Jordan Bryan

Keep Stanford Wrestling

Stanford University recently announced its intention to eliminate its varsity wrestling program after 104 years of history. The coaching staff and current athletes are committed to finding a better resolution of the university’s concerns regarding its varsity sports programs, and are actively engaged in an effort to keep the wrestling team going... Read more

The Laplace transform for computing integrals over the probability simplex

This post concerns taking integrals over the \(K\)-probability simplex, defined as \[\Delta_K = \left\{\boldsymbol{\theta} \in \mathbb{R}^K : \boldsymbol{\theta} \geq 0, \boldsymbol{\theta}^\top \mathbf{1} = 1\right\}\] In general, simplex integrals are difficult to evaluate. However, product functions of the form \[\prod_{k=1}^K f_k (\theta_... Read more

Opportunities and challenges for analyzing cancer data at the inter- and intra-institutional levels

An original report written with collaborators Julie Wu and Lester Mackey was released today. Find the abstract below and read more about the genotypic differences between primary and metastatic samples of breast, colon, and lung tumor samples at JCO Precision Oncology. Abstract Purpose Our goal was to identify the opportunities and challenges... Read more

Minimum relative entropy and Generalized Bayes

Define the relative entropy of a probability distribution \(\nu\) with respect to reference measure \(\rho\) or Kullback-Leibler divergence of \(\nu\) to \(\rho\) as \[D_{\text{KL}}(\nu || \rho) = - \mathrm{E}_\nu \left[ \log \frac{d\rho}{d \nu} (\theta) \right]\] The usual Bayesian update can be seen as an unconstrained minimization problem ... Read more

Smaller \(p\)-values in genomics studies using distilled historical information

New joint work with Peter Hoff is out today. Find the abstract below and read more on about how historical information can power more discoveries in genomics studies. Abstract: Medical research institutions have generated massive amounts of biological data by genetically profiling hundreds of cancer cell lines. In parallel, academic ... Read more