Choose a null model

TL;DR

Choose three things: event family, ensemble, and constraints. For most practical workflows, use the grand-canonical ensemble.

Default recommendation

Start with grand canonical models. They make node pairs independent, which enables streaming, parallel generation/filtering, and lower memory pressure than coupled canonical or microcanonical samplers.

Decision diagram

flowchart TD
  A[What does an occupation t_ij count?] --> B[Distinguishable events]
  A --> C[Aggregated binary layers]
  A --> D[Indistinguishable events]
  B --> ME[ME / Poisson]
  C --> BLayers[Choose layers M]
  BLayers --> BFam[B / Binomial M]
  D --> WLayers[Choose layers M]
  WLayers --> WFam[W / Geometric if M=1, NegBin if M>1]
  ME --> E[Pick constraints]
  BFam --> E
  WFam --> E
  E --> S[Strength]
  E --> SC[Strength + cost]
  E --> SE[Strength + edge count]
  E --> SD[Strength + degree]
  E --> DE[Degree + total events]
  E --> PC[Partial: freeze known pairs]
  S --> G[Grand canonical]
  SC --> G
  SE --> G
  SD --> G
  DE --> G
  PC --> G
  S --> CME[ME only: canonical total events]
  SC -. ME thesis extension .-> CME
  S --> MME[ME only: microcanonical fixed strengths]
  E --> X[Missing thesis case? Extend MENoBiS]

Family choice

Data interpretation	MENoBiS family	Pair law
Events are distinguishable	ModelFamily.ME	Poisson
At most M events/layers per pair	ModelFamily.B	Binomial(M)
Events are indistinguishable	ModelFamily.W	geometric (M=1) or negative-binomial (M>1)

Constraint choice

Constraint	Use when
strength	origin and destination totals are the structural baseline
strength-cost	distance, travel time, or another pair cost is part of the null
strength-edges	total binary support size matters
strength-degree	each node's binary support matters
degree-events	support is primary and total events set positive occupations
partial	some pair occupations are known and must be frozen

Ensemble choice

Ensemble	Available cases
grand canonical	default for ME, B, W; independent pairs
canonical	current public route: ME fixed-strength with fixed total events; strength-cost is a thesis extension path
microcanonical	ME fixed strengths via stub matching

Do not relabel families

Same constraints with different event nature lead to different statistics. ME, B, and W require different pair equations and solver paths.

Practical default

Start with ME strength. Add cost or binary constraints only when they are part of the null hypothesis you want to remove. Use B or W only when the event interpretation requires those families and check Solvers and scaling.

If your case is missing

Do not fake a model by relabeling another family. Add the correct family kernel and constraint layer; see Extending thesis cases.