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FAQ

When should I use the Kalman filter vs. joint likelihood?

  • Kalman filter: Use for linear Gaussian models when you want the marginal likelihood, integrating out the latent noise sequence. This is the standard approach for maximum likelihood estimation (MLE) of parameters.
  • Joint likelihood: Use when conditioning on a specific noise realization. This is useful for Bayesian methods where the noise sequence is sampled as part of inference (e.g., particle MCMC, HMC on latent variables).

Why does Enzyme require all arguments to be Duplicated?

Enzyme tracks activity at the struct level. When constructing a LinearStateSpaceProblem, all matrix arguments (e.g., A, B, C) flow into a single struct. If any argument is active (i.e., being differentiated), Enzyme needs shadow copies for all arguments in the struct. Passing some arguments as Const while others are Duplicated triggers an EnzymeRuntimeActivityError. The solution is to mark all arguments as Duplicated.

What is the observables timing convention?

The tspan(0, T) produces T+1 states: $u_0, u_1, \ldots, u_T$. Observations $z_n$ correspond to state $u_n$. The observables keyword expects T vectors corresponding to $z_1, z_2, \ldots, z_T$ (skipping $z_0$). So when passing simulated data, use sol.z[2:end].

What does observables_noise represent?

The observables_noise keyword specifies the observation noise covariance matrix (entries are variances and covariances, not standard deviations). It must be an AbstractMatrix — use Diagonal([σ₁², σ₂², …]) for diagonal noise or a full Matrix/Symmetric(H * H') for correlated noise.

Its behavior depends on context:

  • During simulation (when observables is not provided): used to generate synthetic measurement noise added to the clean observations sol.z.
  • During likelihood computation (when observables is provided): used as the observation noise covariance in the log-likelihood calculation.

How do I differentiate with respect to only some parameters?

  • Enzyme: All arguments to the likelihood function must be marked Duplicated (see Enzyme AD). However, you only need to read the shadow of the parameter you care about — the other shadows are computed but can be discarded. There is no performance cost to ignoring unused shadows.
  • ForwardDiff: Only the parameter passed through ForwardDiff.gradient's vector argument is differentiated. Other parameters are captured as constants in the closure, so no derivatives are computed for them.

How do I choose between QuadraticStateSpaceProblem and PrunedQuadraticStateSpaceProblem?

  • PrunedQuadraticStateSpaceProblem: Use for second-order perturbation solutions of DSGE models. The pruning prevents explosive dynamics by applying the quadratic term to a separate linear-part state rather than the full nonlinear state.
  • QuadraticStateSpaceProblem: Use if you specifically need the unpruned quadratic form (e.g., for comparison or when the system is known to be stable).