Package: gaussianprocesses 1.0.0.9000

Time is an input, not a special likelihood | Trend, periodicity, and local variation | [k(t,t') | Reproducible example | Interpolation versus extrapolation | Rolling-origin evaluation | Point and probabilistic metrics | Structural breaks | Long series: Kalman filtering and smoothing

Why derivatives | [\frac{\partial}{\partial \theta_j} \log p(y \mid X, \theta) | Log parameters | [\frac | Scaled distances | The variance parameter | Stationary kernels | [\frac | \sigma^2 f'(r^2), \frac | RBF | Matérn 1/2 | Matérn 3/2 | Matérn 5/2 | [g = \frac | Rational quadratic | [\frac | \alpha, k, \frac | Periodic kernel | [\frac | Composite kernels | Product. For (K = \prod_i K_i), the product rule gives[\frac | Parameter paths | The marginal-likelihood gradient | Derivation | [\log p(y \mid X, \theta) | [\frac | -C^ | [\frac | [\frac | Computation | Numerical verification | Derivatives with respect to the inputs | Derivative processes | [\operatorname{cov}!\left(\frac{\partial f(x)}{\partial x_d}, f(x')\right) | \frac{\partial k(x, x')}{\partial x_d},\qquad\operatorname{cov}!\left(\frac{\partial f(x)}{\partial x_d},\frac{\partial f(x')}{\partial x'_e}\right) | Smoothness | Radial kernels | [\frac | Periodic and linear kernels | [\frac | [\frac | The posterior gradient | [\mathrm{E}!\left[\frac{\partial f(x_)}{\partial x_{,d}} ,\middle|, y\right] | [\operatorname{Var}!\left[\frac{\partial f(x_)}{\partial x_{,d}} ,\middle|, y\right] | Verification | Derivative observations | The joint model | Example

Marginal likelihood | [\log p(y\mid X,\theta) | [\log|C| | Hyperparameter estimation | Posterior uncertainty | [\operatorname{Var}[f_*\mid y] | k(x_,x_) | [\operatorname{Var}[y_*\mid y] | Exact leave-one-out diagnostics | [\mu_ | [\sigma_{-i}^2 | Universal kriging

Scaled distance | [r^2(x,x') | Example | Parameter paths | Reproducible two-dimensional simulation | ARD and optimization | Interpretation | Additive models | Components

Why numerical stability matters | Cholesky rather than explicit inversion | Jitter is not observation noise | Jitter is relative to the covariance scale | The trace term of the likelihood gradient | Near-singular scenario | Posterior variances | Benchmarking stability separately from speed

Model | Conditioning | Minimal reproducible fit | Posterior prediction | [\operatorname{Var}\left[y_*\mid y\right] | Function draws | Known heteroscedastic observation variance

Covariance as model structure | Squared-exponential kernel | [k(x,x') | Matérn family | Rational quadratic | [k(r) | Periodic structure | Sums and products | Parameter paths