Fig. 9: Performance of the Rao-Blackwell identification algorithm in experimental data from yeast cells.

A Inference result of cell #78. The top-left panel shows mRNA dynamics measured every two minutes over a 4-hour period. The lower row presents the parameter estimates, with the narrow conditional probability distributions illustrating the high confidence of these estimates. The top-middle panel compares the stationary distributions of the inferred model (using the MAP estimates) and the actual cell (approximated by the occupation time distribution of mRNA measurements). In these distributions, states have been organized in groups of ten. The good agreement between these two distributions (evident from the bimodal structure and low KL divergence) underscores the accuracy of the identification result. Our results indicate that k₃ is positive, implying that the system comprises three gene states. We also inferred the system assuming only two gene states; these results are shown in the gray box. In this case, the stationary distribution of the inferred model does not align with the distribution of the real cell. Specifically, the inferred model fails to capture the bimodality of the actual stationary distribution, leading to a relatively substantial KL divergence of 0.145 between the two distributions. This observation further supports the validity of the three-gene-state model for the real cell. B Inference results of some typical cells. We present the inference results of several cells exhibiting different behaviors. Cell #18 took about 90% of the time staying in the inactive gene state; cell #96 had a shorter duration in the inactive gene state; cell #93 took even less time in the inactive state, and its stationary distribution has a peak different from the origin; cell #88 exhibited a bimodal stationary distribution. In all these cases, the stationary distribution of the inferred model closely matches that measured in the experiment in terms of the shape and KL divergence, indicating the validity of our algorithm. Source data are provided as a Source Data file.