Comprehensive Curriculum in Statistics for Data Science, AI, and Large Language Models (LLMs)




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Part 1: Foundations of Statistical Literacy

1.1 Understanding Data
	•	Data Types in Practice: Categorical (e.g., gender, type), Numerical (e.g., sales, HP), Time-series (e.g., logs), and Spatial (e.g., location data)
	•	Structured Data (tabular format) vs. Unstructured Data (text, images, audio)
	•	Data Preparation: Input design, preprocessing, and type conversion for models

1.2 Descriptive Statistics (Summarization and Distribution Insight)
	•	Central Tendency: Mean, Median, Mode
	•	Variability: Variance, Standard Deviation, Range, Interquartile Range
	•	Distribution Shape: Skewness, Kurtosis, Outlier Detection
	•	Business Applications: Summarizing sales, customer behavior, click-through rates

1.3 Data Visualization (Insight Discovery through Visualization)
	•	Univariate Distributions: Histograms, Density Plots, Box Plots
	•	Bivariate Relationships: Scatterplots, Correlation Matrices, Pair Plots
	•	Practical Use Cases: KPI monitoring, sales distribution, feature correlation analysis

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Part 2: Probability and Probability Distributions

2.1 Fundamentals of Probability
	•	Events, Sample Spaces, and Independence
	•	Conditional Probability and Bayesian Updating
	•	Expectations, Variance, and Standard Deviation (Interpretation and Computation)

2.2 Representative Probability Distributions (Modeling Systems and Phenomena)
	•	Discrete: Bernoulli, Binomial (e.g., click-through, purchase probabilities)
	•	Continuous: Normal (e.g., error and performance modeling), t-Distribution (small sample analysis)
	•	Poisson (e.g., event counts), Chi-square, F-Distribution (hypothesis testing)

2.3 Information Theory Fundamentals
	•	Entropy: Measuring Uncertainty
	•	Cross-Entropy: Quantifying Model Prediction Errors
	•	Kullback-Leibler Divergence: Measuring Information Distance Between Distributions
	•	Applications: Classifier evaluation, generative model training

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Part 3: Statistical Inference and Decision Making

3.1 Estimation
	•	Point Estimation, Interval Estimation, and Confidence Intervals
	•	Managing Population vs. Sample Gaps
	•	Applications: A/B testing, advertising effectiveness measurement

3.2 Hypothesis Testing
	•	Significance Level, p-Value, Type I and Type II Errors
	•	t-Tests (mean comparison), Chi-square Tests (categorical data analysis)
	•	F-Tests (variance comparison), Proportion Tests (rate comparison)
	•	Applications: Evaluating interventions, assessing business risks

3.3 Model Selection and Validation
	•	AIC/BIC (Model Complexity vs. Generalization Balance)
	•	Cross-Validation for Model Stability Assessment
	•	Practical Use: Model tuning and selection

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Part 4: Regression, Classification, and Multivariate Analysis

4.1 Linear and Multiple Regression
	•	Building Predictive Models, Coefficient Interpretation, R², Residual Analysis
	•	Model Validity Checks (Linearity, Normality, Independence, Homoscedasticity)
	•	Applications: Sales forecasting, customer behavior prediction, pricing strategy

4.2 Logistic Regression
	•	Binary Classification Models, Probability Outputs, Odds Ratio Interpretation
	•	Applications: Churn prediction, purchase probability estimation

4.3 Multivariate Analysis and Clustering
	•	Principal Component Analysis (PCA): Dimensionality Reduction and Feature Extraction
	•	Clustering: k-Means, Hierarchical Clustering for Segment Discovery
	•	Applications: Customer segmentation, product categorization

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Part 5: Machine Learning and Statistical Modeling

5.1 Supervised Learning
	•	Linear and Logistic Regression, Decision Trees
	•	Random Forests, SVM, XGBoost
	•	Applications: Marketing analytics, demand forecasting, anomaly detection

5.2 Unsupervised Learning
	•	Clustering, PCA, t-SNE, UMAP for Data Understanding and Visualization
	•	Applications: User profiling, feature engineering

5.3 Model Evaluation Metrics
	•	Regression: MSE, RMSE, R²
	•	Classification: Accuracy, Precision, Recall, F1-Score, ROC, AUC
	•	Applications: Reporting model performance, making improvement decisions

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Part 6: Statistics for GPT and Large Language Models (LLMs)

6.1 Probabilistic Design of Language Models
	•	Sequence Probability Modeling (Chain Rule)
	•	Softmax for Next Token Probability Calculation and Sampling Strategies

6.2 Loss Functions Based on Information Theory
	•	Cross-Entropy and KL Divergence for Model Training
	•	Perplexity as a Performance Metric for Language Models

6.3 Optimization and Bayesian Estimation
	•	Maximum Likelihood Estimation (MLE) and Maximum A Posteriori (MAP)
	•	Bayesian Optimization for Hyperparameter Tuning

6.4 Model Evaluation and Control
	•	Temperature Scaling, Top-K / Top-P (Nucleus) Sampling
	•	Bayesian Uncertainty Quantification and Model Comparison via Statistical Tests

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Learning Outcomes
	•	Master the full pipeline from descriptive statistics to advanced probabilistic modeling
	•	Implement statistical models and machine learning workflows using Python / R
	•	Apply statistical techniques to business problems, AI system evaluation, and LLM optimization