High Dimensional Inference in the Universe

Speaker: Niall Jeffrey; Discussion Facilitator: Nour Fahmy

Motivation:
High-dimensional probability density estimation for inference suffers from the
“curse of dimensionality”. For many physical inference problems, the full posterior
distribution is unwieldy and seldom used in practice. Instead, we propose direct estimation of lower-dimensional marginal distributions, bypassing high-dimensional
density estimation or high-dimensional Markov chain Monte Carlo (MCMC) sampling. By evaluating the two-dimensional marginal posteriors we can unveil the
full-dimensional parameter covariance structure. We additionally propose constructing a simple hierarchy of fast neural regression models, called Moment
Networks, that compute increasing moments of any desired lower-dimensional
marginal posterior density; these reproduce exact results from analytic posteriors
and those obtained from Masked Autoregressive Flows. We demonstrate marginal
posterior density estimation using high-dimensional LIGO-like gravitational wave
time series and describe applications for problems of fundamental cosmology.

[EMDEEW]

Among the words I understood were 'the', good old 'a', and some adjectives.