were made for, I am also not sure if it is allowed to use ot expressions in SymbolicFuntions.

Is there a way to link the output of the uniform distribution to the weights of the mixture?

Thank you!