  Combining the strengths of many existing predictors to obtain a Mixture of
Experts which is superior to its individual components is an effective way to
improve the performance without having to develop new architectures or train a
model from scratch. However, surprisingly, we find that na\"ively combining
expert object detectors in a similar way to Deep Ensembles, can often lead to
degraded performance. We identify that the primary cause of this issue is that
the predictions of the experts do not match their performance, a term referred
to as miscalibration. Consequently, the most confident detector dominates the
final predictions, preventing the mixture from leveraging all the predictions
from the experts appropriately. To address this, when constructing the Mixture
of Experts, we propose to combine their predictions in a manner which reflects
the individual performance of the experts; an objective we achieve by first
calibrating the predictions before filtering and refining them. We term this
approach the Mixture of Calibrated Experts and demonstrate its effectiveness
through extensive experiments on 5 different detection tasks using a variety of
detectors, showing that it: (i) improves object detectors on COCO and instance
segmentation methods on LVIS by up to $\sim 2.5$ AP; (ii) reaches
state-of-the-art on COCO test-dev with $65.1$ AP and on DOTA with $82.62$
$\mathrm{AP_{50}}$; (iii) outperforms single models consistently on recent
detection tasks such as Open Vocabulary Object Detection.
