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Lecture
Lecture

... using another RNG to shuffle a set of random numbers generated by the first one. • Start with an array U=(u1 ,...,un ) of n random numbers generated by RNG 1. Then repeat the following procedure: – Use RNG 2 to generate a random integer M between 1 and n. – Select uM as your next random number and r ...
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... should be. We can combine all the residuals into a single measure of accuracy by adding their squares. (We square the residuals in part to make them all positive.) The sum of the squares of the residuals is called the sum-of-squares error, SSE. Smaller values of SSE indicate more accurate models. ...
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Big Data: Text

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Data assimilation

Data assimilation is the process by which observations are incorporated into a computer model of a real system. Applications of data assimilation arise in many fields of geosciences, perhaps most importantly in weather forecasting and hydrology. The most commonly used form of data assimilation proceeds by analysis cycles. In each analysis cycle, observations of the current (and possibly past) state of a system are combined with the results from a numerical model (the forecast) to produce an analysis, which is considered as 'the best' estimate of the current state of the system. This is called the analysis step. Essentially, the analysis step tries to balance the uncertainty in the data and in the forecast. The result may be the best estimate of the physical system, but it may not the best estimate of the model's incomplete representation of that system, so some filtering may be required. The model is then advanced in time and its result becomes the forecast in the next analysis cycle. As an alternative to analysis cycles, data assimilation can proceed by some sort of nudging process, where the model equations themselves are modified to add terms that continuously push the model towards observations.
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