  Mission-critical applications require Ultra-Reliable Low Latency (URLLC)
wireless connections, where the packet error rate (PER) goes down to $10^{-9}$.
Fulfillment of the bold reliability figures becomes meaningful only if it can
be related to a statistical model in which the URLLC system operates. However,
this model is generally not known and needs to be learned by sampling the
wireless environment. In this paper we treat this fundamental problem in the
simplest possible communication-theoretic setting: selecting a transmission
rate over a dynamic wireless channel in order to guarantee high transmission
reliability. We introduce a novel statistical framework for design and
assessment of URLLC systems, consisting of three key components: (i) channel
model selection; (ii) learning the model using training; (3) selecting the
transmission rate to satisfy the required reliability. As it is insufficient to
specify the URLLC requirements only through PER, two types of statistical
constraints are introduced, Averaged Reliability (AR) and Probably Correct
Reliability (PCR). The analysis and the evaluations show that adequate model
selection and learning are indispensable for designing consistent physical
layer that asymptotically behaves as if the channel was known perfectly, while
maintaining the reliability requirements in URLLC systems.
