Estimating a Structured Covariance Matrix From Multilab Measurements in High-Throughput Biology

We consider the problem of quantifying the degree of coordination between transcription and translation, in yeast. Several studies have reported a surprising lack of coordination over the years, in organisms as different as yeast and human, using diverse technologies. However, a close look at this literature suggests that the lack of reported correlation may not reflect the biology of regulation. These reports do not control for between-study biases and structure in the measurement errors, ignore key aspects of how the data connect to the estimand, and systematically underestimate the correlation as a consequence. Here, we design a careful meta-analysis of 27 yeast data sets, supported by a multilevel model, full uncertainty quantification, a suite of sensitivity analyses and novel theory, to produce a more accurate estimate of the correlation between mRNA and protein levels—a proxy for coordination. From a statistical perspective, this problem motivates new theory on the impact of noise, model mis-specifications and non-ignorable missing data on estimates of the correlation between high dimensional responses. We find that the correlation between mRNA and protein levels is quite high under the studied conditions, in yeast, suggesting that post-transcriptional regulation plays a less prominent role than previously thought

Laplace random variables with application to price indices

Computer programs, Consumer price index, Economics, Estimation, Laplace distribution, Ratio of random variables,

Weakly driven anomalous diffusion in non-ergodic regime: an analytical solution

We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic fluctuations with a given distribution $\psi(\tau)$ of residence times in each velocity state. We obtain analytical solutions for the diffusion process in a generic external potential and for a generic statistics of residence times, including the non-ergodic regime in which the mean residence time diverges. We show that these analytical solutions are in agreement with numerical simulations.Comment: 7 pages, 4 figure