Part 1: a regular regression | Declaring and fitting the model | Checking convergence | The joint posterior | The Cramer-Rao reference | Deciding the relationship | Weighing the evidence for a slope | Head-to-head against the established packages | Part 2: an irregular mixture | The bimodal target | Why the random walk fails, and the Cramer-Rao refusal | Parallel tempering recovers both components | Choosing between one component and two | Observed against the generated distribution | What each tool contributed

The Gumbel model | The joint posterior and the information bound | The return level, with its uncertainty | A design question as a hypothesis | Is the extreme-value law worth it? Gumbel against the Normal | Observed against the generated distribution | Head-to-head against the established packages | The shape parameter, and a limit of the scalar model | What this case exercised

The simple model and its fit | Reading the posterior | Does horsepower add anything? Predictive comparison | Weighing the evidence for horsepower | Observed against the generated distribution | Head-to-head against the established packages | What this case exercised

1. One column, many candidate shapes | 2. Visual inspection | 3. The fitted CDF is the transform to the unit square | 4. The full Sklar workflow on two columns | 5. Where this stops

1. Pseudo-observations, the dependence stripped of the margins | 2. Fitting with automatic family selection | 3. Reading the dependence | 4. Visual inspection | 5. Against the classical estimator | 6. Forcing the eye's hypothesis, and seeing it rejected | 7. Where this stops | References

1. The three ways data stop being i.i.d. | 2. Regime 2: a stationary AR(1) for the flow | 3. Regime 3: the dam as a covariate, dependence plus heterogeneity | 4. Model comparison that respects time | 5. Observed against generated, in time | 6. Where this stops, honestly | References

A real dataset: Oxford annual maximum temperatures | A single Gumbel as the Tier A candidate | Why a Gumbel mixture on Oxford is harder than it looks | A two-regime simulation, the recovery story | The mixture model in the DSL | Parallel tempering on the mixture posterior | Settling the choice by WAIC | Identifiability post-processing | Posterior predictive check | Fair comparison with current practice | Single Gumbel: matched by an established MLE pipeline | Two-component Gumbel mixture: no standard one-liner in R | What is manual today and what becomes automatic in v0.6.0 | References

The model | Random walk against Differential Evolution | The Cramer-Rao reference | Consistency and the n to the minus one-half rate | Honest positioning

The model | The failure mode of diagonal random-walk Metropolis | The fix: Differential Evolution | Reading the result | Honest positioning

Declaring a model | Running the sampler | The fit object | Convergence diagnostics | One source, several backends | A model with more than one parameter | When the GPU helps

The model | The failure mode of plain random-walk Metropolis | Parallel tempering | Inspecting the cold chain directly | Tuning notes for parallel tempering | What the focused re-run shows in numbers | When to reach for parallel tempering