Advanced Topics

This section covers Bayesian inference, per-angle scaling modes, laminar flow analysis, CMA-ES optimization, convergence diagnostics, and memory management strategies for large datasets.

• Bayesian Inference with CMC
  • When to Use Bayesian Inference
  • The NLSQ Warm-Start Pipeline
  • CMC Configuration
  • SamplingPlan and Adaptive Sampling
  • Chain Execution Methods
  • Parameter Reparameterization
  • Shard Scheduling
  • Worker Pool and Shared Memory
  • Heterogeneity Detection
  • ArviZ Diagnostics
  • Posterior Comparison: NLSQ vs CMC
  • Quality Filtering
  • Checkpointing for Long Runs
  • See Also
• Per-Angle Scaling Modes
  • Why Per-Angle Scaling Matters
  • The Four Modes
  • Configuration Examples
  • Parameter Count Summary
  • Diagnosing Degeneracy
  • Fixing Degeneracy Issues
  • See Also
• Laminar Flow Analysis Guide
  • Physical Setup: Taylor-Couette Geometry
  • Configuring for Laminar Flow
  • Anti-Degeneracy System
  • Angular Dependence Visualization
  • Interpreting Shear Parameters
  • Troubleshooting Laminar Flow Fits
  • See Also
• CMA-ES for Multi-Scale Problems
  • When to Use CMA-ES
  • Configuration
  • Python API
  • CMA-ES → NLSQ Refinement Pipeline
  • Warm-Start Optimization
  • Performance Considerations
  • See Also
• Large Dataset Handling and Streaming
  • Overview
  • Memory Thresholds
  • Stratified LS (Full-Batch)
  • Hybrid Streaming
  • Performance Tips for Large Datasets
  • Monitoring Memory Usage
  • CMC Memory Considerations
  • See Also
• Convergence Diagnostics
  • NLSQ Diagnostics
  • CMC Diagnostics
  • Quality Filtering in CMC
  • Diagnosing Common Failures
  • See Also

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What you will learn:

• How to use Consensus Monte Carlo (CMC) for full Bayesian posteriors.

• How the per-angle scaling modes prevent parameter absorption degeneracy.

• How laminar flow analysis captures shear dynamics from angular dependence.

• When and how to use CMA-ES for multi-scale parameter spaces.

• How to manage memory when C2 matrices exceed available RAM.

• How to read convergence diagnostics (R-hat, ESS, BFMI, divergences).

Prerequisites: NLSQ Fitting Guide and a basic familiarity with Bayesian inference.