Figure 2.

Analysis on synthetic data for a system with two system states. In (a), we show a section of synthetic data produced with the values in Table S2. Furthermore, the system state trajectory is shown in blue. Below this, the arrival times of donor and acceptor photons ${\mu }_n^d$ and ${\mu }_n^a$ are shown in green and red, respectively. In (b), we plot the bivariate distribution over escape rates and FRET efficiencies. The ground truth is shown with red dots corresponding to an escape rate of 40 s⁻¹ and FRET efficiencies of 0.22 and 0.59. ${\lambda }_{esc}$${\epsilon }_{FRET}$. As seen, the BNP-FRET sampler clearly distinguishes two system states with maximum a posteriori (MAP) estimates for the associated escape rates of $\approx {38}_{-7}^{+7}$ and $\approx {40}_{-7}^{+7}$ s⁻¹ and for FRET efficiencies of $\approx {0.21}_{-0.03}^{+0.03}$ and $\approx {0.59}_{-0.03}^{+0.03}$. We have smoothed the distributions using kernel density estimation for illustration purposes only.