In active inference, a decision maker actively chooses which data points to use or which experiments to carry out for the purpose of gathering the most relevant information for the inference task at hand. It is particularly relevant in the era of big data when the overabundance of data may well become an obstacle to information gathering. In this talk, we consider a special case of the sequential design of experiments problem pioneered by Chernoff in 1959. For this special problem motivated by anomaly detection, we show that a simple deterministic test with better performance can be constructed as compared to the randomized test developed in Chernoff’s original work.