1. Introduction

Advanced statistics enables AI systems to infer, evaluate, and decide. It helps build more accurate models, manage uncertainty, and ensure valid results.

2. Distributions in AI

Understanding normal, binomial, Poisson, and exponential distributions helps model randomness in classification, anomaly detection, and NLP.

import numpy as np
from scipy.stats import norm
x = np.linspace(-3, 3, 100)
pdf = norm.pdf(x, loc=0, scale=1)

3. Hypothesis Testing

Used to validate assumptions. For example: Does a new feature improve accuracy?

from scipy.stats import ttest_ind
ttest_ind(model_A_scores, model_B_scores)

4. Bayesian Thinking

Bayesian networks model dependencies. Ideal for AI systems involving uncertainty (e.g., medical diagnosis).

Bayes’ Rule: P(H|D) = [P(D|H) * P(H)] / P(D)

5. Correlation and Multicollinearity

Helps in feature selection and identifying redundancy. Too much correlation? Drop features!

6. Dimensionality Reduction

Reduce features with PCA/t-SNE without losing interpretability.

7. ANOVA & Feature Relevance

Test whether mean performance differs across feature categories.

8. Evaluating ML Models Statistically

• Confidence intervals for model accuracy
• Bootstrapping to estimate generalization
• ROC-AUC, precision-recall

9. Time Series Forecasting

Use ACF/PACF, ARIMA models for predictive forecasting.

10. Statistical Inference and Simulation

Monte Carlo methods are widely used for simulating probabilities in deep learning, reinforcement learning, etc.

11. Summary Cheat Sheet

• Distributions → Data Modeling
• Hypothesis Testing → Feature Significance
• Bayesian Stats → Uncertainty Handling
• Inference → Prediction Accuracy
• Simulation → Probabilistic Modeling

12. Suggested Books

• “Pattern Recognition and Machine Learning” – Bishop
• “Bayesian Reasoning and Machine Learning” – Barber
• “The Elements of Statistical Learning” – Hastie, Tibshirani