# Questions tagged [jacobian]

For statistical questions involving the Jacobian matrix (or determinant) of first partial derivatives. For purely mathematical questions about the Jacobian it is better to ask at math SE https://math.stackexchange.com/.

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### How do you solve for inverses when doing the Jacobian transformation method?

Hopefully a very basic question. This is from a textbook exercise I'm doing to prepare for a class. Suppose I have two independent random variables, X and Y, and I am trying to find the joint ...
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### Are Jacobian adjustments necessary when the target parameter is a difference between two parameters in Stan?

[Note on cross-posting: This question has now been posted on the Stan Forums as well.] I want to model the index called Delta P (e.g., p.144 of this paper), which is basically a difference between two ...
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### Jacobian matrix X going from x to the y coordinate system [closed]

In Christoper Bishop's book Pattern Recognition and Machine learning, they use Jacobian to convert covariance matrix x to y. However, according to definitions on Wikipedia, the definition of Jacobian ...
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### Given X and Y are independent ~N(0,1), what is the distribution of $Z=X^2 + Y^2$

Our joint pdf is $f(x,y) = \frac{1}{\sqrt{2π}} e^\frac{x^2+y^2}{2}$ Now we let $U = X^2 + Y^2$ and $V = Y$, we can then get our Jacobian as $J = \frac{1}{\sqrt{u-v^2}}$ Since this ...
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### Jacobian for function including cubic spline

I am trying to fit a measured spectrum with a linear combination of end-member spectra which are approximated by cubic spline functions ($f_1$ and $f_2$). I also need to incorporate terms that account ...
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### Maximum Likelihood - Normal Errors - When is the Jacobian needed?

I am considering the following non-linear model $$h(z) - \lambda_0 - \lambda_1 z - \lambda_2x = v$$ where $v \sim \mathcal N(0,\sigma^2)$ unobserved error and where $\lambda_j$ are unknown ...
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Let $\mathbf{A} \sim \text{Wishart}_m\left(k_a,\mathbf{V} \right)$ and $\mathbf{B} \sim \text{Wishart}_m\left(k_b,\mathbf{V} \right)$ be two full rank Wishart random matrices. Define  \mathbf{S} = \...
When we have a random variable $x$ with a probability density $p(x)$, and a function $y = f(x)$ that is differentiable and can be solved for $x = g(y)$, the change of variable formula leads us to a ...