Probability and Statistics for Data Science

Course Description

This advanced-level course, "Probability and Statistics for Data Science," is part of the Data Science MicroMasters program offered by UCSanDiegoX. It is designed to equip students with the fundamental knowledge and practical skills in probability and statistics essential for data science. The course focuses on teaching students how to reason about uncertainty in noisy datasets, a crucial skill for data scientists. Through a combination of theoretical learning and hands-on experience using Jupyter notebooks, students will gain a deep understanding of the mathematical foundations that underpin machine learning and data analysis techniques.

What Students Will Learn

  • The mathematical foundations for machine learning
  • Statistics literacy, including understanding statements like "at a 99% confidence level"
  • Concepts of random variables, dependence, correlation, and regression
  • Principal Component Analysis (PCA)
  • Entropy and Minimum Description Length (MDL)
  • Practical application of probability and statistics theories to real-world data

Prerequisites

  • Completion of the previous course in the MicroMasters program: DSE200x (Python for Data Science)
  • Undergraduate-level education in:
    • Multivariate calculus
    • Linear algebra

Course Content

  • Foundations of probability and statistics
  • Random variables and their properties
  • Dependence and correlation in data
  • Regression analysis techniques
  • Principal Component Analysis (PCA)
  • Entropy and Minimum Description Length (MDL)
  • Practical data analysis using Jupyter notebooks
  • Reasoning about uncertainty in noisy datasets
  • Application of statistical concepts to real-world data science problems

Who This Course Is For

  • Aspiring data scientists looking to strengthen their mathematical foundation
  • Professionals in data-related fields seeking to enhance their statistical knowledge
  • Students pursuing advanced studies in data science, machine learning, or artificial intelligence
  • Anyone interested in understanding the mathematical underpinnings of modern data analysis techniques

Real-World Applications

The skills acquired in this course are directly applicable to various real-world scenarios:

  • Data Analysis: Analyze complex datasets, extract meaningful insights, and make data-driven decisions in business, research, or other professional contexts.
  • Machine Learning: Understand and implement advanced machine learning algorithms more effectively.
  • Research: Critically evaluate research findings and conduct statistically sound studies.
  • Risk Assessment: Apply reasoning about uncertainty for risk analysis and management in finance or insurance.
  • Product Development: Improve product features, user experience, and performance based on data-driven insights in tech companies.
  • Healthcare: Analyze patient data, clinical trials, and epidemiological studies in medical research and healthcare management.
  • Marketing: Apply understanding of correlation and regression to customer behavior analysis and predictive modeling for marketing strategies.

By mastering the concepts taught in this course, learners will be well-equipped to tackle real-world data science challenges across various industries, making them valuable assets in the increasingly data-driven job market.