Welcome to a seminar on Bayesian Inference and Prior-Data Conflict
On the 15th of December Dr. Gero Walter from Technische Universiteit Eindhoven gave a seminar about the problem of prior-data conflict, that is, when the information from data is in conflict with prior assumptions (abstract is below). His talk was followed by a hands on session where the attendees will learned how to handle and mitigate prior-data conflict in practice. The half-day was be rounded off by a complimentary lunch. 10 persons attended the seminar.
10.00 – 11.00 Talk on prior-data conflict by Dr. Gero Walter
11.15 – 12.00 Hands on exercises
12.15 – 13.00 Complimentary Lunch
The event is organised by the Advanced Study Group on Calculating and Communicating Uncertainty and takes place at the Pufendorf institute (https://goo.gl/maps/xjruS9HLzvz) at Lund University and is open to all interested and is free to attend.
Some of the exercises were made with the R statistical language. R is free and can be downloaded here: https://www.r-project.org/ Gero will do some of the exercises using his R-package luck. The package can be installed by the following lines of code
install.packages(“TeachingDemos”)
install.packages(“http://download.r-forge.r-project.org/src/contrib/luck_0.9.tar.gz”, repos = NULL, type = “source”)
Gero has prepared a document explaining Generalized Bayesian Inference with sets of conjugate priors for dealing with prior-data conflict.
The solutions to the exercises are kindly provided.
Geros talk is found at talk-lund
Link to the WPMSIIP workshop 2016:
The web page of the Society for Imprecise probability
/Ullrika Sahlin on behalf of the Pufendorf Advanced Study Group on Calculating and Communicating Uncertainty 2015-2016
Seminar abstract
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In the Bayesian approach to statistical inference, (possibly subjective) knowledge on model parameters can be expressed by so-called prior distributions. A prior distribution is updated, via Bayes’ Rule, to the so-called posterior distribution, which combines prior information and information from data into a ‘complete picture’, thus expressing our state of knowledge about model parameters after having seen the data.
A problem that then can arise is called prior-data conflict: from the viewpoint of the prior, the observations seem very surprising, i.e., the information from data is in conflict with the prior assumptions. Unfortunately, models based on conjugate priors (which allow for straight-forward calculation of the posterior), are insensitive to prior-data conflict, in the sense that the spread of the posterior distribution does not increase in case of such a conflict. The posterior then conveys a false sense of certainty, by communicating that we can quantify uncertainty on model parameters quite precisely when in fact we cannot.
It is however possible to preserve tractability and have a meaningful reaction to prior-data conflict by using sets of conjugate priors for modelling prior information. This approach, which can be seen as imprecise probability method or robust Bayesian procedure, avoids the spurious over-precision of standard Bayesian methods and allows to adequately express vague or partial prior knowledge. With the precision of prior probability statements intuitively modelled through the magnitude of the set of priors, the posterior set appropriately reflects the prior precision, the amount of data, and prior-data conflict.
Warning! This seminar could make you think in a different way. 
Ullrika and Gero together with two new made friends at the last ESREL conference in Zurich.
In dark December we are happy to host Aki Vehtari from Aalto University, Finland, who will show us how to implement Bayesian methods using the Stan software.
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