  Emerging applications of sensor networks for detection sometimes suggest that
classical problems ought be revisited under new assumptions. This is the case
of binary hypothesis testing with independent - but not necessarily identically
distributed - observations under the two hypotheses, a formalism so orthodox
that it is used as an opening example in many detection classes. However, let
us insert a new element, and address an issue perhaps with impact on strategies
to deal with "big data" applications: What would happen if the structure were
streamlined such that data flowed freely throughout the system without
provenance? How much information (for detection) is contained in the sample
values, and how much in their labels? How should decision-making proceed in
this case? The theoretical contribution of this work is to answer these
questions by establishing the fundamental limits, in terms of error exponents,
of the aforementioned binary hypothesis test with unlabeled observations drawn
from a finite alphabet. Then, we focus on practical algorithms. A
low-complexity detector - called ULR - solves the detection problem without
attempting to estimate the labels. A modified version of the auction algorithm
is then considered, and two new greedy algorithms with ${\cal O}(n^2)$
worst-case complexity are presented, where $n$ is the number of observations.
The detection operational characteristics of these detectors are investigated
by computer experiments.
