Package: adlaplaceFem 0.7.1

Data | Knot lines | Fit | Summary | Estimated field

Continuous model: Matérn via Whittle SPDE | $$\operatorname{Cov}\bigl(u(\mathbf{s}),u(\mathbf{s}')\bigr) | Parameterization: range and sd | Finite-element weights and Grams | Derivatives | $$\log\pi(\mathbf{w}\mid\theta) | Quadratic form | $$\frac{\partial}{\partial\theta_k}\Bigl(\mathbf{v}^\top\frac{\partial^2 f}{\partial\mathbf{w},\partial\mathbf{w}^\top}\mathbf{v}\Bigr) | Log-determinant atomic | $$\frac | \operatorname{Tr}(\mathbf{Q}^{-1}\mathbf{M}_j) | $$\frac | Tensor-product B-splines | Hierarchical B-splines | Numerical comparison: Matérn vs FEM | References

The term | Structure that makes closed forms possible | The coefficient map | The derivatives | The third-order term | What this replaces | Storage and the three primitives | Per-evaluation state | Where AD survives | Wiring into adlaplace | Two modes | Verification | Why the log-determinant is an atomic instead

FEM ingredients | Hierarchical toy model | Joint density, gradient, and Hessian | Finite-difference checks | Laplace log-likelihood: AD vs finite differences