SCHEDULE
Bayesian Predictive Modeling: Towards Martingale Posterior Distributions for Dynamical Systems
by Clark Ikezu
Bayesian inference is a principled way to quantify uncertainty over parameters. The predominant approach involves specifying a prior and a likelihood in order to compute a posterior distribution. Prediction is then achieved through computing the posterior predictive distribution. However, prediction can also be viewed as the primary task of Bayesian inference, in which specifying a predictive model comes first, and inferring the posterior distribution follows next. This approach is appealing in several ways, including that one reasons over quantities we can observe, as opposed to parameters that cannot be observed. In this talk I will introduce this Bayesian "predictive approach", and discuss a particular method called the martingale posterior distribution implemented by the predictive resampling algorithm. Next I will present preliminary work in which I show how the predictive resampling algorithm can be useful for posterior inference in the setting of non-i.i.d observations generated by a dynamical system.
[Canceled] Modeling group interactions of heterogenous voters in the US Senate
by Gavin Rees
Statistical models of interacting systems on discrete spaces can be effective causal models - for example, of yes/no voting - but their discrete sample space can turn normalization into a combinatorially complex endeavour: for example, normalizing the pairwise Ising model on the N dimensional binary (hyper)cube is NP-Complete. This lack of normalization can limit their utility and prevent rigorous comparisons to other models. Pairwise interacting models also suffer from quadratic parameter growth as the dimensionality of the sample space grows, unless interactions are structured in some way: for example, homogeneous interactions between groups (a block structured model). Group-structured pairwise interacting models can be effective causal models as well, and are easily normalizable, but aren’t able to capture individual heterogeneity that we suspect exists in some systems, e.g., political systems where every representative/voter has their own ideology (that there is individual heterogeneity is part of our prior). We describe results in exactly normalizing group-interacting pairwise Ising models with heterogeneous individual (linear and local) preferences within polynomial time complexity N^k, where N is the number of individuals and k is the number of groups. We discuss generalizations of this approach to effective low rank approximations of interacting systems, as well as potential applications to social systems, namely the US Senate.
Holiday Party
End of the Fall semester - Hooray! Join us for a holiday celebration to wrap up another successful semester of student research presentations.