Stochastic and deterministic approaches Sample Clauses

Stochastic and deterministic approaches. ‌ By looking at the approaches that can be used in DA, we can identify two main categories: - stochastic approaches: in this case, the goal is to find probability distributions and confidence intervals for the system state x and output y, starting from some a priori probabilistic knowledge on the model and the data. - deterministic approaches: in this case, one is typically interested in recon- structing, predicting or estimating with no a priori probabilistic knowledge of the problem of interest. It is worth noting that, in the second case, one can still incorporate statistical knowledge about the model, as we will discuss in Section 2.4.2. Among the methods used in the two approaches, of particular importance are the Kalman filter (with its extensions) for the stochastic approach and the varia- tional method for the deterministic one. These constitute the subject of the next two sections. To make the description of the methods easier, we introduce a model problem to which we will apply the Kalman filter and the variational method. We will consider the following simple (discrete) dynamical problem: xn Apµqxn 1 bnpµq εn