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Questions related to various forms of integration including the Riemann integral, Lebesgue integral, Riemann–Stieltjes integral, double integrals, line integrals, contour integrals, surface integrals, integrals of differential forms, ...

2 votes
0 answers
349 views

An integral problem related to matrix determinant

I am stuck in an integral problem: $$\int_{\mathbb{R}^d}(\det(\mathbf{A}+k(\mathbf{x}-\mathbf{y}_0)(\mathbf{x}-\mathbf{y}_0)^T))^{-r_1}\prod_{i=1}^n(\det(\mathbf{B}+(\mathbf{x}-\mathbf{y}_i)(\mathbf{ …
Yicong Liang's user avatar
0 votes
1 answer
215 views

Behavior of the integral of products of probability densities

Assume $z \in \mathbb{R}^m$ and $x \in \mathbb{R}^n$. Assume we have proper density function $P(z)$ and proper conditional density function $P(x|z)$. We give the definition $$ T(x_1,\ldots,x_n) := \in …
Yicong Liang's user avatar