Probability And Statistics For Data Science Training - United States

Probability and Statistics for Data Science​ Training Course Outline

The following modules will be covered during this Probability and Statistics for Data Science Course:

Basic Probability Theory

• Probability Spaces
• Conditional Probability
• Independence

Random Variables

• Definition
• Discrete Random Variables 
• Continuous Random Variables
• Conditioning on an Event
• Functions of Random Variables
• Generating Random Variables
• Proofs

Multivariate Random Variables

• Discrete Random Variables
• Continuous Random Variables
• Joint distributions of Discrete and Continuous Variables
• Independence
• Functions of Several Random Variables
• Creating Multivariate Random Variables
• Rejection Sampling

Expectation

• Expectation Operator
• Mean and Variance
• Covariance
• Conditional Expectation
• Proofs

Random Processes

• Definition
• Mean and Autocovariance Functions
• Independent Identically-Distributed Sequences Gaussian Process
• Poisson Process
• Random Walk

The convergence of Random Processes

• Types of Convergence Law of Large Numbers
• Central Limit Theorem
• Monte Carlo Simulation

Markov Chains

• Time-Homogeneous Discrete-Time Markov Chains
• Recurrence
• Periodicity
• Convergence
• Markov-Chain Monte Carlo

Descriptive Statistics

• Histogram
• Sample Mean and Variance
• Order Statistics
• Sample Covariance
• Sample Covariance Matrix

Frequentist Statistics

• Independent Identically-Distributed Sampling
• Mean Square Error
• Consistency
• Confidence Intervals
• Nonparametric Model Estimation
• Parametric Model Estimation
• Proofs

Bayesian Statistics

• Bayesian Parametric Models
• Conjugate Prior
• Bayesian Estimators

Hypothesis Testing

• The Hypothesis-Testing Framework
• Parametric Testing
• Nonparametric Testing: The Permutation Test
• Multiple Testing

Linear Regression

• Linear Models
• Least-Squares Estimation
• Overfitting