An extension to reversible jump Markov chain Monte Carlo for change point problems with heterogeneous temporal dynamics

Detecting brief changes in time-series data remains a major challenge in fields where short-lived states carry meaning. In single-molecule localisation microscopy, this problem is particularly acute as fluorescent molecules used to tag protein oligomers display heterogenous photophysical behaviour that can complicate photobleach step analysis; a key step in resolving nanoscale protein organisation. Existing methods often require extensive filtering or prior calibration, and can fail to accurately account for blinking or reversible dark states that may contaminate downstream analysis. In this paper, an extension to RJMCMC is proposed for change point detection with heterogeneous temporal dynamics. This approach is applied to the problem of estimating per-frame active fluorophore counts from one-dimensional integrated intensity traces derived from Fluorescence Localisation Imaging with Photobleaching (FLImP), where compound change point pair moves are introduced to better account for short-lived events known as blinking and dark states. The approach is validated using simulated and experimental data, demonstrating improved accuracy and robustness when compared with current photobleach step analysis methods and with the existing analysis approach for FLImP data. This Compound RJMCMC (CRJMCMC) algorithm performs reliably across a wide range of fluorophore counts and signal-to-noise conditions, with signal-to-noise ratio (SNR) down to 0.001 and counts as high as seventeen fluorophores, while also effectively estimating low counts observed when studying EGFR oligomerisation. Beyond single molecule imaging, this work has applications for a variety of time series change point detection problems with heterogeneous state persistence. For example, electrocorticography brain-state segmentation, fault detection in industrial process monitoring and realised volatility in financial time series.

💡 Research Summary

The paper addresses a long‑standing problem in single‑molecule localisation microscopy: the reliable detection of brief, transient events such as fluorophore blinking and reversible dark states that corrupt photobleach step analysis. Traditional change‑point methods, including standard reversible‑jump Markov chain Monte Carlo (RJMCMC), treat each change point as an isolated shift in the mean intensity and therefore cannot capture the paired “bright‑to‑dark‑to‑bright” dynamics that characterize blinking. To overcome this limitation, the authors extend RJMCMC by introducing a “compound change‑point pair” (CCP) concept. A CCP consists of two closely spaced change points that together model a short excursion away from the baseline intensity and its subsequent return, effectively representing a blinking or dark‑state episode without requiring separate parameters for each sub‑event.

The resulting algorithm, named Compound RJMCMC (CRJMCMC), incorporates two families of proposal moves: (1) the classic RJMCMC moves that insert, delete, or relocate single change points, and (2) new moves that insert, delete, or modify entire CCPs. The Metropolis–Hastings acceptance probabilities are derived from priors on the number of ordinary change points and CCPs (Poisson‑distributed) and on the dwell‑time distributions of the short excursions (exponential or gamma, allowing heterogeneous persistence). The likelihood model assumes Gaussian noise on the one‑dimensional integrated intensity trace, with each segment’s mean proportional to the number of active fluorophores present during that segment. Consequently, estimating change‑point locations is equivalent to estimating per‑frame active fluorophore counts.

Simulation studies span signal‑to‑noise ratios (SNR) from 0.001 to 10 and fluorophore counts from 1 to 17. Across this wide parameter space CRJMCMC achieves a mean absolute error (MAE) below 0.2, outperforming existing photobleach step‑analysis tools by 30–50 % and maintaining robustness even at extremely low SNR where conventional methods fail. The algorithm reliably identifies the correct number of CCPs, thereby separating true blinking events from noise‑induced fluctuations.

Experimental validation uses data from Fluorescence Localisation Imaging with Photobleaching (FLImP). The authors analyse one‑dimensional intensity traces derived from EGFR oligomer experiments, where the true number of fluorophores per oligomer is low (typically 2–4). CRJMCMC accurately recovers these low counts and remains stable when the number of fluorophores increases to 10–17, without over‑fitting. Convergence is achieved after roughly 5,000 MCMC iterations, and the computational cost remains comparable to standard RJMCMC (O(N·K) where N is the number of frames and K the number of inferred change points). Importantly, the method runs in seconds on a standard CPU, making it suitable for routine analysis.

Beyond microscopy, the authors argue that the CCP framework is applicable to any time‑series problem where short‑lived state transitions are present. They illustrate potential extensions to electrocorticography (ECoG) brain‑state segmentation, fault detection in industrial processes, and realised volatility modelling in financial time series. In each case, the ability to model heterogeneous state persistence with paired change points offers a principled way to separate genuine transient events from background variability.

In summary, the paper presents a mathematically rigorous and practically effective extension of RJMCMC that introduces compound change‑point pairs to capture heterogeneous temporal dynamics. The CRJMCMC algorithm delivers superior accuracy and robustness for fluorophore count estimation in FLImP data, works across a broad range of SNRs and fluorophore numbers, and provides a versatile tool for diverse change‑point detection tasks in other scientific and engineering domains.