Conditional probability P(A|B), Bayes' formula for inverting evidence, law of total probability. Foundation for Bayesian inference.
graph TD
D1["Def: Conditional prob\nP(A|B) = P(A∩B)/P(B)"]
T1["Thm: Product rule\nP(A∩B) = P(A|B)P(B)"]
T2["Thm: Law of total prob\nP(A) = Σⱼ P(A|Bⱼ)P(Bⱼ)"]
T3["Thm: Bayes' formula\nP(H|E) = P(E|H)P(H)/P(E)"]
T4["Thm: Bayes with partition\nposterior ∝ likelihood × prior"]
D2["Def: Prior P(H)\nhypothesis probability"]
D3["Def: Posterior P(H|E)\ngiven evidence"]
D4["Def: Likelihood P(E|H)"]
T5["Thm: Independence\n⇔ P(A|B)=P(A)"]
D1 --> T1
D1 --> T2
T1 --> T3
T2 --> T3
T3 --> T4
D2 --> T4
D3 --> T4
D4 --> T4
D1 --> T5
classDef definition fill:#b197fc,color:#fff
classDef theorem fill:#51cf66,color:#fff
class D1,D2,D3,D4 definition
class T1,T2,T3,T4,T5 theorem
Process Statistics
- Nodes: 14
- Edges: 13
- Definitions: 4
- Theorems: 5
Frontier: Bayesian nonparametrics, variational inference, PAC-Bayes bounds. math.ST