Lectures related to Importance Sampling: Change of Variable

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Importance Sampling: Change and Distribution

Explores importance sampling in Monte Carlo calculations, emphasizing variable changes and distribution selection for efficiency.

Basics of Risk Analysis and Management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Spatial Dependence: Concepts and Analysis

Explores spatial dependence, spatial autocorrelation, and bias in statistical analysis due to spatial relationships.

Continuous Random Variables

Covers continuous random variables, probability density functions, and distributions, with practical examples.

Monte Carlo Integration: Uncorrelated Sampling

Explores Monte Carlo integration through uncorrelated sampling and its error scaling with the number of points used.

Probabilities and Statistics: Key Theorems and Applications

Discusses key statistical concepts, including sampling dangers, inequalities, and the Central Limit Theorem, with practical examples and applications.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Multivariate Statistics: Normal Distribution

Introduces multivariate statistics, covering normal distribution properties and characteristic functions.

Families of Distributions: PDFs and CDFs

Explores PDFs and CDFs for discrete and continuous random variables, including Gaussian, uniform, and exponential distributions.

Probability Theory: Midterm Solutions

Covers the solutions to the midterm exam of a Probability Theory course, including calculations of probabilities and expectations.

Normal Distribution: Properties and Calculations

Covers the normal distribution, including its properties and calculations.

Probability and Statistics: Fundamental Theorems

Explores fundamental theorems in probability and statistics, joint probability laws, and marginal distributions.

Normal Distribution: Characteristics and Examples

Covers the characteristics and importance of the normal distribution, including examples and treatment scenarios.

Elements of Statistics: Estimation & Distributions

Covers fundamental statistics concepts, including estimation theory, distributions, and the law of large numbers, with practical examples.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Air Pollution Analysis

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Sampling Theory: Statistics for Mathematicians

Covers the theory of sampling, focusing on statistics for mathematicians.