The immune system has long been attributed cognitive capacities such as "recognition" of pathogenic agents; "memory" of previous infections; "regulation" of a cavalry of detector and effector cells; and "adaptation" to a changing environment and evolving threats. Ostensibly, in preventing disease the immune system must be capable of discriminating states of pathology in the organism; identifying causal agents or ``pathogens''; and correctly deploying lethal effector mechanisms. What is more, these behaviours must be learnt insomuch as the paternal genes cannot encode the pathogenic environment of the child. Insights into the mechanisms underlying these phenomena are of interest, not only to immunologists, but to computer scientists pushing the envelope of machine autonomy. This thesis approaches these phenomena from the perspective that immunological processes are inherently inferential processes. By considering the immune system as a statistical decision maker, we attempt to build a bridge between the traditionally distinct fields of biological modelling and statistical modelling. Through a mixture of novel theoretical and empirical analysis we assert the efficacy of competitive exclusion as a general principle that benefits both. For the immunologist, the statistical modelling perspective allows us to better determine that which is phenomenologically sufficient from the mass of observational data, providing quantitative insight that may offer relief from existing dichotomies. For the computer scientist, the biological modelling perspective results in a theoretically transparent and empirically effective numerical method that is able to finesse the trade-off between myopic greediness and intractability in domains such as sparse approximation, continuous learning and boosting weak heuristics. Together, we offer this as a modern reformulation of the interface between computer science and immunology, established in the seminal work of Perelson and collaborators, over 20 years ago.