Some thoughts about the landing page example

[bertdv]

The example on the landing page is great. Very clear code and it shows neatly how (1) model specification can be separated from inference; (2) inference can be automated.

At the same time, here are some thoughts for possible improvements in the future:

On randomvar

Do you need to specify x = randomvar(n)? What happens if you omit this specification? Why not just specify that x is a vector of float64s or omit it altogether and the rxinfer/model compiler infers from x[i] ~ MvNormal( \mu = , \Sigma = ) that x is a float64? If you say x is distributed as a Gaussian, then it must be a float64, unless specified otherwise (like a double float, or whatever you have in Julia). What do you really say by specifying that x is a randomvar? The probability distribution over x is not its type, but rather a statement of beliefs. (It's too big a discussion for this issue but the whole concept of a random variable is very shady (if not plainly wrong) in a Bayesian framework).

On datavar

Withy = datavar, you are really specifying that y is observed, but that should not be part of the knowledge base in the generative model specification. y is just a vector of float64's, which can be inferred from the statement y[i] = MvNormal(\mu= ,\Sigma= ). I am not a fan of double type assignments (first by y = datavar and then by y[i]=MvNormal()), unless the type is not the default type that is associated with MvNormal. Another serious problem is that this model can not be used "as a node" in a bigger graph, since we cannot pass messages towards y, other than delta distributions. The fact that y is observed is not a property of the model, but rather a feature of how we want to use the model. In this case, you happen to use the model for state estimation, given a data set y, ie for $p(x|y)$. If you happen to use this model for prediction of future y (instead of state estimation), ie, for $p(y_{n+1} | y_{1:n})$ then it would be wrong to say that y=datavar, namely $y_{n+1}$ will be inferred as a Gaussian.

On x_prior

This is really minor but it's a bit odd that you introduce x_prior and then copy it into x_prev, seemingly because you don't like the variable name x_prior in the loop. Better to just not use the variable name x_prior (saves a line). I also don't like the explanation of ~ in the comment. I think ~ simply means: is distributed as.

On for i in 1:n

Technically, I don't even think that the iteration for i in 1:n should be part of the model specification. I think you just want to specify $p(y_i,x_i | x_{i-1})$ with parameters $x0, A, B, P, Q$ inside the @model function. How you use the model (in this case roll out for n samples) is determined by the inference task (in this case: infer p(x|y)). So, I think it should be written as

result = infer(
  model = SSM( x0, A, B, P, Q ),
  data = (y = observations,)
)

ie, without the n in the SSM. Then, when rxinfer executes this inference task, the model gets rolled out over length(y). And I like infer() rather than inference() because I think it should be our convention to express the action of the function by a verb. It reads better.

In short, my main feedback is that I think that we don't want to specify how we use the model in the model specification phase. This is important, since I think these prescribed roll-outs and data-type assignments limit the usage of the model.

[bvdmitri]

Good points, we should consider them when refactoring GraphPPL and creating an actual graph for a model.