Introduction | Case-crossover: PM10 at 80 | Fit (outer MLE) | Quantity of interest and influence scores | Approximate most influential set | Confirm by dropping nominated strata | Refit without AMIP strata | Bacteria: sign-flip of the drug effect | Notes

Data | Model | Adaptive Gauss–Hermite quadrature | Posterior of (\sigma) | Fitted probabilities and child effects

Introduction | Data | Building AD shards | Combining shards | Joint log density derivatives | Inner optimization | Joint density derivative checks | Profile likelihood | Outer optimization | Spatial effects

Introduction | Data | Model specification | Fit | AD development check | Joint log density | Likelihood

check by shard | Profile derivative checks | Joint density derivative checks

Model | Simulated data | Building AD shards | Observations and hyperparameters | Random effects | Observation likelihood check | Combining shards | Joint log density derivatives | Inner optimization | likelihood | Outer optimization | Derivative checks | Joint density derivative checks | nicer interface | mean estimation

Data | Knot lines | Fit | Summary | Estimated field

Simulated data | True parameter values | Building the AD pack | Log density per shard | Manual evaluation of the random shards | Label ordering and random_info()

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

\begin{equation}\label{eq:multinom}P(\mathbf{y} \mid \boldsymbol{\lambda}, \sum_{k=1}^K Y_k = N) | \begin{equation}\label{eq:dm}P(\mathbf{y} \mid \alpha, \boldsymbol{\mu}, N) | Simplificaiton | \begin | \begin{equation}\label{eq:dm_ratio}P(\mathbf{y} \mid \alpha, \boldsymbol{\mu}, N)

Parameterization | [\operatorname | Correlation matrices | Skew loadings | sn cross-covariance quantities | Parameter order | Free vector to dp (summary) | Simulation | Build a reusable log-likelihood tape | MLE with optim() and an analytic gradient | MLE with C++ sun_mle() (trustOptim) | Comparison with sn::dsun | Parameter recovery | Gradient check at the fitted MLE

Parameterization | Unit-row Cholesky from free $z$ | [B_ | t_ | Parameter order | Simulation | Build a reusable log-likelihood tape | MLE with optim() and an analytic gradient | MLE with C++ sun_mle() (trustOptim) | Comparison with sn::dsun | Parameter recovery | Gradient check at the fitted MLE

True SUN(3,3) | Discrete target from the true law | Start far from the truth | Minimise KL | Recovery diagnostics | Parameter profiles: AD vs finite-difference gradients

True SUN(3,3) | Discrete target from the true law | Start far from the truth | Minimise KL | Recovery diagnostics | Parameter profiles: AD vs finite-difference gradients

title: Mapping Hans Island | Mapping Antipodes Island

Introduction | Downloading background maps and city locations | Making maps | Legends | More plots | Inset maps

Data | Model and AD setup | Laplace log-likelihood at starting values | Outer optimization | Fitted values and density overlay | Derivative check along one parameter

Model | Simulated data | Building AD shards | Observations and hyperparameters | Random effects | Observation likelihood check | Combining shards | Inner optimization | Profile likelihood | Outer optimization | Profile derivative checks | Joint density derivative checks | Nicer interface

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