What is Autoregressive Model

In order to control a process, especially in a computer and instrumented assisted way, like in Brain Intensive Therapy (IT), a model of its behavior is needed. In order to do that, a first point is to be able to select the best set of a few (thus understandable and manageable) truly relevant variables. In manufactured systems, also used in Brain IT, physics is in fact often quite known, with a manageable number of degrees of freedom: for instance, in robots kinematics, natural state variables may be (angular) positions and velocities. Some natural systems are also as well easily characterized by state variables with physical meaning: for instance reservoirs, like lakes, but also body organs with respect to soluble substances, may be characterized by volumes, concentrations, fluxes, gradients among compartments (Liberati and Turkheimer 1999). In other cases, the "natural" variables of the systems are not the best ones for identifying and control a process: a transformation of some of them may be needed: for instance, in the autonomous nervous control of the hearth system, the differential inter-beat measure is the one that almost linearly interact with baro-reflex in the feedback control loop (Baselli et al., 1986). In many cases, mainly for natural, especially neural processes, it is not easy to formulate a model based on variables whose physical meaning is a-priori known: for instance the electroencephalogram (EEG) is a very far field shielded measure of the interacting activity of billions of neurons: many actors are thus playing, each one with many meaningful state variables, also depending on the investigated level, but with high reciprocal correlation. It would not be efficient to model every single variable for global monitoring, like it is not useful to take into account the kinetics of every single molecule of a gas when only global effects of pressure are of interest. A quest of some higher level variables, even without a direct physical meaning, is thus natural, in order to easily manage the complexity of the problem. Once such salient variables are found, the problem often arises to correlate in logical and/or mathematical sense their dynamics, in order to properly model, forecast and control the patient features. Such interrelated problems will be briefly addressed in the present contribution, where Intensive Therapy is chosen as a paradigmatic application because of its critical conditions, while the approaches described in the following, and whose rationale is better analyzed in the referred bibliography, are of a quite general use in health information systems.