Some class projects blend art and science by producing beautiful interactive visualizations.
Konstantin Kashin is a graduate student in the Government Department at Harvard University. His primary research interests include quantitative political methodology, with a focus on automated text analysis and causal inference. He is interested in applying these methods to the study of business-state relations, interest group politics, and the comparative political economy of welfare states.
This is a visualization project of the Metropolis MCMC illustrating the algorithm on the example of a two-dimensional target distribution - a Bivariate Normal. The visualization illustrates the trajectory that the bivariate sample takes in time, and the trace plots of the parameter draws. If the proposal distribution matches the target distribution, but has lower marginal variance, the sampler has nearly 100% acceptance rate. In many cases, however, the proposal distribution is suboptimal, the chain is not mixing well, and the acceptance rate is low.
Interactive visualization on the class website allows users to change the parameters and see how the visualization changes accordingly - make sure to play with it on the course website!