Using an information point of view, we discuss deterministic versus stochastic tools for residual generation and evaluation for fault detection and isolation (FDI) in linear time invariant (LTI) state-space systems. In both types of approaches to off-line FDI, residual generation can be viewed as the design of a linear transformation of a Gaussian vector (the finite-window input-adjusted observations). Several statistical isolation methods are revisited, using both a linear transform formulation and the information content of the corresponding residuals. We formally state several multiple fault cases, with or without causality assumptions, and discuss an optimality criterion for the most general one. New information criteria are proposed for investigating the residual optimization problem.