Bayesian Nonparametrics

Nonparametric and semiparametric methods are used to allow for additional flexibility in probabilistic modeling. Unlike traditional Bayesian methods, which use parametric univariate and mulitvariate probability distributions to characterize stochastic quantities of interest, nonparametric Bayesian methods involve assigning probabilities to elements in the space of probability distributions itself. Some common nonparametric Bayesian methods involve Dirichlet processes and Polya trees, which provide probabilities for the spaces of discrete and continuous probability distributions respectively.

Bayesian Model Selection

George Box famously said, "All models are wrong, but some are useful." Model selection determines which among a collection of candidate models are most useful for a particular scientific task (e.g. hypothesis generation, prediction). Research on Bayesian model selection takes many forms, from the analysis of Bayesian model selection criteria to the careful use of informative prior distributions to learn more about posterior probabilities for various models.

Decision Theory

Decision theory is the one-player version of game theory. In a given situation, it relates the actions one can take to the unknown states of nature that will determine the consequences of taking that action. The discipline of decision theory attempts to choose the optimal action under uncertainty, given one's valuation of the consequences that may ensue and one's beliefs about the probability that those consequences will eventuate. Decision theory underlies a great deal of the development of modern statistics.

Philosophical Foundations

Good statistical thinking depends on our understanding of epistemology and the philosophical roots of scientific inquiry. How do we know what we know? What constitutes knowledge? Bayesian notions of probability and learning provide the best solution to Hume's problem of induction. Statistics functions best when informed by a sense of how statistical methods address important difficulties in the rational acquisition of knowledge.

Biostatistics

My biostatistical collaborations have focused on the study of environmental toxicants on human fertility (work with Ulrike Luderer of UCI) and on brain connectivity differences between Schizophrenia patients and healthy controls (work with the Mind Research Network).

Cognitive Science

I am looking for collaborations in the area of psychology and the cognitive sciences. My own background with psychology—particularly industrial-organizational psychology and meta-analytic methods—makes this an area of special interest for me.

Other Collaborations

I am currently looking for collaborations across academic disciplines. If you have a problem you think I might find interesting, please let me know by email.

Wikihistory

by Desmond Warzel

Extracts from the International Association of Time Travelers: Members' Forum.

A Tall Tail

by Charles Stross

Interesting stories get told at scientific conferences.

Firstborn

by Brandon Sanderson

The pain of living in your brother's shadow, except in space with lasers.

The Last Question

by Issac Asimov

"How can the net amount of entropy of the universe be massively decreased?"

Writing Excuses Podcast

This podcast, now in its 12th season, is run by four high-profile genre fiction authors: Brandon Sanderson, Dan Wells, Howard Tayler, and Mary Robinette-Kowal. Not only are their insights pretty phenomenal, but they regularly bring in guests for alternative perspectives. Podcast episodes run about 15 minutes—but they always end with a writing prompt, so you might wind up spending more time than that on each episode.

Brandon Sanderson's BYU Writing Class

Brandon Sanderson, one of the hosts of the Writing Excuse podcast and my favorite author, teaches a yearly creative writing class at Brigham Young University (BYU). His lectures occasionally get recorded and posted online (with his endorsement).