- Maria De Lorio, University College London, UK, Bayesian Variable Model Selection
- Jesus F. Lopez-Fidalgo, Universidad de Navarra, Bayesian approach to Optimal Experimental Design
A unified view of the topic is presented by putting experimental design in a decision theoretic framework. Experimental design is the only situation where it is meaningful within the Bayesian theory to average over the sample space. As the sample has not yet been observed the general principle of averaging over what is unknown applies. This framework justifies many optimality criteria and opens new possibilities. Various design criteria become part of a single coherent approach. Linear and nonlinear models will be considered as well as a particular application of an optimality criterion for discriminating between any two statistical models in the presence of prior information. If the rival models are not nested then, depending on which model is true, two different Kullback-Leibler distances may be defined. The Bayesian KL-optimality criterion is a convex combination of the expected values of these two possible Kullback-Leibler distances between the competing models. Concavity of the Bayesian KL-optimality criterion allows the use of the classical results of Optimal Design Theory. A standardized version of the proposed criterion is also given in order to take into account possible different magnitudes of the two Kullback-Leibler distances. Some illustrative examples will be provided.
- Steven L. Scott, Google, Comparing Consensus Monte Carlo Strategies for Distributed Bayesian Computation
Consensus Monte Carlo is an algorithm for conducting Monte Carlo based Bayesian inference on large data sets distributed across many worker machines in a data center. The algorithm operates by running a separate Monte Carlo algorithm on each worker machine, which only sees a portion of the full data set. The worker-level posterior samples are then combined to form a Monte Carlo approximation to the full posterior distribution based on the complete data set. We compare several methods of carrying out the combination, including a new method based on approximating worker-level simulations using a mixture of multivariate Gaussian distributions. We find that resampling and kernel density based methods break down after 10 or sometimes fewer dimensions, while the new mixture-based approach works well, but the necessary mixture models take too long to fit.
- Roseann White, Duke Clinical Research Institute, The past is prologue: the use of prior information and Bayesian methodologies in designing medical device regulatory approval
There have been many paper on the advantages and disadvantages of the Bayesian power prior in clinical trials. However, there have been several roadblocks to the acceptance of this methodology when planning medical device feasibility and approval clinical trials that are required regulatory approval in key geographies. Some of the challenges that MDIC has trying to address are the following:
- Clarifying for the clinical community does it mean to design a clinical trial where one can combine the prior information about the device with the current trial data to improve the precison in the outcome estimates or potentially reduce the sample as compared to a frequentist approach
- Clarifying what is expected by CDRH when putting together a protocol so that the review and approval process goes smoothly
- Developing a transparent process that allows one to pre-specify how the prior information will be weighted based on type I error, assuring that the bias that will be introduced by the prior is clinically acceptable and the probability of success of the trial given the assumed true outcome is acceptable (the loss function).
This talk will highlight some of efforts that are currently under way or have already been completed for bullets 1 and 2 but will mostly focus on role of the statistician and methods that the statistician will employ to address bullet 3 when designing a clinical trial using Bayesian analysis with an informative prior trial.
- Harry Yang, MedImmune, USA, Bayesian statistics in pharmaceutical Research and Development