Probability & Statistics - Introduction to Time Series
Data often depends on when it happened. We explore temporal structure, autocorrelation (correlation with past values), and trends, moving beyond independent samples to model history and forecast future values.
Probability & Statistics - Bayesian Inference
A shift in philosophy. Instead of fixed parameters, we treat them as random variables. We combine prior beliefs with observed data (likelihood) to calculate a "Posterior" probability, mathematically updating our view of the world.
Probability & Statistics - Non-Parametric Tests
When data isn't Normal or sample sizes are tiny, standard tests fail. We use methods based on ranks (like Mann-Whitney or Kruskal-Wallis) to draw valid conclusions without assuming a specific distribution shape (Normality).
Probability & Statistics - Chi-Square Goodness of Fit
Does our data match expectations? This test compares observed counts to theoretical expected counts (e.g., "is this die fair?"). A large discrepancy suggests the data does not follow the hypothesized distribution.
Probability & Statistics - Post-hoc Testing
ANOVA tells us "there is a difference," but not where. Post-hoc tests (like Tukey’s HSD) act as detectives after a significant ANOVA result, comparing specific pairs of groups while correcting for false positives to identify the exact outlier.
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