Uninformed Bayesian quantum thermometry

We study the Bayesian approach to thermometry with no prior knowledge about expected temperature scale, through example of energy measurements on fully or partially thermalized qubit probes. show that most common estimators, namely mean and median, lead high-temperature divergences when used for uninformed thermometry. To circumvent this achieve better overall accuracy, we propose two new estimators based an optimization relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements Cram\'er-Rao bound smaller probe numbers unrestricted ranges. Furthermore, that, using probes, one can increase range temperatures thermometer is sensitive at cost local accuracy.