Inference from particulars to particulars is also called analogy.
Peirce gave a pretty fair account of the logic behind statistical inference, as actually used in the research sciences from before his time until today. This logic depends on a fair amount of probability theory, which Boole had already begun to cast as a generalization of classical logic, but a lot of the underlying logic of inquiry is already visible in the infrastructure, at the level of propositional and predicate logic. And that much of the basic structure was more or less roughly outlined by Aristotle himself.
Here are some rough notes and sketches that I collected on the role of abduction, deduction, induction, and analogy in inquiry, as seen in the works of Aristotle and Peirce.
More discussion of these topics can be found on the following pages.