Fundamental estimation and detection limits in linear non-gaussian systems

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Alain Monfort. E-mail: alain. Jean-Paul Renne. Faculty of Business and Economics, University of Lausanne.

Independent component analysis

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Limits of Detection, Limits of Quantitation, and Reporting Limits

Advance article alerts. Article activity alert. Then, the second step is to estimate the parameter of the model. MDL can be used as a criterion for model selection.

It measures the universal code length of the data, given a model. One can compare two different models based on their MDLs using the data available and favor one with shorter code length.

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However, it is not clear how to optimize from a model set functional space with infinite models based on MDL. Note that MDL is used for comparing given models in a parameterized family, rather than searching for the best model over the whole functional space. Kalman filters requires 1 linear system equation, 2 Gaussian noise. The linearity of system equation preserves the Gaussianity of the process Gauss Markov process, actually, AR process.

Since the state process is a Gauss Markov process, Kalman filters only have to propagate mean and covariance.

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Kalman filters can be used to estimate the state of time-varying linear system. Just change the system matrices from constant ones to time varying ones. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity -- and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms.

Fundamental to the idea of a graphical model is the notion of modularity -- a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data.

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