# Minimize a quadratic form on the 2d probability simplex

For a symmetric $$2 \times 2$$ matrix $$\Sigma$$, consider the following problem: \begin{aligned} & \underset{x}{\text{minimize}} & & x^T \Sigma x \\ & \text{subject to} & & x \geq 0, \; \mathbf{1}^T x = 1 \end{aligned} Let $\Sigma = \left[ \begin{array}{cc} a & c \\ c & b \end{array} \right]$ and note t... Read more

# The bias-variance circuit under g-priors

The bias-variance tradeoff is usually discussed in terms of the mean squared error (MSE) of a predictor. However, it can also be applied to estimates of coefficients in a linear model. Below we examine how bias and variance figure into the MSE of coefficient estimates under a $$g$$-prior. Assume a linear model of the form \[Y = X \beta + \epsi... Read more

# DEMETER2

The Cancer Data Science team and others at the Broad Institute came out with an article in Nature Communications today detailing a new method for normalizing and integrating multiple large RNAi screening datasets. It’s called DEMETER2, named after the Roman goddess of the harvest. DEMETER2 uses a hierarchical Bayesian model to estimate gene dep... Read more