Probability and Statistics
Overview
This hub tracks uncertainty, estimation, probabilistic modeling, inference, calibration, hypothesis testing, learning curves, and statistical reasoning across learning, science, and verification.
Core Questions
- How should uncertainty, evidence, and estimation be represented and updated?
- Which probabilistic assumptions or statistical claims are essential versus incidental in a paper?
- How do statistical-learning curves change with sample size, model complexity, and saturation assumptions?
- Where do probabilistic tools recur across learning, verification, causality, robotics, and decision-making?
- When can probability questions be reduced to exact finite counts?
- Which causal claims depend on statistical association, structural mechanisms, or explicit temporal update equations?
- When do finite-sample confidence bounds support conservative safety certification rather than only estimation?
- When do iterative probability estimates need certified upper/lower bounds before they can control a learned system?
- Which causal estimands remain identifiable under SUTVA, no-unmeasured-confounding, and positivity assumptions?
- When can sequential Monte Carlo turn intractable counterfactual conditioning into asymptotically valid simulation?
Current Research Touchpoints
- Formal Methods
- Causal Decision Making
- Probabilistic Controlled Invariant Sets
- Probabilistic Shielding
- Sound Value Iteration
- Causality
- Safe Multi-Agent Reinforcement Learning
- AI Evaluation and Benchmarking
- Counterfactual Simulation
Key Concepts
- Counting in Probability
- Causal Decision Making
- Probabilistic Controlled Invariant Sets
- Structural Equation Models
- Actual Causality
- Temporal Causal Models
- Beta Distribution
- Probabilistic Model Checking
- Sound Value Iteration
- Distributional Value Iteration
- Predicate Abstraction
- Causality
- Safe Reinforcement Learning
- Calibration
- Brier Score
- Sigmoid Functions
- Double Descent
- S-Curves and Saturating Growth
- Counterfactual Simulation