This thesis is concerned with Bayesian forecasting and sequential estimation. The\ud concept of multiple discounting is introduced in order to achieve parametric and\ud conceptual parsimony. In addition, this overcomes many of the drawbacks of the Normal\ud Dynamic Linear Model (DLM) specification which uses a system variance matrix. These\ud drawbacks involve ambiguity and invariance to the scale of independent variables. A\ud class of Normal Discount Bayesian Models (NDBM) is introduced to overcome these\ud difficulties. Facilities for parameter learning and multiprocess modelling are provided.\ud Unlike the DLM's, many limiting results are easily obtained for NDBMM's. A general class\ud of Normal Weighted Bayesian Models (NWBM) is introduced. This includes the class of\ud DLM's as a special case. Other important subclasses of Extended and Modified NWBM's\ud are also introduced. These are particularly useful in modelling discontinuities and for\ud systems which operates according to the principle of Management by Exception. A\ud number of illustrative applications are given
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