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Have a look at codes generating random inverse wishart matrices (e.g, Jones 2007). For example, the scipy implementation (https://github.com/scipy/scipy/blob/v1.6.0/scipy/stats/_multivariate.py#L2754 functions rvs, _rvs and _standard_rvs) use chi² and normal random draws and combines them with linalg. You can take each normal/chi² variable based on a ...


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You are corrent that Zellner's g-prior depends on the design matrix in the regression. The prior is often used in "empirical Bayesian" analysis where there is no objection to this, but it is not a "pure" Bayesian procedure. One counter-argument to this is that the design matrix is a conditioning object in regression, and so if we treat ...


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I disagree with the other answers here asserting that there is no good reason for this, and that it is merely a simplifying assumption. From a metapphysical perspective, causal effects in nature generally operate in a roughly "smooth" manner, and so small changes in the input quantities in a causal system generally result in small changes in the ...


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One intuitive way to view it is that a smooth function can be described with less information than a less smooth function. If we restrict ourselves to vector spaces of functions, the dimension of the vector space (finite or infinite) is the number of coefficients we need to give for a complete specification of the function. For a linear function we need two ...


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A function is a map $f: X \to Y$, Gaussian Process learns to approximate the functions given the data. The example description says that you are given two points $\mathcal{D} = \{(\mathbf{\mathrm{x}}_1,y_1),(\mathbf{\mathrm{x}}_2,y_2)\}$, presumably around $0.2$ and $0.55$, what could be guessed from the second plot showing the posterior predictive ...


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While the author mentions it as an "example", it is true that, generally, smoother functions are often preferred in modelling the characteristics of the "true" underlying function, and therefore may be assigned a higher "prior probability", as the author maintains. Why is this? You may learn more about it by reading this ...


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Your approach is correct and good, especially if the components are distant from each other. An alternative could be to go one coordinate at a time and think about the conditional probability distribution. Specifically, the CDF of the first parameter is just the weighted sum of the CDFs of the components. Now that you have picked and sampled the first ...


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