Statistical Foundations for Data Science

This course builds the statistical foundation for applied data science by connecting core statistical ideas to decisions under uncertainty, data design, variation, and communication.

By the end, a reader should be able to describe a data-generating process, distinguish signal from variability, explain sampling and measurement bias, summarize data responsibly, fit and critique basic models, and communicate statistical evidence in a decision-facing way.

Figure: A skewed service-resolution distribution used to show why summary statistics need context before they become decision evidence (adapted from Lecture 04: Distributions, Variability, and Tail Risk).

Lecture Sequence

01. Statistical Thinking for Decision Science

This lecture connects Statistical Thinking for Decision Science to data quality, uncertainty, and communication, so the ideas remain grounded in practical statistical judgment.

02. Populations, Units, Variables, and Data-Generating Processes

This lecture develops Populations, Units, Variables, and Data-Generating Processes with examples that make assumptions, diagnostics, and interpretation visible.

03. Probability, Randomness, and Expectation

This lecture uses Probability, Randomness, and Expectation to clarify the analyst’s question, evidence, assumptions, and decision implications.

04. Distributions, Variability, and Tail Risk

This lecture shows how distributions, variability, and tail risk change what summary statistics mean in practice.

05. Conditional Probability, Bayes Rule, and Base Rates

This lecture frames Conditional Probability, Bayes Rule, and Base Rates as a decision problem and asks what evidence can be trusted, challenged, and communicated.

06. Sampling, Measurement, and Data Collection Bias

This lecture builds intuition for Sampling, Measurement, and Data Collection Bias and ties the result to model choice, uncertainty, and action.

07. Simulation, Monte Carlo, and Bootstrap Intuition

This lecture applies Simulation, Monte Carlo, and Bootstrap Intuition with emphasis on diagnostics, tradeoffs, and evidence limits.

08. Estimators: Bias, Variance, Consistency, and Efficiency

This lecture develops Estimators: Bias, Variance, Consistency, and Efficiency as a practical pattern for analysis, diagnostics, and decision support.

09. Confidence Intervals and Uncertainty Quantification

This lecture connects Confidence Intervals and Uncertainty Quantification to data quality, variability, and communication, so intervals are interpreted as evidence rather than decoration.

10. Hypothesis Testing, Type I/II Errors, and Power

This lecture develops Hypothesis Testing, Type I/II Errors, and Power with examples that make assumptions, diagnostics, and interpretation visible.

11. Effect Sizes, Practical Significance, and Decision Thresholds

This lecture uses Effect Sizes, Practical Significance, and Decision Thresholds to clarify the analyst’s question, evidence, assumptions, and decision implications.

12. Exploratory Data Analysis, Visualization, and Summary Statistics

This lecture uses exploratory analysis and visualization to turn raw data into defensible summaries.

13. Linear Regression: Interpretation, Assumptions, and Limits

This lecture frames Linear Regression: Interpretation, Assumptions, and Limits as a decision problem and asks what evidence can be trusted, challenged, and communicated.

14. Classification, Probability Models, and Calibration

This lecture builds intuition for Classification, Probability Models, and Calibration and ties the result to model choice, uncertainty, and action.

15. Resampling, Regularization, Validation, and Model Selection

This lecture applies Resampling, Regularization, Validation, and Model Selection with emphasis on diagnostics, tradeoffs, and evidence limits.

16. Decision Analysis, Risk Communication, and Statistical Recommendations

This lecture develops Decision Analysis, Risk Communication, and Statistical Recommendations as a practical pattern for analysis, diagnostics, and decision support.