Home Page for Astrostatistics Course, Part III Mathematical Tripos
Lent Term Tuesday, Thursday & Saturday at 12 noon. CMS Meeting Room 5.
IMPORTANT: Starting Saturday, 27 Jan, we will meet in a bigger room, MR5, to better accomodate the attendance.
Example Sheet 1 and datasets uploaded!
Example class on Fri, 16 Feb at 2:30pm in MR5. HAVE FUN!
Office Hours: Fridays @ 1pm
Statistical Laboratory
CMS Pavilion D, Office 1.07
Recommended Texts:
(Both texts are freely available through the Cambridge Library website.)
F&B = Feigelson & Babu. "Modern Statistical Methods for Astronomy"
Ivezić = Ivezić, Connolly, VanderPlas & Gray. "Statistics, Data Mining, and Machine Learning in Astronomy"
Week 1
Lecture 01 (Thu 18 Jan) has been uploaded!
- Introduction to Astrostatistics
- Introduction to Case Studies
Lecture 02 (Sat 20 Jan) has been uploaded!
- Introduction to Astronomical Data Types
- Overview of Case Study on Modelling Stellar Spectra with Gaussian Processes
- Reference: Czekala et al. 2017, The Astrophysical Journal, 840 49
Lecture 03 (Tue 23 Jan) covered material on probability from
- Feigelson & Babu (F & B): Chapter 2, or
- Ivezić: Chapter 3 (through Ch 3.1.3)
Week 2
Lecture 04 (Thu 25 Jan) slides uploaded. Covered:
- Limit theorems and started statistical inference (up to maximum likelihood)
- F & B: finished Ch 2, start Ch 3, or
- Ivezić: finished Ch 3, start Ch 4
Lecture 05 (Sat 27 Jan) slides uploaded. Covered:
- Frequentist properties of estimators (unbiasedness, MSE, consistency, asymptotics)
- Maximum likelihood estimators, frequentist properties, Fisher Matrix and Cramer-Rao bound
- F & B: Chapter 3, or
- Ivezić: Chapter 4
Lecture 06 (Tue 30 Jan) slides uploaded. Covered:
- Multi-parameter maximum likelihood, Fisher Matrix, and Cramer-Rao bound
- Example: Fitting a Gaussian to data
- Example: Fitting a Gaussian to data with measurement errors (Normal-Normal model)
Week 3
Lecture 07 (Thu 01 Feb) slides uploaded. Covered:
- Demo about fitting Normal-Normal latent variable model with MLE
- Rant about minimum chi^2 methods
Lecture 08 (Sat 03 Feb) slides uploaded. Covered:
- Statistical Modeling wisdom
- Ordinary Least Squares (OLS) and Generalised Least Squares (GLS) solutions to Linear Regression
- Introduction to Latent Variable modeling to account for (y,x)-measurement errors and intrinsic dispersion (TBC)
Lecture 09 (Tue 06 Feb) slides uploaded. Covered:
- Review Multivariate Normal Distribution. See also Ivezić, Chapter 3
- Probabilistic Generative / Forward Modeling of Data
- example: Linear Regression with (y,x) measurement errors and intrinsic dispersion
- reference: Kelly et al. 2007, The Astrophysical Journal, 665, 1489
Week 4
Lecture 10 (Thu 08 Feb) slides uploaded. Also Covered:
- Frequentist vs. Bayesian probability
- confidence vs. credible intervals
Lecture 11 (Sat 10 Feb) slides uploaded. Also covered:
- Frequentist vs. Bayesian results for simple Gaussian
- Null hypothesis testing, p-values
- Likelihood principle, sufficient statistics, conjugate prior
- Bayesian inference of simple Gaussian data with conjugate prior (Gelman BDA Ch 2-3)
Lecture 12 (Tue 13 Feb)...
- Multi-parameter Bayesian analysis example (Gelman BDA, Sec 3.2-3.3),
Conjugate and "non-informative" prior - Posterior summaries & estimation
- Monte Carlo Sampling
- Importance Sampling
Week 5
Bayesian Computation and Sampling Algorithms
Lecture 13 (Thu 15 Feb). Covered:
- Kernel Density Estimation (F & B Ch 6, Ivezić, Sec 6.1.1)
- Monte Carlo error
- Importance Sampling
- Case Study: Bayesian Estimates of the Milky Way Galaxy Mass
- reference: Patel, Besla & Mandel. 2017, MNRAS, 468, 3428
MNRAS = Monthly Notices of the Royal Astronomical Society
Example Class (Fri 16 Feb):
- Solved Example Sheet 1, problems 1 & 2
- Bootstrap Sampling
Lecture 14 (Sat 17 Feb). Covered:
- Kernel Density Estimation (F & B Ch 6, Ivezić, Sec 6.1.1)
- Review Bayesian Estimates of the Milky Way Galaxy Mass Case Study in more detail
- Code Demonstration using Importance Sampling
- Highest Posterior Density credible intervals
Week 6
Probabilistic Graphical Models & Hierarchical Bayes
- Case Study: Hierachical Bayesian Models for Type Ia Supernova Inference
- reference: Mandel et al. 2017, The Astrophysical Journal, 842, 93.
Week 7
Gaussian Processes in Astrophysics
- Case Study:
Disentangling Time Series Spectra with Gaussian Processes: Applications to Radial Velocity Analysis - reference: Czekala et al. 2017, The Astrophysical Journal, 840, 49.
Week 8
Approximate Bayesian Computation
Under Construction...