  Factor analysis is a critical component of high dimensional biological data
analysis. However, modern biological data contain two key features that
irrevocably corrupt existing methods. First, these data, which include
longitudinal, multi-treatment and multi-tissue data, contain samples that break
critical independence requirements necessary for the utilization of prevailing
methods. Second, biological data contain factors with large, moderate and small
signal strengths, and therefore violate the ubiquitous "pervasive factor"
assumption essential to the performance of many methods. In this work, I
develop a novel statistical framework to perform factor analysis and interpret
its results in data with dependent observations and factors whose signal
strengths span several orders of magnitude. I then prove that my methodology
can be used to solve many important and previously unsolved problems that
routinely arise when analyzing dependent biological data, including high
dimensional covariance estimation, subspace recovery, latent factor
interpretation and data denoising. Additionally, I show that my estimator for
the number of factors overcomes both the notorious "eigenvalue shadowing"
problem, as well as the biases due to the pervasive factor assumption that
plague existing estimators. Simulated and real data demonstrate the superior
performance of my methodology in practice.
