Simple syntax for querying the model and posterior sample

[mohdibntarek]

In this issue, I propose the creation of a new macro @logprob to query Turing models as well as the sampled posterior. Let's take the following model as an example using the syntax of #965:

@model demo(x, y) = begin
    a ~ Normal()
    b ~ Gamma()
    y .~ Normal.(a .* x, b)
end
model = demo(rand(100), rand(100))
chain = sample(model, NUTS(10, 0.65), 10000)

I propose the following syntax:

• @logprob a = 1.0, b = 2.0 | model = model -> returns log the prior
• @logprob a = 1.0, b = 2.0, x = rand(100), y = rand(100) | model = model -> returns log the joint probability
• @logprob 0.2 <= a <= 0.3, 1.0 <= b <= 1.1 | model = model, chain = chain -> returns log the ratio of the number of samples in chain with 0.2 <= a <= 0.3, 1.0 <= b <= 1.1. For discrete distributions, we can also use a = 2 or a == 2 for example. Passing model here can be optional.
• @logprob x = rand(10), y = rand(10) | model = model, chain = chain returns the log likelihood of x = rand(10), y = rand(10) for each sample in chain
• @logprob x = rand(10), y = rand(10) | model = model, a = 1.0, b = 2.0 returns the log likelihood of x = rand(10), y = rand(10) using a = 1.0, b = 2.0.

Let me know if you have comments on the syntax or if I missed any use case.

[mohdibntarek]

I can also provide an @prob macro that returns the probability instead of log the probability.

[mohdibntarek]

I suggest we also allow = and == to be used interchangeably in the examples above.

[cpfiffer]

I like it, I think it'd be a good tool to have. I have no helpful comments, so I guess you're welcome?

[mohdibntarek]

I am working on it.

[xukai92]

@logprob a = 1.0, b = 2.0, x = rand(100), y = rand(100) | model = model -> returns log the joint probability

model is created by demo(rand(100), rand(100)) in which x and y are already provided. It's unclear to me what the log joint is supposed to return.

[devmotion]

I agree, it feels a bit strange to me. I think it would be more natural to write

@logprob a = 1.0, b = 2.0 | model = demo

for the prior probabilities p(a = 1.0, b = 2.0) and

@logprob a = 1.0, b = 2.0, x = x, y = y | model = demo

for the joint probability p(a = 1.0, b = 2.0, x = x, y = y). I'm not even sure if it should be a macro, couldn't one just define a function logprob that allows to evaluate logprob(demo, (a = 1.0, b = 2.0)) or logprob(demo, (a = 1.0, b = 2.0, x = x, y = y))? Maybe for convenience one could even define demo.logprob instead which allows to write demo.logprob(a = 1.0, b = 2.0).

[mohdibntarek]

@xukai92 the log joint probability case will replace the data inside model and compute the log joint probability for the given data and parameters. If that's not intuitive enough, I can limit this macro to the likelihood and posterior only. Convenience functions can then be made to calculate the prior and joint probability for NamedTuple parameters as @devmotion suggested. In case of the joint probability, the data inside the model can be used.

Actually, for all of them I can just make a function under the hood that can be called instead of the macro. So I have a few questions for you all:

1. Do you prefer a macro and a function API, a function only API or a macro only API?
2. Should I include the prior and joint probability syntax in the macro with the model = demo suggestion?
3. Is conveniently calculating the log joint probability for new data and new parameters useful in practice or not?

[cpfiffer]

I would actually prefer to have both. People who do a lot of automated model stuff would prefer a function API, whereas all the folks who are messing around with the REPL prefer the macro API. Might be that one ends up being better than the other, so we could deprecate one if it is just less useful.

[mohdibntarek]

Sounds good.

[xukai92]

Re 1: I agree with Cameron that we do need both.
Re 2: I feel model = demo is more intuitive than model = model
Re 3: I think it's useful in general.

[jonasmac16]

Will this allow this also allow to return the point logp of the each data point given a parameter set?

[mohdibntarek]

Yes

[jonasmac16]

That's pretty cool. Is this available once the referenced PR is accepted?

[mohdibntarek]

Yup!