BUDAPEST: A Fast and Reliable Bayesian Algorithm for TMS Threshold Estimation with an Open-Source GUI and Human Validation

Abstract Background Motor threshold (MT) estimation is fundamental to transcranial magnetic stimulation (TMS), guiding individualized stimulation intensity in research and therapy. Conventional methods such as the 5-out-of-10 rule require many stimuli, while adaptive approaches like Parameter Estimation by Sequential Testing (PEST) improve efficiency but can exhibit poor convergence under certain conditions. Objective This study introduces the Bayesian Uncertainty Dynamic Algorithm for Parameter Estimation by Sequential Testing (BUDAPEST), a Bayesian adaptive method for fast, accurate MT estimation with user-controlled uncertainty. The aims were to validate its accuracy in simulations and human data, promote usability through a MATLAB-based graphical interface, and evaluate experimental utility through resting and active MT comparisons and session-to-session reliability. Methods BUDAPEST infers MT from binary MEP responses using sequential Bayesian updating and terminates when a user-defined uncertainty threshold is reached. Performance was evaluated in 10,000 virtual simulations and in human rMT and aMT measurements across two sessions per subject, including 3×5 cortical motor mapping to assess physiological spatial patterns. Results In simulations, BUDAPEST achieved a mean absolute error of 1.9% MSO within ~10 pulses using a 2% uncertainty criterion while avoiding PEST misestimations. In human data, MT estimates were accurate within ±4% MSO and robust to initialization; rMT showed strong session-to-session reliability (r = 0.78), whereas aMT exhibited greater variability. Motor mapping revealed coherent excitability gradients centered on the hotspot. Conclusion BUDAPEST enables rapid, reliable, and uncertainty-controlled MT estimation while reducing procedure time and participant burden. The accompanying GUI facilitates immediate adoption in research and clinical TMS environments. Highlights Introduces BUDAPEST, a Bayesian uncertainty-aware algorithm for rapid and reliable TMS motor threshold estimation. Achieves accurate MT estimates (≈2% MSO error) in ~10 pulses with user-controlled trade-offs between precision and procedure duration. Demonstrates robust performance in simulations and human data, with strong resting MT reliability and an open-source GUI enabling immediate adoption.