Living cells stochastically switch their phenotypic states in response to environmental cues to maintain persistence and viability. Estimating the state transition probabilities from biological observations of cell populations gives valuable insight to the underlying processes, and gives insights as to how the transition statistics are influenced by external factors. In this work, we present two Bayesian estimation approaches. The first is applicable when individual cell state trajectories are observed. The second approach is applicable when only aggregate population statistics are available. Estimation of transition probabilities when individual cell state trajectories are available is a straightforward problem, whereas estimation from only aggregate statistics can be computationally expensive. In the latter case, we present an algorithm that relies on three key ideas to cut down computational time: i) approximating high-dimensional multinomial distributions with multi-variate Gaussians, ii) employing Monte-Carlo techniques to efficiently integrate over high dimensional spaces, and iii) explicitly incorporating sampling constraints by computing lower dimensional distributions over the constrained variable. Simulation results demonstrate the viability of the algorithm.

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