Bayesian Probability
Understand the Bayesian approach to probability, contrasting it with the frequentist perspective. Learn how Bayesian reasoning applies to real-world data science problems.
Bayes' Theorem
Dive deep into Bayes’ Theorem with practical examples and applications. Learn how to update probabilities based on new evidence.
Conjugate Priors and Posterior Distributions
Study the concept of conjugate priors, their importance in simplifying Bayesian computations, and how to derive posterior distributions.
Bayesian Estimation
Explore estimation techniques within the Bayesian framework, including point estimates and posterior predictive distributions. Compare Bayesian estimation with MLE.
Maximum Likelihood Estimation (MLE)
Learn the principles of MLE, its properties, and how to apply it to estimate parameters in various statistical models.
Likelihood Ratio Tests
Explore the Likelihood Ratio Test (LRT), its mathematical foundation, applications, and how it is used to compare competing models in statistics and machine learning.
Multivariate Distributions
Explore joint, marginal, and conditional distributions, covariance and correlation in a multivariate context, and the properties and applications of the multivariate normal distribution.
Bayesian Model Selection
Explore Bayesian Model Selection, including methods like Bayes factors and the Bayesian Information Criterion (BIC). Understand how to compare models in a Bayesian framework.
T-tests, Z-tests, and ANOVA
Learn the fundamentals of T-tests, Z-tests, and ANOVA. Extend your knowledge to more complex scenarios, including assumptions, extensions, and best practices.
Markov Chain Monte Carlo (MCMC) Methods
Understand Markov Chain Monte Carlo (MCMC) methods, including the Metropolis-Hastings algorithm and Gibbs sampling. Learn how these techniques are used in Bayesian inference and machine learning.
Non-parametric Tests
Understand non-parametric testing methods such as the Mann-Whitney U Test, Wilcoxon Signed-Rank Test, and Kruskal-Wallis H Test. Learn when and how to apply these tests when parametric assumptions are not met.
Bootstrap Sampling
Learn the concept of bootstrap sampling, how to create bootstrap confidence intervals, and its applications in estimation and hypothesis testing.
Expectation-Maximization (EM) Algorithm
Understand the Expectation-Maximization (EM) Algorithm, its mathematical foundation, and how it is used to find maximum likelihood estimates in models with latent variables. Learn about its applications in clustering, missing data problems, and Gaussian Mixture Models.
Stratified Sampling
Explore stratified sampling methods, including the definition, benefits, stratification criteria, and comparisons with simple random sampling. Understand when and how to implement stratified sampling effectively.
Dimensionality Reduction Techniques
Explore various dimensionality reduction techniques, including Principal Component Analysis (PCA), t-SNE, and Linear Discriminant Analysis (LDA). Understand their applications in data preprocessing, visualization, and machine learning.
Survival Analysis
Explore the fundamentals of Survival Analysis, including key concepts like survival functions, hazard functions, and popular models like Kaplan-Meier, Cox Proportional Hazards, and Weibull models. Learn their applications in various fields such as medicine, finance, and customer analytics.
Introduction to Stochastic Processes
Explore the fundamentals of stochastic processes, including definitions, classifications, key properties, and applications in fields like finance, physics, biology, and data science.
Autoregressive (AR) and Moving Average (MA) Models
Explore the foundational concepts of Autoregressive (AR) and Moving Average (MA) models, including their mathematical formulations, properties, and applications in time series analysis.
Introduction to ARIMA Models
Learn about ARIMA models, a powerful tool in time series forecasting, including their components, mathematical foundation, and applications in modeling temporal data.
Mathematical Foundations of Exponential Smoothing
Explore the mathematical principles behind exponential smoothing, a powerful technique for time series forecasting, including simple, double, and triple exponential smoothing methods.
Spectral Analysis of Time Series
Delve into spectral analysis, a powerful technique for understanding the frequency domain characteristics of time series data, including the mathematical foundations, methods, and practical applications.