Introduction | Installing RTMB | Poisson Regression | Simulating Data | Defining the Log-Likelihood | Performance Comparison | Results | Logistic Regression | Gaussian Mixture Model | Time Series: AR(1) Model | Quick Approximation with Pathfinder

Introduction | Setup Data | Title Settings | Canvas Settings | SPC Example | Funnel Example | Axis Settings | X Axis | SPC: Rotating Ticks | Funnel: Axis Label | Y Axis | Date Settings (SPC Only) | Line Settings | SPC: Main Line | Funnel: Limit Lines | Scatter Settings | Basic Point Styling | Point Label Styling (Funnel Only) | Label Settings | Conditional Formatting | Conditional Point Colours | Conditional Line Segments (SPC Only)

Overview | SPC Chart Types | Basic Charts | Run Chart | Individuals Chart (i-chart) | Individuals Chart with Ratios | Individuals Chart with Median Centerline (i_m) | Individuals Chart with Median Limits (i_mm) | Moving Range Chart (mr) | Proportion Charts | p-chart (Proportions) | p-prime Chart (pp) | Rate Charts | u-chart (Rates) | u-prime Chart (up) | Count Charts | c-chart (Counts) | Sample-Based Charts | xbar Chart (Sample Means) | s Chart (Sample Standard Deviations) | Event-Based Charts | g Chart (Geometric) | t Chart (Time Between Events) | Funnel Plot Types | PR - Proportion Funnel | PR Funnel with Overdispersion Adjustment | SR - Standardised Ratio Funnel | SR Funnel with Overdispersion Adjustment | RC - Rate Funnel | RC Funnel with Overdispersion Adjustment | Chart Selection Guide | SPC Chart Selection | Funnel Plot Selection | Overdispersion Adjustment | Data Requirements Summary | SPC Charts | Funnel Plots | Additional Resources

Introduction | Outlier Detection Methods | Astronomical Points | Shift Detection | Trend Detection | Two-in-Three Detection | Improvement Direction and Flag Types | Improvement Direction | Process Flag Type | NHS Icons | Variation Icons | Assurance Icons | Example: Consistent Pass | Example: Consistent Fail | Example: Variable Performance | Combined Variation and Assurance Icons | Settings Reference | Outlier Detection Settings | NHS Icon Settings | Additional Resources

Getting Started | Constructing SPC Charts | Funnel Plot

Quadrature and Differentiation | Trapezoidal Quadrature | Gauss-Legendre Quadrature | Gauss-Kronrod Quadrature | Double-Exponential Quadrature | Fourier Integrals | Numerical Differentiation

Special Math Functions | Number Series | Gamma Functions | Factorials and Binomial Coefficients | Beta Functions | Error Functions | Polynomials | Logistic Functions | Bessel Functions | Hankel Functions | Airy Functions | Elliptic Integrals | Jacobi Elliptic Functions | Jacobi Theta Functions | Lambert W Function | Zeta Functions | Exponential Integrals | Hypergeometric Functions | Basic Functions | Sinus Cardinal and Hyperbolic Sinus Cardinal Functions | Inverse Hyperbolic Functions | Owen's T Function

Introduction | Creating the package skeleton | Read-and-delete-me file | Stan files | R files | Documentation | Install and use | Advanced options | Adding additional Stan models to an existing R package with Stan models | Links

Introduction | Prerequisites | Typical Workflow | Example | Write a Stan Program | Preparing the Data | Sample from the Posterior Distribution | Arguments to the stan Function | Data Preprocessing and Passing | Methods for the "stanfit" Class | Sampling Difficulties | Additional Topics | User-defined Stan Functions | The Log-Posterior (function and gradient) | Optimization in Stan | Model Compilation | Running Multiple Chains in Parallel | See Also

Floating Point Utilities | Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values | Floating-point Comparison | Condition Numbers

Statistics | Arcsine Distribution | Bernoulli Distribution | Beta Distribution | Binomial Distribution | Cauchy Distribution | Chi-Squared Distribution | Exponential Distribution | Extreme Value Distribution | F Distribution | Gamma Distribution | Geometric Distribution | Holtsmark Distribution | Hyperexponential Distribution | Hypergeometric Distribution | Inverse Chi-Squared Distribution | Inverse Gamma Distribution | Inverse Gaussian Distribution | Kolmogorov-Smirnov Distribution | Landau Distribution | Laplace Distribution | Logistic Distribution | Log Normal Distribution | Map-Airy Distribution | Negative Binomial Distribution | Noncentral Beta Distribution | Noncentral Chi-Squared Distribution | Noncentral F Distribution | Noncentral T Distribution | Normal Distribution | Pareto Distribution | Poisson Distribution | Rayleigh Distribution | SaS Point5 Distribution | Skew Normal Distribution | Student's T Distribution | Triangular Distribution | Uniform Distribution | Weibull Distribution

Statistics | Univariate Statistics | Bivariate Statistics | Signal Statistics | Anderson-Darling Test | T-Tests | Z-Tests | Runs Tests | Ljung-Box Tests | Linear Regression

Introduction | Motivations | Estimating a Model | Specifying the Function | Estimating the Function | Parameter Bounds | Running the Model | Inspecting the Results | Model Checking and Comparison - Leave-One-Out Cross-Validation (LOO-CV)

Interpolation | Cardinal Cubic B-Spline | Barycentric Rational Interpolation | Bezier Polynomial | Bilinear Uniform | Cardinal Quadratic B-Spline | Cardinal Quintic B-Spline | Catmull-Rom | Cubic Hermite | Cardinal Cubic Hermite | Modified Akima | PCHIP | Quintic Hermite

Filters | Daubechies Filters

Vector Functionals - Norms

Constants | Retrieve Specific Constants | List All Available Constants

Root Finding & Minimisation Algorithms | Root Finding Without Derivatives | Root Finding With Derivatives | Polynomial Roots | Quadratic Roots | Cubic Roots | Quartic Roots | Finding Function Minima with Brent's Algorithm

Using the StanHeaders Package from Other R Packages | Calling functions in the StanHeaders Package from R | Using Higher-Order Functions in the StanHeaders Package | Derivatives and Minimization | Integrals and Ordinary Differential Equations | Parellelization | map_rect Function | reduce_sum Function | Defining a Stan Model in C++

Introduction | Installing CmdStan | Compiling a model | Running MCMC | Posterior summary statistics | Summaries from the posterior package | CmdStan's stansummary utility | Posterior draws | Extracting draws | Plotting draws | Sampler diagnostics | Extracting diagnostic values for each iteration and chain | Sampler diagnostic warnings and summaries | CmdStan's diagnose utility | Running optimization and variational inference | Optimization | Laplace Approximation | Variational (ADVI) | Variational (Pathfinder) | Saving fitted model objects | Comparison with RStan | Additional resources

Mappings and Conversions Between R and JS Types | Primitive & Scalar Types | Container Types | Functions and Closures | Working with R Environments | Accessing Package Namespaces & Functions

Summary statistics | Extracting posterior draws/samples | Structured draws similar to rstan::extract()

Introduction | Compilation | Immediate compilation | Delayed compilation | Pedantic check | Stan model variables | Executable location | Processing data | Named list of R objects | JSON file | R dump file | Writing CmdStan output to CSV | Default temporary files | Non-temporary files | Reading CmdStan output into R | Lazy CSV reading | read_cmdstan_csv() | as_cmdstan_fit() | Saving and accessing advanced algorithm info (latent dynamics) | Developing using CmdStanR | Pre-compiled Stan models in R packages | Troubleshooting and debugging

Option 1: Using RStan for all chunks | Option 2: Using CmdStanR for all chunks | Example | Option 3: Using both RStan and CmdStanR in the same R Markdown document | Caching chunks | Running interactively

Introduction | Adding profiling statements to a Stan program | Accessing the profiling information from R | Comparing to a faster version of the model | Per-gradient timings, and memory usage | Accessing and saving the profile files | References

Note to developers | Guidelines for R packages providing interfaces to Stan | General package structure and development | Stan code | R code and documentation | Recommended resources

References

Posterior draws | extract() | as.matrix(), as.data.frame(), as.array() | Posterior summary statistics and convergence diagnostics | Sampler diagnostics | Model code | Initial values | (P)RNG seed | Warmup and sampling times