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1st Italian Astrostatistics School

The primary goal of the school is to train astronomers to the use of modern statistical techniques, specifically parameter estimation and model selection. The INTENSIVE course is characterized by extended laboratory sessions (i.e. individual work at the computer), taking about two third of the school attendance. The program includes: probability axioms, probability models, regression, Bayesian model comparison, comparison with frequentist hypothesis testing and p-values, other advanced topics. Instructors are Roberto Trotta and Stefano Andrion.
When 12 June 2017 07:25 AM to
16 June 2017 07:25 AM
Where Milan IT
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Program

1) Probability axioms. Computation of the posterior: analytical vs numerical sampling. Upper limits. Initial discussion on the role of the prior. Importance of checking numerical convergence. A glimpse on sensitivity analysis.
2) Single parameters models. Combining information coming from multiple data. The prior (and the Malmquist-like effect). Prior sensitivity. Two-parameters models. Joint probability contours. Comparison of the performances of state-of-the-art methods to measure a dispersion.
3) Introduction to regression. Comparison of regression fitters. Regressions (of increasing difficulty): non-linear regression with non-gaussian errors of different sizes (but no error on predictor and no intrinsic scatter). Allowing systematics (intrinsic scatter). Allowing errors on x. Regressions with two (or more) predictors. A glimpse on other important issues such as mixture of regressions, non-random data collection, model checking.
4) Introduction to Bayesian model comparison. Automatic implementation of Occam's razor. Model likelihood as predictive data probability. The three three levels of inference.
5) Comparison with Frequentist hypothesis testing and p-values. The Bayesian evidence: Meaning and interpretation. Asymptotic behaviour. Prior-free evidence bounds. Sensitivity analysis. Dependency on the choice of prior.
6) Computation of the evidence: Savage-Dickey Density ratio (SDDR); Laplace approximation; nested sampling and MultiNest implementation. Model complexity and Kullback-Leibler divergence. Bayesian Model Averaging and applications in cosmology.

Instructors

Stefano Andreon and Roberto Trotta
The lecturers in the last few years have taught at over 30 advanced courses and postgraduate schools on topics of Bayesian inference. They are respected authors of textbooks on the school subject, Astrostatistics: Bayesian Methods in Cosmology Astrostatistical Challenges for the New AstronomyBayesian methods for the physical sciences. Learning from examples in astronomy and physics.

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