Graduate Students Seminar

Speaker 1: Reetam Majumder

Title

Variational Bayes Parameter Estimation in Hidden Markov Models for Daily Precipitation Data

Abstract

Stochastic precipitation generators (SPGs) are statistical models which generate synthetic data that can simulate dry and wet rainfall stretches for long durations. Generated precipitation time series data are used in climate projections, impact assessment of extreme weather events, and water resource and agricultural management. We constructed SPGs for daily precipitation data that is specified as a semi-continuous distribution with a point mass at zero for no precipitation and a mixture of Exponential or Gamma distributions for positive precipitation. Our generators are obtained as hidden Markov models (HMMs) where the underlying climate conditions form the states.

Maximum likelihood estimation of an HMM's parameters has historically relied on the Baum-Welch algorithm, which is a modification of the Expectation Maximization algorithm. We implement variational Bayes (VB) as an alternative estimation procedure for HMMs with semi-continuous emissions. While this HMM can reproduce key statistics of daily precipitation at individual locations, the lack of an explicit correlation parameter leads to very low spatial correlations in synthetic data.

Speaker 2: Harrison Lewis

Title

(Some of) The Mathematics of Crypto and NFT

Abstract

Cryptocurrencies, NFTs, and Blockchain technology are quickly growing to become massive emerging technologies that proliferate through every aspect of technological advancement. We discuss in-depth the underlying mathematics and cryptography that allow for these systems to function and briefly cover their advanced applications outside of financial speculation.