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Use the rGARMA function in the ts.extend package If you don't mind using R instead of MATLAB, you can generate random vectors from any stationary Gaussian ARMA model (including AR models) using the ts.extend package. This package generates random vectors directly form the multivariate normal distribution using the computed autocorrelation matrix for the ...


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Consider the model \begin{cases} x_t = \sum_i \alpha_i x_{t-i}\\ y_t = x_t + \nu_t \end{cases} Substituting $$y_t = \sum_i \alpha_i x_{t-i} + \nu_t\\ y_t = \sum_i \alpha_i (y_{t-i}-\nu_{t-i}) + \nu_t\\$$ This is an ARMA model in $y$ with a very specific constraint. \begin{cases} y_t = \sum_i \phi_i y_{t-i} + \sum_i \theta_i \nu_{t-i} + \nu_t\\ \theta_i=-\...


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Yule process is the same as the pure birth process, although the two names are apparently used in somewhat different contexts. One speaks of birth&death process when it is described in terms of differential equations and Markovian dynamics, as, e.g., here. The pure birth process then would be usually described by a set of rate equations $$ \dot{P_n}(t) = ...


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Frequentist statistics are optimal methods. Maximum likelihood-based statistics are optimal methods. Bayesian statistics are optimal methods. They are each optimal at different things. Each method is very good at solving certain types of problems. For some problems, the differences are minimal enough in practice that the differences are interpretive. ...


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Statistics, in general, is about learning from the data, that is thought as intrinsically random. There’s no truly deterministic models in statistics. Even when statistician does build a model that is based on some mechanistic model of the phenomenon of interest, she would additionally account for the noise in the data. The name “frequentism” itself is about ...


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If you are reporting to physicists or chemicists, I would recommend the Gaussian error propagation law, because that is what they usually apply in such cases: $$(\Delta f)^2 = \left(\frac{\partial f}{\partial a} \Delta a\right)^2 + \left(\frac{\partial f}{\partial b} \Delta b\right)^2 + \ldots$$ If you are reporting to statisticians, a resampling method like ...


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