RBI2023

Materials for the 2023 Lecture Series: "Bayesian statistics, Data Mining and Machine Learning”, at the Ruđer Bošković Institute, Zagreb, Croatia.

To clone: git clone [email protected]:ivezic/RBI2023.git

Lectures are available from subdirectory notebooks: https://github.com/ivezic/RBI2023/tree/main/notebooks

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Lecture 1, May 4, 2023: "Overview of the course and introduction to statistics"

• Motivation, Goals and Roadmap
• IPython (jupyter) notebooks
• Basics about statistics
• Distributions and Random samples
• Robust statistics

Zoom recording for Lecture 1

Lecture 2, May 8, 2023: "Introduction to the Maximum Likelihood Estimation method"

• Introduction: what likelihood is and what it is good for?
• Simple examples of MLE: one-dimensional Gaussian
• MLE in action: fitting a parametrized model with heteroscedastic gaussian errors on y axis
• Goodness of fit
• Cost functions and penalized likelihood
• Non-gaussian likelihood: binomial distribution (coin flip problem)
• Conceptual difficulties with the MLE (example: "waiting for a bus" problem)
• What if we cannot write down the likelihood function?

Zoom recording for Lecture 2

Lecture 3, May 11, 2023: "Introduction to Bayesian statistics and inference"

• Bayes Rule extended to Bayesian Inference
• The role of priors in Bayesian Inference
• A simple parameter estimation example
• Nuisance parameters and marginalization

Zoom recording for Lecture 3

Lecture 4, May 15, 2023: "Applications of Bayesian statistics and inference"

• Simple parameter estimation examples
• Bayesian model selection
• Simple model selection examples
• For overachievers: ABC and Hierarchical Bayes

Zoom recording for Lecture 4

Lecture 5, May 22, 2023: "Introduction to Markov Chain Monte Carlo"

• Introduction to MCMC
• Non-linear Regression with MCMC

Zoom recording for Lecture 5

Lecture 6, June 1, 2023: "Bayesian model selection with MCMC"

• Model selection example: finding bursts in time series
• Bayesian Blocks Algorithm

Zoom recording for Lecture 6

Lecture 7, February 5, 2024: "Density Estimation"

• Searching for Structure in 1-D Point Data
• Gaussian Mixture Models
• Extreme Deconvolution

Zoom recording for Lecture 7

Lecture 8, February 8, 2024: "Clustering (Unsupervised Classification)"

• Introduction to Clustering
• K-means clustering algorithm
• Clustering with Gaussian Mixture models (GMM)
• Hierarchical clustering algorithm

Zoom recording for Lecture 8

Lecture 9, February 12, 2024: "Density Estimation"

• Introduction to Supervised Classification
• An example of a discriminative classifier: Support Vector Machine classifier
• An example of a generative classifier: star/galaxy separation using Gaussian Naive Bayes classifier
• Comparison of many methods using ROC curves

Zoom recording for Lecture 9

Lecture 10, February 15, 2024: "Dimensionality Reduction"

• The curse of dimensionality
• Principal Component Analysis
• Comparing PCA, NMF and ICA

Zoom recording for Lecture 10

Lecture 11, February 19, 2024: "Introduction to Artificial Neural Networks"

Zoom recording for Lecture 11

Lecture 12, February 22, 2024: "Image Classification with Deep Learning"

Zoom recording for Lecture 12