1.1 Bayesian Inference

Inference methods consist of estimating the current values for a set of parameters based on a set of observations or measurements. The estimation procedure can follow one of two models. The first model assumes that the parameters to be estimated, usually unobservable, are nonrandom and constant during the observation window but the observations are noisy and thus have random components. The second model assumes that the parameters are random variables that have a prior probability and the observations are noisy as well. When the first model is used for parameter estimation, the procedure is called non-Baysian or Fisher estimation [1]. Parameter estimation using the second model is called Bayesian estimation.

Bayesian estimation is conceptually very simple. It begins with some initial prior belief, such as the statement “See that ship. It is about 1000 yards from shore and is moving approximately Northeast at about 10 knots.” Notice that the initial belief statement includes an indication that our initial guess of the position and velocity of the ship are uncertain or random and based on some prior probability distribution. Based on one's initial belief, one can then make the prediction “Since the ship appears to be moving at a constant velocity, it will be over there in about 10 minutes.” This statement includes a mental model of the ship motion dynamics as well as some additional uncertainty. Suppose now, that one has a small portable radar on hand. The ...

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