"Three open-discussions on Bayesian inferences via Monte Carlo sampling of solutions: from simple tools to complex algorithms”, 3 days course with Dr Nicola Piana Agostinetti (DIAS)
15th -17th May 2017
3 days course
Dr. Nicola Piana Agostinetti from DIAS will hold a short 3-days course on Monte Carlo methods at DIAS Geophysics, 5 Merrion Square, Dublin 2.
Title: ”Three open-discussions on Bayesian inferences via Monte Carlo sampling of solutions: from simple tools to complex algorithms”
Abstract: The term “Bayesian inferences” usually describes all those probabiistic data-analysis techniques which make use of the Bayes’ theorem at some stage, for linking observations to parameters. Bayes’ theorem defines the new knowledge on an investigated parameter (so called “posterior probability distribution or PPD”) combining prior information to observations. Due to its straightforward formulation, Bayes’ theorem is widely used in geophysics, but, despite of its simplicity, it needs to be applied with great care, for obtaining meaningful results (i.e. realistic inferences on the investigated parameters). In particular, assumptions both on prior knowledge and on the measure of the likelihood of the model predictions to the observed data (the so called “Likelihood function”) could introduce strong bias in the final outputs. Inferences on an investigated parameters can be done using analytical representations of the PPD, if such formulations are available. Alternatively, numerical simulations of the PPD can be used. In particular Monte Carlo sampling of the model space is a powerful tools related to Bayesian inferences, as it allows to numerically reconstruct the PPD through importance sampling of the model-space.
Dr. Nicola Piana Agostinetti will present a suite of Monte Carlo algorithms applied to geophysical inverse problems, from simple alternatives tools for data analysis (e.g. Single Values Decomposition and Cross-correlation) to more complex algorithms based on trans-dimensional sampling. Example from the geophysical "world" will be used to illustrate how wrong assumptions can bias probabilistic inferences on the investigated parameters. The theoretical formulations and geophysical results will be presented during 1-hour morning seminars. Afternoon sessions will be devoted to low-level analysis of the codes which translate theoretical concepts into results. Personal laptop are requested for the afternoon sessions, for running practical examples.
Monday 15/5: Bayesian inferences as an “alternative” tool for data-analysis
Tuesday 16/5: Bayesian inferences in the model-space: trans dimensional MC sampling
Wednesday 17/5: Bayesian inferences in the data-space: hierarchical Bayes and beyond
Morning seminars at 11.30
Afternoon session at 14.30
Venue: DIAS Geophysics library, 5 Merrion square, Dublin 2.
Registration: Due to logistic reasons DIAS can guarantee limited (20) seating to the afternoon sessions. If you want to attend, please send an email to DIAS Geophysics secretary (email@example.com)
Nicola Piana Agostinetti, PhD
Geophysics Section, School of Cosmic Physics
Dublin Institute for Advanced studies
5 Merrion Square, Dublin 2, Ireland
Phone +353 86 3243287
Official webpage: https://www.dias.ie/2012/05/16/dr-nicola-piana-agostinetti/