This repository contains companion tutorials for the textbook Statistical Machine Learning for Astronomy by Yuan-Sen Ting.

These tutorials provide hands-on, practical implementations of the concepts covered in the textbook. Each tutorial is designed as a standalone Jupyter notebook that explores key statistical and machine learning concepts through real astronomical applications.

We are currently in the process of cleaning up and standardizing all tutorials. The tutorials listed below have been fully revised and are ready for use. Additional tutorials will be added as they are completed.

• File: tutorial_chapter_2a.ipynb
• Topics: Probability distributions, Poisson processes, maximum likelihood estimation, spatial statistics
• Application: Detecting stellar clusters through statistical analysis of spatial point patterns

• File: tutorial_chapter_2b.ipynb
• Topics: Bayesian inference, likelihood functions, posterior distributions, marginalization over nuisance parameters, grid-based inference, uncertainty propagation
• Application: Inferring binary star eccentricities from single-epoch velocity-position angle measurements

• File: tutorial_chapter_3.ipynb
• Topics: Statistical moments, correlation functions, bootstrap methods, two-point statistics
• Application: Detecting the Baryon Acoustic Oscillation signal in simulated cosmological data

• File: tutorial_chapter_4a.ipynb
• Topics: Maximum likelihood estimation for linear regression, regularization (L2/Ridge regression), feature engineering with basis functions, model evaluation with train/test splits
• Application: Predicting stellar properties from APOGEE infrared spectra

• File: tutorial_chapter_4b.ipynb
• Topics: Calibration as regression, weighted least squares with heteroscedastic uncertainties, bootstrap uncertainty analysis, sparse design matrices
• Application: Calibrating radial velocity measurements from telescope networks using standard stars to correct for systematic instrumental and atmospheric effects

• File: tutorial_chapter_5.ipynb
• Topics: Bayesian linear regression, heteroscedastic noise modeling, conjugate priors, posterior distributions, predictive uncertainty quantification, model calibration, uncertainty decomposition
• Application: Predicting stellar temperatures from APOGEE spectra with properly calibrated uncertainties, demonstrating how Bayesian methods provide principled uncertainty quantification beyond point estimates

• File: tutorial_chapter_6.ipynb
• Topics: Attenuation bias (regression dilution), Deming regression, measurement uncertainties in both variables, heteroscedastic error modeling, latent variable inference, forward vs inverse regression
• Application: Using Deming regression to properly account for velocity measurement uncertainties in the Tully-Fisher relation, enabling unbiased calibration of the mass-velocity scaling laws

• File: tutorial_chapter_7.ipynb
• Topics: Logistic regression, sigmoid transformation, gradient descent optimization, classification metrics, hyperparameter tuning
• Application: Distinguishing Red Clump from Red Giant Branch stars using stellar parameters from APOGEE

• File: tutorial_chapter_8.ipynb
• Topics: Softmax regression, multi-class logistic regression, cross-entropy loss, feature extraction from images, confusion matrices, classification metrics
• Application: Classifying strong gravitational lensing features in James Webb Space Telescope images using pre-trained vision models and multi-class logistic regression

• File: tutorial_chapter_9.ipynb
• Topics: Bayesian inference for classification, Laplace approximation, predictive distributions, uncertainty quantification, prior specification
• Application: Quantifying classification uncertainty for Red Clump vs Red Giant Branch stars with parameter uncertainty propagation

• File: tutorial_chapter_10.ipynb
• Topics: Principal Component Analysis, Singular Value Decomposition, eigendecomposition, dimensionality reduction, variance analysis, image reconstruction
• Application: Analyzing galaxy morphology from Hyper Suprime-Cam images to identify fundamental patterns of variation and achieve efficient data compression

• File: tutorial_chapter_11a.ipynb
• Topics: K-means clustering, K-means++ initialization, Gaussian Mixture Models, Expectation-Maximization algorithm, model selection with AIC/BIC
• Application: Identifying stellar populations in the Sculptor dwarf galaxy through chemical abundance clustering to reveal episodic star formation history

• File: tutorial_chapter_11b.ipynb
• Topics: Principal Component Analysis for extreme dimensionality reduction, physical interpretation of principal components, Gaussian Mixture Models in reduced parameter spaces, generative modeling for synthetic spectra, likelihood-based outlier detection
• Application: Analyzing quasar spectra from simulated datasets and identifying unusual objects through probabilistic modeling

• File: tutorial_chapter_12.ipynb
• Topics: Inverse transform sampling, rejection sampling, importance sampling, Monte Carlo integration, effective sample size
• Application: Generating realistic stellar populations using the Kroupa Initial Mass Function and estimating population properties

• File: tutorial_chapter_13.ipynb
• Topics: Metropolis-Hastings algorithm, Gibbs sampling, convergence diagnostics (Geweke and Gelman-Rubin tests), autocorrelation analysis, effective sample size, proposal tuning, burn-in and thinning

• File: tutorial_chapter_14a.ipynb
• Topics: Gaussian Process regression, kernel functions, marginal likelihood optimization, hyperparameter learning, Cholesky decomposition, predictive uncertainty quantification
• Application: Analyzing Kepler stellar light curves to extract oscillation timescales through GP regression, revealing the relationship between stellar surface gravity and asteroseismic properties

• File: tutorial_chapter_14b.ipynb
• Topics: Gaussian Process Classification, latent variable models, Laplace approximation, fixed-point iteration, kernel hyperparameter selection
• Application: Star-galaxy separation using Gaia photometric colors, demonstrating how GP classification learns flexible nonlinear decision boundaries

• File: tutorial_chapter_15a.ipynb
• Topics: Backpropagation implementation from scratch, automatic differentiation, computational graphs, PyTorch tensors and autograd, optimizer comparison (SGD vs Adam), gradient flow visualization

• File: tutorial_chapter_15b.ipynb
• Topics: Autoencoder architecture, encoder-decoder networks, latent representations, latent space visualization, interpolation in latent space, anomaly detection through reconstruction error
• Application: Analyzing galaxy morphology from Hyper Suprime-Cam images through nonlinear dimension reduction, demonstrating how autoencoders extend beyond PCA's linear constraints to capture complex morphological relationships

• File: tutorial_chapter_15c.ipynb
• Topics: Mixture Density Networks, conditional density estimation, probabilistic regression with neural networks, Gaussian mixture outputs, maximum likelihood training, multimodal predictions, uncertainty quantification
• Application: Modeling stellar lithium abundance in open clusters as a function of effective temperature and age, demonstrating how MDNs capture both systematic trends and intrinsic astrophysical scatter that deterministic models miss

• File: tutorial_chapter_15d.ipynb
• Topics: Normalizing flows, RealNVP architecture, invertible neural networks, change of variables formula, Jacobian computation, coupling layers, likelihood-free inference, generative modeling
• Application: Modeling the 13-dimensional chemical abundance distribution of stars from APOGEE survey data, demonstrating how normalizing flows learn complex multimodal distributions without parametric assumptions and enable both density estimation and sample generation

To run these tutorials, you'll need:

• Python 3.7 or higher
• NumPy
• Matplotlib
• SciPy
• Jupyter Notebook or JupyterLab

Each tutorial is self-contained and includes:

• Theoretical background connecting to the textbook chapters
• Step-by-step code implementations
• Visualizations and interpretations

The tutorials are designed to be worked through sequentially within each notebook.

If you find these resources useful in your research or teaching, please cite the textbook or this tutorial repository.

@article{ting2025statistical,
  title={Statistical Machine Learning for Astronomy},
  author={Ting, Yuan-Sen},
  journal={arXiv preprint arXiv:2506.12230},
  year={2025}
}

@software{ting2025statisticaltutorial,
  author       = {Ting, Yuan-Sen},
  title        = {{tingyuansen/statml: Statistical Machine Learning 
                 for Astronomy - Tutorials (v1.0)}},
  month        = jul,
  year         = 2025,
  publisher    = {Zenodo},
  version      = {v1.0},
  doi          = {10.5281/zenodo.16495692},
  url          = {https://doi.org/10.5281/zenodo.16495692}
}

© 2025 Yuan-Sen Ting. All rights reserved.

These tutorials may be redistributed by sharing the original GitHub repository link for educational purposes. Any other reproduction or adaptation requires explicit permission from the author.