A modeling language which uses mathematically familiar syntax to interface with SSMProblems.jl
Consider a local level trend model with two parameters σε and ση
@statespace function UC(ση, σε)
# local level model
y[t] = x[t] + η[t]
x[t] = x[t-1] + ε[t]
# noise
ε[t] ~ Normal(0, σε)
η[t] ~ Normal(0, ση)
endThe aim of this macro is to define a LatentDynamics and ObservationProcess from the above block.
Additionally, the above block defines a linear and Gaussian model; which is easy to detect by rearranging the AST such that the first expression is an addition call with subsequent layers containing the multiplication. In theory, we should be able to rearrange any affine transformation to this structure and define a respective linear system.
For conditionally linear Gaussian models, this again should be easy by only defining the scope of the first 2 layers of the AST.
- In it's nascant state, this module will only define the recursive calls; therefore the user must define the initial draws
- I only intend for automatic marginalization on linear Gaussian models
- Compared to something like OnlineSampling.jl, this macro refrains from symbolic execution, leading to an enormous gain in computation time.
- My demo cases in
tests/linear_models.jlandtests/conditionally_linear_models.jlonly consider scalar time series