Theory Background (Advanced)

The website is intentionally split into two layers:

• Workflow pages (start/ and examples/): how to assemble a model and run MCMC.
• Theory pages (this section): what the model components mean mathematically, why the package is “spliced” for heavy tails, and how causal quantities are defined as functionals of treatment-specific conditional distributions.

Recommended reading order

1. GPD tails + DPM bulk + splicing
2. Predictor-dependent clustering + clustering outputs
3. Causal building blocks (potential outcomes + estimands)
4. Restricted mean / extreme quantiles + interpretation
5. Posterior functionals + prediction (and how intervals are formed)
6. Customization maps and extension points

How these pages connect to the package API

• One-arm density modeling and tail extrapolation: dpmix() / dpmgpd()
• Clustering: dpmix.cluster() / dpmgpd.cluster()
• Causal (two-arm) models with optional propensity-score augmentation: dpmix.causal() / dpmgpd.causal()

This theory layer uses the same objects that the package’s S3 methods summarize and predict from (densities, survival, quantiles, means, restricted means, and causal contrasts).

Canonical diagrams (link targets)

To keep pages non-redundant, the site uses a small number of canonical diagrams and links back to them:

• Workflow decision diagrams: Start → Usage diagrams
• Model decomposition and “where customization lives”: Advanced → Model umbrella

Prereqs

• Required packages and data for this page are listed in the setup chunks above.

Outputs

• This page renders model fits, diagnostics, and summary artifacts generated by package APIs.

Interpretation

• Canonical concept page: Index
• Treat this page as an application/example view and use the canonical page for core definitions.

Next

• Continue to the linked canonical concept page, then return for implementation-specific details.