How to define reasonable observed data

Questions
1

I want to test a math function ,like y=x1+x2 , but no observed data.

x1=pm.Normal(‘x1’,mu=0.5,sd=0.5)

x2=pm.Normal(‘x1’,mu=0.5,sd=0.5)

y=x1+x2

Y=pm.Normal(‘Y’,mu = y,sd=1,observed =obs)

so how to define reasonable observed data? and why ?

2

Not sure I understand your question, but if the function is not directly observed, and you want to do inference on this latent variable, the code you wrote above is correct.

3

I don’t understand this question either.

4

I mean there is no observed data. so may I run it with no observed data. if not, how to define the observed data?

x1=pm.Normal(‘x1’,mu=0.5,sd=0.5)

x2=pm.Normal(‘x2’,mu=0.5,sd=0.5)

y=x1+x2

Y=pm.Normal(‘Y’,mu = y,sd=1)

5

I still don’t understand what you are asking. If you run the model you defined in your last post, it will sample from the priors on x1, x2, and Y. There is no connection and no observations defined, so your traces of the three parameters should be independent. The model will also sample y from its implicit prior.

6

Do you mean sampling from the prior predictive? If so, you can do:

with pm.Model() as model:
    x1 = pm.Normal('x1', mu=0.5, sd=0.5)
    x2 = pm.Normal('x2', mu=0.5, sd=0.5)
    y = pm.Deterministic('y', x1 + x2)

with model:
    trace = pm.sample(1000)

and then look at the trace of y.

7

Isn’t that the prior? I don’t understand the difference.

8

oh, thanks very much. I maybe wrong that I think It’s necessary to define oberserved data.