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Questions tagged [normalizing-constant]

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How do I compute the closed form normalizing constant for this distribution?

The funnel distribution for random variable $X = (x_1,x_2,..,x_D)$is $$P(X) = N(x_1|0,9)\prod_{d=2}^D N(x_d | 0,exp(x_1))$$ The closed form normalizing constant for normal distribution $N(x|0,\...
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weighted sum of posterior Dirichlet distributions

I have the following distribution: $q(\vec\theta) = \frac{\sum_k \alpha_k}{\sum_k \beta_k \alpha_k} (\sum_k\theta_k\beta_k) \frac{\Gamma(\sum_k \alpha_k)}{\prod_k\Gamma(\alpha_k)} \prod_k \theta_{k}^{...
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What is the relationship between the normalization constants of the normal distribution and the (Inverse-)Wishart distribution?

I was looking at the probability density function of the multivariate normal distribution and that of the inverse-Wishart distribution: $$ \begin{array}{rccll} p_{\mathcal{N}}\left(\mathbf{x}; \...
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Bayesian inference, finding unknown function of parameter

I'm completely new to Baayesian statistics and am having some questioning about the following: Given a probability distribution defined by the pdf $\pi(x|\theta) = C(\theta)x^2 e^{-\theta x^{3}}$ ...
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Deriving the normalizing constant for the multivariate Gaussian

I am trying to derive the normalizing constant for the multivariate Gaussian. The book I'm following suggests diagonalizing the covariance matrix and then using a change of variables. So, we consider ...
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403 views

Dropping the normalization constant in Bayesian inference

Could anyone please explain to me (or provide a situation) where one would drop the normalising constant (or marginal probability term) from Bayes rule when performing Bayesian Inference? New to ...
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244 views

Sampling a random binary matrix with “Gaussian” probability distribution

Let $A_{ij}$ be a $n\times n$ random binary matrix with probability mass function $P(A)$ given by $$ \log P(A)=-\frac 12 \mathrm{tr}\left[\left(A-M\right)^TV\left(A-M\right)\right] + C, $$ where $M$ ...