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Statistics

In this section I will collect all my posts about statistics.

Sometimes dataviz is not sufficient to understand your data. In this case there’s only one way you can rigorously approach your problem: statistics.
This is a huge field, and it’s quite easy to get lost within it. In the following you will find some material which helped me to clarify my ideas and to face data-related problems.


Have fun!

Stippe

Post list

Introduction
  1. An overview to statistics: What well we talk about
  2. Introduction to Bayesian inference: A little bit more about Bayesian inference
  3. How does MCMC works: Getting an idea of what's happening behind the scenes
  4. Some notation about probability: Notation and conventions
Simple models
  1. Section introduction: Understanding the building blocks
  2. The Beta-Binomial model: Dealing with binary outcomes
  3. The Poisson model: How to describe count data
  4. The Negative Binomial model: An evolution of the Poisson model
  5. Bonus: counting animals in a park: The hypergeometric distribution and the capture-mark-recapture method
  6. The Gaussian model: Handling real-valued data
  7. Multidimensional distributions: Dealing with more than two categories
  8. Mixture models: When your population is made by subpopulations
Bayesian workflow
  1. Introduction to the Bayesian workflow: How to make bayesian inference in practice
  2. Trace inspection: Finding issues in MCMC convergence
  3. Predictive checks: Verifying the predictions of your model
  4. Re-parametrizing your model: Building equivalent models with less numerical issues
  5. Model comparison: How to choose between models
  6. Model comparison, cont.: Cross validation in Bayesian statistics
Regression
  1. Introduction to the linear regression: Including dependence on external variables
  2. Linear regression with binary input: Extending regression to discrete variables
  3. Multi-linear regression: Including many covariates
  4. Robust linear regression: Reducing sensitivity to large deviations
  5. Logistic regression: How to perform regression on binary data
  6. Poisson regression: Regression on count data
Hierarchical models
  1. Hierarchical models: How to implement hierarchies
  2. Hierarchical models and meta-analysis: How hierarchical models can be used to analyze scientific literature
  3. Random models and mixed models: Making inference on subgroups
  4. Leveraging mixed-effect models: When and how to use mixed-effect models
  5. Mixed effects models with more than two levels: When hierarchies become complex
Experiments
  1. The problem solving workflow: A broader view of the data science workflow
  2. Things that could go wrong: If something can go wrong, it probably will
  3. Data collection: Choosing how to collect data
  4. Random sampling: Methods for selecting units from a population
  5. Stratification: Grouping units in a useful way
  6. Design of experiments: An application to the DOE principles
  7. Completely randomized design: When only one factor is relevant
  8. Full factorial design: Handling multiple factors of interest together
  9. Latin square design: Blocking two factors
  10. Crossover design: How to quantify the treatment order effect
  11. Split plot design: Handling hard-to-change factors
  12. Repeated measures: When time is one of the factors
  13. Nested factor: Saving yourself from mis-labelling
Causal inference
  1. Causal inference: When association implies causation
  2. Causal inference and Bayesian networks: When does association imply causation?
  3. Validity: How to weight evidence from a study
  4. Randomized controlled trials: When association implies causation
  5. Instrumental variable regression: Making causal inference without randomization
  6. Difference in difference: Causal inference from 1850
  7. Regression discontinuity design: Introducing an arbitrary threshold to infer causality
Advanced models
  1. Introduction to survival analysis: Estimating waiting times
  2. Application of survival analysis 1: Survival analysis with continuous time
  3. Application of survival analysis with discrete times: Survival analysis with discrete time
  4. Accelerated Failure Time models: More advanced models from survival analysis
  5. Frailty models and cure rate models: Hierarchical and mixture models in survival analysis
  6. Introduction to Extreme Values theory: Describing rare events
  7. Quantile regression: Describing less common events
Time series
  1. Time series: Taking into account time dependence
  2. Structural time series: Adding other kinds of temporal dependencies
  3. Stochastic volatility models: How to quantify volatility
Non-parametric models
  1. Nonparametric models: When your focus in on flexibility
  2. Gaussian processes: How to make the normal distribution infinite dimensional
  3. Gaussian processes regression: Using GPs for flexible regression
  4. Splines: Wisely using piecewise functions
  5. Bayesian Additive Regression Trees: Flexible interpolation with regression trees
  6. Dirichlet Process Mixture Models: Mixture models with variable number of components
Other random thoughts
  1. Differential equations: When your mathematical model cannot be explicitly solved
  2. Application of the Lotka-Volterra model: Testing the predictive power of a scientific model
  3. MRP: The one who guessed US election results
  4. Prior sensitivity analysis: How to quantify the relevance of the priors
  5. Horseshoe priors: Dealing with multi-collinearity
  6. Directional statistics: Inference for angular variables
  7. Periodic splines: Using splines to account for periodic patterns