With the technological advances of the past decade, all natural sciences are seeing an explosion in the availability of high-quality scientific data. Modeling these datasets with complicated underlying processes requires developing complex models with an increasingly larger number of unknown parameters that need to be inferred - the simulations of which are computationally expensive. In this talk, I will discuss how advances in scientific computing, automatic differentiation, and Bayesian inference techniques allow us to approach this high-dimensional inference.

In the first part of the talk, I will consider a challenging problem in cosmology- how to model the three-dimensional distribution of galaxies and use it to reconstruct the initial conditions of our Universe, enabling optimal cosmological analysis. With this example, I will first demonstrate the potential of the existing Bayesian inference techniques like Hamiltonian Monte Carlo and variational inference in tackling high dimensional inference.

Then I will also use this example to highlight two limitations of the existing algorithms- i) the failure of Hamiltonian Monte Carlo in robustly sampling multiscale distributions that arise in hierarchical models, and ii) the optimization challenges posed by variational inference. This will lead to the second part of the talk, where I will present new algorithms to overcome these limitations. I will develop a delayed rejection framework for Hamiltonian Monte Carlo to efficiently explore multiscale distributions, and show how score-matching approaches can lead to more stable, and faster variational inference. Together, these developments pave the way for doing robust Bayesian inference with complex models in natural and applied sciences

Pierce 301 or Zoom (password: 687666)