Abstract
A number of previous approaches to pseudotime estimation have provided point estimates of the ordering of cells for scRNA-seq data, while more recently, Gaussian process latent variable models and MCMC methods have been applied to understand the uncertainty associated with the pseudotemporal ordering. We present a new type of Gaussian process latent variable model for pseudotemporal ordering, which samples a distribution on the probability space of the orderings, that is on the group of permutations, rather than on the hugely high-dimensional vector space of possible pseudotimes, as done by previous models.
We determine the best proposal distribution for our Metropolis-Hastings sampler for different types of data in an extensive simulation study, and show on a microarray data set that it is both able to capture complicated posterior distributions with modes close to pseudotime estimates found by state-of-the-art methods for point estimation of pseudotime orderings, and identify a global maximum of the distribution close to the true order. Finally, in an application to scRNA-seq data we demonstrate the particular potential of our method to identify phases of lower and higher pseudotime uncertainty during a biological process.
Software in the form of Matlab code, together with sample input data sets, is available on request from the first author.