Titlebook: Statistical Physics; An Advanced Approach Josef Honerkamp Textbook 20022nd edition Springer-Verlag Berlin Heidelberg 2002 linear optimizati

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Signal Analysis: Estimation of Spectratimes, e.g., ., . + ., . + 2.,... The time step . is called the sampling time and 1/. the sampling frequency. A sampling frequency of, say, 1 kHz implies that a value is registered 1000 times a second, i.e., each millisecond. If we choose the unit of time such that . = 1, the sampling times are .,.

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Estimating the Parameters of a Hidden Stochastic Modelds for estimating the parameters in the model by which one wants to interpret the observations. In the first case, this will be a hidden Markov model, in the second case, a state space model will be assumed. In each case, all of the parameters will be collected in the vector .. As an estimator we us

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Signal Analysis: Estimation of Spectrad therefore we should denote the values by small letters .(.), since they are to be considered as realizations of random variables. For later purposes, however, we will use the random variable .(.) associated with each observation .(.).

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Quantum Random Systems the state of a system has to be described by a vector in a Hilbert space. If the quantum state is not known completely, one has to introduce the density operator, which contains information about the possible quantum states and their probabilities.

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Statistical Tests and Classification MethodsSince it is often necessary to make hypotheses about the properties of random variables, it is important to have a well-defined procedure to test these hypotheses. Typical hypotheses are.or