Continuous, real-time bit error ratio (BER) test of modern communication and storage channels is a ubiquitous problem: the noises tend to vary in space and time, and are difficult to fully characterize offline. Traditional method requires time consuming accumulation of samples for which Bayesian method has shown its promise in alleviating by incorporating a priori knowledge. However, the method has so far depended on a simplistic linear search algorithm that suffers from long running time which defeats the purpose of sample reduction. We reveal the existence of a convex solution space for the problem generally thought to be non-convex. This results in an improved performance by orders of magnitude.