Glossary
The following list includes the names and symbols of recurring concepts in EnsembleKalmanProcesses.jl. Some of these variables do not appear in the codebase, which relies on array programming for performance. Contributions to the codebase require following this notational convention. Similarly, if you find inconsistencies in the documentation or codebase, please report an issue on GitHub.
| Name | Symbol (Theory/Docs) | Symbol (Code) |
|---|---|---|
| Parameter vector, Parameters (unconstrained space) | $\theta$, $u$, $\mathcal{T}(\phi)$ | θ,u |
| Parameter vector, Parameters (physical / constrained space) | $\phi$, $\mathcal{T}^{-1}(\theta)$ | ϕ |
| Parameter vector size, Number of parameters | $p$ | N_par |
| Ensemble size | $J$ | N_ens |
| Ensemble particles, members | $\theta^{(j)}$ | |
| Number of iterations | $N_{\rm it}$ | N_iter |
| Observation vector, Observations, Data vector | $y$ | y |
| Observation vector size, Data vector size | $d$ | N_obs |
| Observational noise | $\eta$ | obs_noise |
| Observational noise covariance | $\Gamma_y$ | obs_noise_cov |
| Hilbert space inner product | $\langle \phi , \Gamma^{-1} \psi \rangle$ | |
| Forward map | $\mathcal{G}$ | G |
| Dynamical model | $\Psi$ | Ψ |
| Transform map (constrained to unconstrained) | $\mathcal{T}$ | T |
| Observation map | $\mathcal{H}$ | H |
| Prior covariance (unconstrained space) | $\Gamma_{\theta}$ | prior_cov |
| Prior mean (unconstrained space) | $m_\theta$ | prior_mean |
When observations or parameters are being batched, then their size (e.g., N_obs or N_par) will refer to the size of elements of each batch, summed over the batch. For example, when calibrating 100 observations of a 15-dimensional output space, but using a minibatching procedure with batch size 5, then N_obs = 75.