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Would it be possible to somehow combine the models with the bayesian techniques, so that the system could "learn" to spot when the weather is likely to do something unexpected that the rigid maths won't pick up?
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I just noticed that. The algorithms used in Bayesian classifiers are
heavily mathematical. If youre programming a computer to notice things about the real world and make inferences, then youre going to have to use a lot of maths at some point.