Tetrad Manual
About
📚 Project Background
👥 Contributors
📄 Papers and Books
📬 Questions or Suggestions?
Workflows
Causal Analysis Workflows
🧭 What You’ll Learn
📌 Why a Workflow Matters
🗺️ How the Workflow Is Organized
🧠 Practical Advice Before You Begin
🙌 Where to Start
Data Exploration: Understanding Your Data Before Causal Discovery
1. Load and Inspect Your Data
2. Review Variable Types
3. Examine Marginal Distributions with Histograms
4. Explore Pairwise Relationships with the Plot Matrix
5. Consider Linearity and Gaussianity (Informally)
6. Reflect on Causal Sufficiency and Latent Variables
7. Clarify Your Modeling Goals
8. Moving Forward
Practical Notes
Algorithm Selection and Assumptions
What This Page Covers
1. Which Assumptions Matter?
1.1. Causal Sufficiency
1.2. Functional Form and Distribution
1.3. Modeling Goal
1.4. Sample Size and Dimensionality
2. Major Algorithm Families in Tetrad
2.1. Constraint-Based Methods
2.2. Score-Based Methods
2.3. Hybrid Methods
2.4 Time Series Data (Lagged Variables)
3. Mapping Assumptions to Starting Choices
4. Choosing Tests and Scores
4.1. Independence Tests
4.2. Scores
5. What If You’re Unsure?
6. Using Grid Search Effectively
7. Summary
🧭 Next Step
Manual Exploration: Try Searches Interactively
Why Use Manual Exploration?
When Manual Exploration Is Useful
Pipelines: The Interactive Workflow
Building a Simple Pipeline
Examples of Manual Exploration
A. Varying Test Sensitivity
B. Comparing Algorithms
C. Adding Background Knowledge
D. Exploring Nonlinearity or Non-Gaussianity
Inspecting Results
How Manual Exploration Leads to Grid Search
Tips for Effective Manual Exploration
Summary
🧭 Next Step
Running Searches and Grid Search Tips
Why Use Grid Search?
From Single Runs to Systematic Search
Running a Basic Search
What to Sweep in Grid Search
1. Significance Level (α) — Test-Based Methods
2. Penalty or Discount — Score-Based Methods
3. Algorithm Choice
4. Tests and Scores
Interpreting Grid Search Results
1. Markov Consistency
2. Model Complexity
A Practical Starter Pattern
Reading Grid Search Output
Common Pitfalls to Avoid
Sweeping Too Many Parameters at Once
Changing Background Knowledge Too Early
Delaying Diagnostics
Not Recording What Was Tried
Where Grid Search Fits in the Workflow
🧭 Next Step
Model Evaluation and Markov Checking
Why Model Evaluation Matters
What the Markov Checker Does
Intuition
Running the Markov Checker in Tetrad
Interpreting Markov Checker Output
Key Outputs
How to Read the Results
Minimal Markov-Consistent Models
Comparing Models from Grid Search
Important Caveats
Markov Checking Is Not a Proof
Test Choice Matters
Sampling Variability Exists
Beyond Markov Checking
Practical Tips
Summary
🧭 Next Step
Interpreting Results
1. What a Discovered Graph Represents
2. Types of Output and Their Meaning
2.1 Fully Directed Acyclic Graphs (DAGs)
2.2 Completed Partially Directed Acyclic Graphs (CPDAGs)
2.3 Partial Ancestral Graphs (PAGs)
3. Interpreting Common Edge Marks
4. Robustness and Stability
5. What You
Can
Say (With Care)
6. What You Should Avoid Saying Unqualified
7. Using Background Knowledge
8. Communicating Uncertainty Clearly
9. Documenting Your Analysis
10. Summary
🧭 What’s Next
Example: Auto MPG Analysis with Grid Search
1. The Auto MPG Dataset
Data Preparation
2. Loading and Exploring the Data in Tetrad
Visual Exploration
3. Algorithm Choice and Assumptions
Causal Sufficiency
Algorithm: BOSS
Score: Degenerate Gaussian BIC
4. Setting Up the Grid Search
Step 1: Connect the Data
Step 2: Algorithms Tab
Step 3: Table Columns Tab
Step 4: Comparison Tab (Initial Setup)
Step 5: Set Parameter Ranges
5. Running the Comparison
6. Interpreting the Comparison Results
Choosing a Model
7. Viewing the Selected Graph
8. What This Example Illustrates
9. Next Steps
Tetrad Interface
Overview
Main Window
Project tree
Work area and tabs
Menus and toolbar
Status bar, logging pane, and messages
Working with Data
Importing data
Viewing and editing data
Linking data and graphs
Saving and exporting data
Graph Editor
Opening and creating graphs
Basic editing operations
Layout and visualization
Background knowledge and tiers
Saving and exporting graphs
Running Algorithms
Launching a search
Choosing tests and scores
Setting parameters
Running and monitoring
Re-running with modified settings
Estimate model parameters
Basic workflow
Inspecting the fitted model
Relationship to graphs and search
Where to look next
Viewing and Exporting Results
Graph results
Tabular and numeric results
Exporting graphs and tables
Reusing results in pipelines
Simulation and Utilities
Simulating data on the workbench
Resampling and bootstrap workflows
Grid Search (overview)
Other utilities
Box by Box
Graph Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Compare Box
Purpose
Typical workflow
Types of comparisons
Key controls
Common patterns & tips
Related pages
Grid Search Box (Data)
Purpose of Data-Based Grid Search
When This Mode Is Used
Basic Setup
Algorithms Tab
Table Columns Tab
Comparison Tab
Interpreting Results
View Graphs Tab
Notes and Best Practices
Summary
Grid Search (Simulation)
When to Use Simulation-Based Grid Search
Key Difference from Data-Based Grid Search
Step 1: Select a Simulation
Step 2: Algorithms Tab
Step 3: Table Columns Tab
Step 4: Comparison Tab
Step 5: Run Counts and Randomness
Running the Comparison
Interpreting Simulation Results
Common Pitfalls
Summary
🧭 Next Steps
Parametric Model Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Instantiated Model Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Estimator Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Estimator types and detail pages
Related pages
Data Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Simulation Box
Purpose
Simulation setup
Running a simulation
Using simulated graphs and data in other boxes
Common patterns & tips
Related pages
Search Box
Purpose
Wizard workflow
Connecting data, knowledge, and outputs
Common patterns & tips
Related pages
Latent Clusters Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Latent Structure Box
Purpose
Wizard workflow
Connecting data, clusters, knowledge, and outputs
Common patterns & tips
Related pages
Knowledge Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Updater Box
Purpose
Typical workflow
Updater types and detail pages
Connecting the Updater with other boxes
Common patterns & tips
Related pages
Regression box
Multiple Linear Regression
Logistic Regression
Adjustment Total Effects
IDA Check
Interpretation and workflow notes
Summary
Note Box
Purpose
Typical workflow
Key controls
Common patterns & tips
Related pages
Data Preparation
Where data preparation happens in Tetrad
Typical data preparation workflow
What the rest of this section covers
Detail Callouts
Data subset / resample
Inputs and outputs
Variable selection
Rows and sampling
Typical use cases
Detail: Graph Menu (Graph Box)
Random Graph
Graph Properties
Underlinings
Paths
Highlight
Check Graph Type
Manipulate Graph
PAG Edge Specialization Markups
Summary
Detail: Display Subgraphs
Purpose
Basic workflow
Subgraph types
Summary
Detail: Markov Checker
Purpose
Basic workflow
Outputs
Interpreting results
Detail: Bootstrapping and Ensemble Graphs
What Bootstrapping Does
Enabling Bootstrapping
Running a Bootstrapped Search
The Edges Tab: Bootstrap Frequencies
Ensemble Graph Display Options
How to Use Bootstrapping Effectively
Important Caveats
Summary
Detail: Parametric & Instantiated Model Types
Model families
Interaction with Estimator and Simulation
Detail: Simulation types
Bayes net
Linear structural equation model
Linear Fisher model
Nonlinear additive SEM (CAM)
General noise SEM
Additive noise SEM
Lee and Hastie
Conditional Gaussian
Time series
Choosing a simulator
Detail: Bayes (Multinomial) Parametric Model
When to use Bayes models
Main panel layout
Typical workflow
Tips and caveats
Detail: Bayes (Multinomial) Instantiated Model
How Bayes instantiated models are created
Instantiated Model box layout (Bayes)
Typical uses
Tips
Detail: ML Bayes Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
Tips and common issues
Related pages
Detail: Dirichlet Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
Tips and common issues
Related pages
Detail: EM Bayes Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
Tips and common issues
Related pages
Detail: SEM (Linear) Parametric Model
When to use SEM models
Main panel layout
Typical workflow
Tips and caveats
Detail: SEM (Linear) Instantiated Model
How SEM instantiated models are created
Instantiated Model box layout (SEM)
File menu options (SEM instantiated model)
Detail: SEM (Linear) Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
File menu options (SEM Estimator)
Detail: Hybrid (Conditional Gaussian) Parametric Model
When to use Hybrid models
Main panel layout
Typical workflow
Tips and caveats
Detail: Hybrid (Conditional Gaussian) Instantiated Model
How Hybrid instantiated models are created
Instantiated Model box layout (Hybrid)
Typical uses
Tips
Detail: Hybrid CG Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
Tips and common issues
Related pages
Detail: Generalized Parametric Model
When to use Generalized models
Main panel layout
Typical workflow
Tips and caveats
Detail: Generalized Instantiated Model
How Generalized instantiated models are created
Instantiated Model box layout (Generalized)
Typical uses
Tips
Detail: Generalized SEM Estimator
Purpose
Inputs and requirements
How it works (conceptually)
Output
Tips and common issues
Related pages
Detail: Junction Tree Updater
Purpose
Inputs and setup
How it works (conceptually)
Output
Tips
Related pages
Detail: Approximate Updater
Purpose
Inputs and setup
How it works (conceptually)
Output
Tips
Related pages
Detail: Row Summing Updater
Purpose
Inputs and setup
How it works (conceptually)
Output
Tips
Related pages
Detail: SEM Updater
Purpose
Inputs and setup
How it works (conceptually)
Output
Tips
Related pages
Detail: Adjustment and Total Effects: Amenability and Discrete Variables
What Is an Amenable Pair?
Amenability via Visible Edges
How Amenability Is Reported in the Tool
Discrete Variables and Regression Output
Amenability and Refining Equivalence Classes
Summary
Detail: IDA Check (Regression box)
Layout and controls
Table columns
Summary statistics (bottom)
Typical usage
Notes and references
Detail: N-tad Explorer
Basic workflow
Interpretation
Tips and notes
Using N-tad Explorer with SEMs
Python and R Bindings
py-tetrad (Python Binding)
rpy-tetrad (R Binding)
When to Use These Bindings
Related Python Ecosystem Tools
Relationship to Tetrad
Recommendation
Graphs and DataSets
Graph Types and Formats
1. Core Graph Types in Tetrad
1.1 DAG — Directed Acyclic Graph
1.2 CPDAG — Completed Partially Directed Acyclic Graph
1.3 MAG — Maximal Ancestral Graph
1.4 PAG — Partial Ancestral Graph
2. Endpoint Marking System
3. PAG Edge-Specialization Markup (Optional GUI Feature)
3.1 Two Independent Attributes
(A) Visibility
(B) Directness
3.2 The Four Directed-Edge Types
3.3 Undirected Edges Represent
Selection Bias
4. Saving and Loading Graphs
4.1 Conceptual Plain-Text Format
5. Graphs and Data: Name Matching
6. Summary
Data Types and Formats
1. Overview of Supported Formats
2. Dataset Format (Tabular Data)
Notes
3. Discrete Data
4. Continuous Data
5. Covariance and Correlation Matrices
5.1 Required Structure
5.2 Lower Triangle Covariance Matrix Example
5.3 Full Square Covariance Matrix Example (Current Default)
5.4 Correlation Matrices
5.5 Common Parsing Errors for Covariance/Correlation Files
6. Lower-Triangular Format
6.1 Note on GUI Display
7. Exporting Data from Tetrad
8. Summary
Search Algorithms
Choosing an Algorithm
🔍 Choosing an Algorithm
🧭 Recommended Algorithms (At a Glance)
🔍 DAG / CPDAG Methods (No Latent Confounders)
🌀 PAG Methods (Hidden Confounders Allowed)
🔧 Other Useful Algorithm Classes
🎛 Choosing CI Tests & Scores (Quick Guide)
⚠️ Common Pitfalls and Fixes
Search Algorithms — By Type
Legend — Algorithm Categories
Extra Structural Badges
🔍 Constraint-Based Algorithms (CPDAG / PAG)
📏 Score-Based Algorithms (CPDAG)
🌀 Hybrid Algorithms (Score + FCI)
🎨 Non-Gaussian, Moment-Based, and Orientation Algorithms
Nonlinear & Distribution-Shift Algorithms
📦 Stability / Resampling / Ensemble Wrappers
🧪 Specialized / Utility Algorithms
Latent Clustering (Measurement Block Discovery)
Latent Structure / Measurement-Model Construction
Search Algorithms — Alphabetical
1. BOSS — Best Order Score Search
1.1. Key idea
1.2. When to use
1.3. How it works (at a glance)
1.4. Strengths
1.5. Limitations
1.6. How it relates to other Tetrad algorithms
1.7. Prior knowledge support
1.8. Parameters
1.9. Reference
1.10. Summary
2. BOSS-FCI — Best-Order Score Search + FCI Refinement
2.1. Key Idea
2.2. When to Use
2.3. Strengths
2.4. Limitations
2.5. How It Differs From Related Algorithms
2.6. Prior Knowledge Support
2.7. Key Parameters in Tetrad
2.8. Reference
2.9. Summary
3. BPC — Build Pure Clusters
3.1. Basic Assumptions
3.2. High-Level Algorithm
3.3. Output and Interpretation
3.4. Parameters in Tetrad
3.5. Strengths
3.6. Limitations
3.7. Reference
3.8. Summary
4. CAM — Causal Additive Model
4.1. Key Idea
4.2. When to Use CAM
4.3. Prior Knowledge Support
4.4. Strengths
4.5. Limitations
4.6. Key Parameters in Tetrad
4.7. Reference
4.8. Summary
5. CCD — Cyclic Causal Discovery
5.1. Key Idea
5.2. When to Use
5.3. Prior Knowledge Support
5.4. Strengths
5.5. Limitations
5.6. Key Parameters in Tetrad
5.7. Reference
5.8. Summary
6. CD-NOD — Causal Discovery from Nonstationary / Distribution-Shifted Data
6.1. Key Idea
6.2. When to Use
6.3. Prior Knowledge Support
6.4. Strengths
6.5. Limitations
6.6. Key Parameters in Tetrad / Scripting
6.7. Reference
6.8. Summary
7. Conservative PC (CPC) — Conservative Collider Orientation
7.1. Key Idea
7.2. When to Use
7.3. Prior Knowledge Support
7.4. Strengths
7.5. Limitations
7.6. Key Parameters in Tetrad
7.7. Reference
7.8. Summary
8. CStaR (Causal Stability Ranking)
8.1. High-level idea
8.2. Inputs
8.3. Outputs
8.4. Parameters
8.5. When to use CStaR
8.6. References
8.7. Summary
9. DAGMA — Learning DAGs via M-Matrices and Log-Determinant Acyclicity
9.1. Key Idea
9.2. When to Use
9.3. Prior Knowledge Support
9.4. Strengths
9.5. Limitations
9.6. Key Parameters in Tetrad
9.7. Reference
9.8. Summary
10. DirectLiNGAM
10.1. Key Idea
10.2. When to Use
10.3. Prior Knowledge Support
10.4. Strengths
10.5. Limitations
10.6. Key Parameters in Tetrad
10.7. Reference
10.8. Summary
11. DM (Detect–Mimic)
11.1. DM-PC
11.2. DM-FCIT
12. Factor Analysis
12.1. Purpose
12.2. When to Use
12.3. How It Works (Conceptual)
12.4. Strengths
12.5. Limitations
12.6. Relation to Other Latent Tools
12.7. References
12.8. Summary
13. FAS — Fast Adjacency Search
13.1. Key Idea
13.2. When to Use
13.3. Case Study: High-dimensional fMRI Preprocessing
13.4. Prior Knowledge Support
13.5. Strengths
13.6. Limitations
13.7. Key Parameters in Tetrad
13.8. Reference
13.9. Summary
14. FASK — Fast Adjacency Skewness
14.1. Key Idea
14.2. When to Use
14.3. Prior Knowledge Support
14.4. Strengths
14.5. Limitations
14.6. Key Parameters in Tetrad
14.7. Reference
14.8. Summary
15. FASK-Vote — Multi-Dataset FASK Voting over IMaGES
15.1. Key Idea
15.2. When to Use
15.3. Prior Knowledge Support
15.4. Strengths
15.5. Limitations
15.6. ImagES Parameters
15.7. FASK Parameters
15.8. Reference
15.9. Summary
16. FCI — Fast Causal Inference
16.1. Key idea
16.2. When to use FCI
16.3. Assumptions
16.4. How it works (at a glance)
16.5. How it relates to other Tetrad algorithms
16.6. Strengths
16.7. Limitations
16.8. Prior knowledge
16.9. Key parameters in Tetrad
16.10. References
17. FCI-IOD — FCI with Independent Overlapping Datasets
17.1. Key Idea
17.2. When to Use
17.3. Prior Knowledge Support
17.4. Strengths
17.5. Limitations
17.6. Key Parameters in Tetrad
17.7. Reference
17.8. Summary
18. FCIT — FCI with Targeted Testing
18.1. Key Idea
18.2. When to Use
18.3. Strengths
18.4. Limitations
18.5. How It Differs From Related Algorithms
18.6. Prior Knowledge Support
18.7. Key Parameters in Tetrad
18.8. Reference
18.9. Summary
19. FGES — Fast Greedy Equivalence Search
19.1. Key Idea
19.2. A Nuanced View of Scalability and Sparsity
19.3. When to Use FGES
19.4. Prior Knowledge Support
19.5. Strengths
19.6. Limitations
19.7. Key Parameters in Tetrad
19.8. Reference
19.9. Summary
20. FGES-MB — FGES Markov Blanket Search
20.1. Key idea
20.2. When to use FgesMb
20.3. Prior knowledge support
20.4. Strengths
20.5. Limitations
20.6. Key parameters in Tetrad
20.7. Reference
20.8. Summary
21. FOFC — Find One-Factor Clusters
21.1. Key Idea
21.2. When to Use
21.3. Prior Knowledge Support
21.4. Strengths
21.5. Limitations
21.6. Key Parameters in Tetrad
21.7. Reference
21.8. Summary
22. FTFC — Find Two-Factor Clusters (Sextad-Based)
22.1. Key Idea
22.2. Relation to FOFC and GFFC
22.3. When to Use FTFC
22.4. Strengths
22.5. Limitations
22.6. Parameters in Tetrad
22.7. Reference
22.8. Summary
23. GFCI — Greedy Fast Causal Inference
23.1. 🔍 Key Idea
23.2. 🎯 When to Use GFCI
23.3. 🧠 Prior Knowledge
23.4. ⭐ Strengths
23.5. ⚠️ Limitations
23.6. 🔧 Key Parameters (Tetrad)
23.7. ⛓ Relation to Other Algorithms
23.8. 📚 Reference
24. GFFC — Generalized Find Factor Clusters
24.1. Key Idea
24.2. Algorithm Overview
24.3. Why Use GFFC?
24.4. Strengths
24.5. Limitations
24.6. Parameters in Tetrad
24.7. Reference
24.8. Summary
25. GIN (Generalized Independent Noise)
25.1. Overview
25.2. Requirements
25.3. Parameters
25.4. How the Algorithm Works
25.5. Output
25.6. When to Use
25.7. When Not to Use
25.8. Notes
25.9. References
26. GRaSP — Greedy Relaxations of the Sparsest Permutation
26.1. Key idea
26.2. When to use
26.3. How it works (at a glance)
26.4. Strengths
26.5. Limitations
26.6. How it relates to other Tetrad algorithms
26.7. Prior knowledge support
26.8. Key parameters in Tetrad
26.9. Reference
26.10. Summary
27. GRaSP-FCI — Greedy Relaxations of Sparsest Permutation + FCI Refinement
27.1. Key Idea
27.2. When to Use
27.3. Strengths
27.4. Limitations
27.5. How It Differs From Related Algorithms
27.6. Prior Knowledge Support
27.7. Key Parameters in Tetrad
27.8. Reference
27.9. Summary
28. ICA Lingam — ICA-Based LiNGAM
28.1. Key Idea
28.2. When to Use
28.3. Prior Knowledge Support
28.4. Strengths
28.5. Limitations
28.6. Key Parameters in Tetrad
28.7. Reference
28.8. Summary
29. ICA LingD — Cyclic LiNGAM (Lacerda et al.)
29.1. Key Idea
29.2. When to Use
29.3. Prior Knowledge Support
29.4. Strengths
29.5. Limitations
29.6. Key Parameters in Tetrad
29.7. Reference
29.8. Summary
30. IMaGES — Independent Multiple-sample Greedy Equivalence Search
30.1. Key Idea
30.2. Variants
30.3. When to Use
30.4. Prior Knowledge Support
30.5. Strengths
30.6. Limitations
30.7. Key Parameters in Tetrad
30.8. Reference
30.9. Summary
31. Latent Clusters
31.1. Key Idea
31.2. When to Use
31.3. Prior Knowledge Support
31.4. Strengths
31.5. Limitations
31.6. Latent Cluster Algorithms in Tetrad
31.7. Relationship to Latent Structure Algorithms
31.8. Summary
32. LV-Heuristic — Heuristic Latent-Variable PAG from a Single DAG
32.1. What LV-Heuristic Is (and Is Not)
32.2. Key Idea
32.3. When to Use LV-Heuristic
32.4. Strengths
32.5. Limitations
32.6. How LV-Heuristic Differs From Other Mixed-Strategy Algorithms
32.7. Prior Knowledge Support
32.8. Key Parameters in Tetrad
32.9. Reference
32.10. Summary
33. Mimbuild Bollen
33.1. Purpose
33.2. How It Works (Conceptual)
33.3. Strengths
33.4. Limitations
33.5. Relation to Other Latent Tools
33.6. References
33.7. Summary
34. Mimbuild PCA
34.1. Purpose
34.2. How It Works (Conceptual)
34.3. Strengths
34.4. Limitations
34.5. Relation to Other Latent Tools
34.6. References
34.7. Summary
35. PagSamplingRfci
35.1. Key Idea
35.2. When to Use
35.3. Prior Knowledge Support
35.4. Strengths
35.5. Limitations
35.6. Key Parameters in Tetrad
35.7. Reference
35.8. Summary
36. Pairwise Orientation Methods — FaskPw & RSkew
36.1. Overview
36.2. FaskPw — FASK Pairwise Left–Right Orientation
36.3. Key Idea
36.4. When to Use
36.5. Strengths
36.6. Limitations
36.7. Parameters in Tetrad
36.8. RSkew — Robust Skewness Orientation (Hyvärinen & Smith, 2013)
36.9. Key Idea (informal)
36.10. When to Use
36.11. Strengths
36.12. Limitations
36.13. Parameters in Tetrad
36.14. Prior Knowledge Support
36.15. Summary
37. PC — Peter–Clark Algorithm
37.1. Key Idea
37.2. When to Use
37.3. Prior Knowledge Support
37.4. Strengths
37.5. Limitations
37.6. Key Parameters in Tetrad
37.7. Historical Notes
37.8. Additional Reference
37.9. Summary
38. PC-Max — PC with Maximum-p Collider Orientation
38.1. Key Idea
38.2. When to Use
38.3. Relation to Standard PC
38.4. Prior Knowledge Support
38.5. Strengths
38.6. Limitations
38.7. Key Parameters in Tetrad
38.8. Reference
38.9. Summary
39. PCD — PC for Deterministic Relations
39.1. Key Idea
39.2. When to Use
39.3. Prior Knowledge Support
39.4. Strengths
39.5. Limitations
39.6. Key Parameters in Tetrad
39.7. Summary
40. PC-MB — PC Markov Blanket Search
40.1. Key Idea
40.2. When to Use
40.3. Prior Knowledge Support
40.4. Strengths
40.5. Limitations
40.6. Key Parameters in Tetrad
40.7. Reference
40.8. Summary
41. PCMCI — Time-Series Causal Discovery (Runge et al.)
41.1. Key Idea
41.2. When to Use
41.3. Prior Knowledge Support
41.4. Strengths
41.5. Limitations
41.6. Key Parameters in Tetrad
41.7. Reference
41.8. Summary
42. Restricted BOSS — Target-Focused Best Order Score Search
42.1. Key Idea
42.2. When to Use
42.3. Prior Knowledge Support
42.4. Strengths
42.5. Limitations
42.6. Key Parameters in Tetrad
42.7. Reference
42.8. Summary
43. RFCI — Really Fast Causal Inference
43.1. Key Idea
43.2. When to Use
43.3. Prior Knowledge Support
43.4. Strengths
43.5. Limitations
43.6. Key Parameters in Tetrad
43.7. Reference
43.8. Summary
44. RFCI-BSC
44.1. Key Idea
44.2. When to Use
44.3. Prior Knowledge Support
44.4. Strengths
44.5. Limitations
44.6. Key Parameters in Tetrad
44.7. Reference
44.8. Summary
45. SingleGraphAlg (Imported Graph Wrapper)
45.1. What it does
45.2. Typical workflow
45.3. When to use (and when not to)
46. SP — Sparsest Permutation
46.1. Key idea
46.2. When to use
46.3. How it works (at a glance)
46.4. Strengths
46.5. Limitations
46.6. How it relates to other Tetrad algorithms
46.7. Prior knowledge support
46.8. Reference
46.9. Summary
47. SP-FCI — Sparsest-Permutation FCI
47.1. Key Idea
47.2. When to Use
47.3. Strengths
47.4. Limitations
47.5. Key Parameters in Tetrad
47.6. Knowledge Support
47.7. Relation to Other Algorithms
47.8. References
47.9. Summary
48. StabilitySelection
48.1. Key Idea
48.2. When to Use
48.3. Prior Knowledge Support
48.4. Strengths
48.5. Limitations
48.6. Key Parameters in Tetrad
48.7. Reference
48.8. Summary
49. StARS
49.1. Key Idea
49.2. When to Use
49.3. Prior Knowledge Support
49.4. Strengths
49.5. Limitations
49.6. Key Parameters in Tetrad
49.7. Reference
49.8. Summary
50. TSC — Trek Separation Clusters
50.1. Intended use
50.2. Model assumptions (NOLAC version)
50.3. High-level algorithm sketch
50.4. Inputs and outputs
50.5. Key parameters
50.6. Practical guidance
50.7. Limitations
50.8. Related methods
50.9. Summary
Tests & Scores
Choosing Tests & Scores
1. Continuous, Approximately Gaussian Data
Recommended Tests
Recommended Scores
Best-Fit Algorithms
2. Discrete Data (Binary / Ordinal / Categorical)
Recommended Tests
Recommended Scores
Best-Fit Algorithms
3. Mixed Continuous/Discrete Data
A. Conditional Gaussian (CG)
B. Degenerate Gaussian (DGC)
C. Basis Function (BF) Tests/Scores
4. Non-Gaussian Linear Models
Recommended Tests
Recommended Scores
Best-Fit Algorithms
5. Nonlinear Models
A. Kernel Conditional Independence Test (
KCI
)
B. Random Conditional Independence Test (
RCIT
)
B. Basis Function Test / Score (
Recommended for scalability
)
6. Latent Variable Workflows (Block-Based Search)
Block-Based Tests/Scores
Compatible Algorithms
Typical Workflow
Summary Table (Practical Defaults)
Next Steps
Tests and Scores: By Type
Independence Tests
Independence Tests Overview
Scores
Scores Overview
How Tests and Scores Are Used in Algorithms
Tests and Scores — Alphabetical
1. Basis Function BIC Score
1.1. Summary
1.2. When to use
1.3. Model class
1.4. Score form (conceptual)
1.5. Parameters
1.6. Strengths
1.7. Limitations
1.8. References
2. Basis Function Likelihood Ratio Test
2.1. Summary
2.2. When to use
2.3. Assumptions
2.4. Test details (conceptual)
2.5. Parameters
2.6. Strengths
2.7. Limitations
2.8. References
3. BDeu Score
3.1. Summary
3.2. When to use
3.3. Model class
3.4. Score form (conceptual)
3.5. Parameters
3.6. Strengths
3.7. Limitations
3.8. References
4. Chi-Square Test
4.1. Summary
4.2. When to use
4.3. Assumptions
4.4. Test details (conceptual)
4.5. Parameters
4.6. Strengths
4.7. Limitations
4.8. References
5. Conditional Gaussian BIC Score
5.1. Summary
5.2. When to use
5.3. Model class
5.4. Score form (conceptual)
5.5. Parameters
5.6. Strengths
5.7. Limitations
5.8. References
6. Conditional Gaussian Likelihood Ratio Test
6.1. Summary
6.2. When to use
6.3. Assumptions
6.4. Test details (conceptual)
6.5. Parameters
6.6. Strengths
6.7. Limitations
6.8. References
6.9. References
7. Degenerate Gaussian BIC Score
7.1. Summary
7.2. When to use
7.3. Model class
7.4. Score form (conceptual)
7.5. Parameters
7.6. Strengths
7.7. Limitations
7.8. References
8. Degenerate Gaussian Likelihood Ratio Test
8.1. Summary
8.2. When to use
8.3. Assumptions
8.4. Test details (conceptual)
8.5. Parameters
8.6. Strengths
8.7. Limitations
8.8. References
9. Discrete BIC Score
9.1. Summary
9.2. When to use
9.3. Model class
9.4. Score form (conceptual)
9.5. Parameters
9.6. Strengths
9.7. Limitations
10. Extended BIC (EBIC) Score
10.1. Summary
10.2. When to use
10.3. Model class
10.4. Score form (conceptual)
10.5. Parameters
10.6. Strengths
10.7. Limitations
10.8. References
11. Fisher Z Test
11.1. Summary
11.2. When to use
11.3. Assumptions
11.4. Test details (conceptual)
11.5. Parameters
11.6. Strengths
11.7. Limitations
11.8. References
12. G-Square Test
12.1. Summary
12.2. When to use
12.3. Assumptions
12.4. Test details (conceptual)
12.5. Parameters
12.6. Strengths
12.7. Limitations
12.8. References
13. Generalized Information Criterion (GIC) Scores
13.1. Summary
13.2. When to use
13.3. Model class
13.4. Score form (conceptual)
13.5. Parameters
13.6. Strengths
13.7. Limitations
13.8. References
14. Kernel Conditional Independence Test (KCI)
14.1. Summary
14.2. When to use
14.3. Assumptions
14.4. Test details (conceptual)
14.5. Parameters
14.6. Strengths
14.7. Limitations
14.8. References
15. m-Separation Test
15.1. Summary
15.2. When to use
15.3. Assumptions
15.4. Test details (conceptual)
15.5. Parameters in Tetrad
15.6. Strengths
15.7. Limitations
15.8. References
16. m-Separation Score
16.1. Summary
16.2. When to use
16.3. Model class
16.4. Score form (conceptual)
16.5. Parameters in Tetrad
16.6. Strengths
16.7. Limitations
17. MVP BIC Score
17.1. Summary
17.2. When to use
17.3. Model class
17.4. Score form (conceptual)
17.5. Parameters
17.6. Strengths
17.7. Limitations
18. Multivariate Polynomial Likelihood Ratio Test (MVPLRT)
18.1. Summary
18.2. When to use
18.3. Assumptions
18.4. Test details (conceptual)
18.5. Parameters
18.6. Strengths
18.7. Limitations
19. Poisson BIC Test
19.1. Summary
19.2. When to use
19.3. Relation to Poisson Prior Score
19.4. Test details (conceptual)
19.5. Parameters
19.6. Strengths
19.7. Limitations
20. Poisson Prior Score
20.1. Summary
20.2. When to use
20.3. Model class
20.4. Score form (conceptual)
20.5. Parameters
20.6. Strengths
20.7. Limitations
20.8. Relation to other penalties
21. Probabilistic Independence Test
21.1. Summary
21.2. When to use
21.3. Assumptions
21.4. Test details (conceptual)
21.5. Parameters
21.6. Strengths
21.7. Limitations
22. Random Conditional Independence Test (RCIT)
22.1. Summary
22.2. When to use
22.3. Assumptions
22.4. Test details (conceptual)
22.5. Parameters
22.6. Strengths
22.7. Limitations
22.8. Relationship to other CI tests in Tetrad
22.9. References
23. SEM BIC Score
23.1. Summary
23.2. When to use
23.3. Model class
23.4. Score form (conceptual)
23.5. Parameters
23.6. Strengths
23.7. Limitations
24. SEM BIC Test
24.1. Summary
24.2. When to use
24.3. Relation to SEM BIC Score
24.4. Test details (conceptual)
24.5. Strengths
24.6. Limitations
25. Zhang–Shen Bound Score
25.1. Summary
25.2. When to use
25.3. Model class
25.4. Score form (conceptual)
25.5. Parameters
25.6. Strengths
25.7. Limitations
25.8. References
Parameters
Contributors
🌟 Founders & Early Leadership
🧭 Project Direction & Architecture
🔬 Algorithmic & Research Contributions
🛠 Software Engineering & Infrastructure
🏛 Funding Acknowledgment
Papers and Books
Change Log
Tetrad Manual
Index
Index