# 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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### Cross validation from Jacobian matrix of likelihood for glm(poisson, identity)

The difference of Standard Error between glm(y~x, family=poisson(link=identity)) and optim() in R Following the above question... And actually, I have an another question now. I could cross ...
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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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### Computing directly the pdf of $Y=X^2$ for the pdf $f_X(x) = \frac{2}{9}(x+1)$

In the book Statistical inference by Casella and Berger, given that the pdf of X is $f_X(x) = \frac{2}{9}(x+1)$ for $-1 \le x \le 2$, we want to find the pdf of $Y=X^2$. But it says we are not able to ...
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### Express the density of a function of two random variables using the Gradient and the joint density

I would like to know if it is possible to express the density $f_Z(z)$ of a function $Z = g(X,Y)$ of two continuous "nice" random variables $X$ and $Y$ only using the joint density $f_{XY}(x,y)$ and ...
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### Calculating the Jacobian of a neural network

I'm trying to calculate confidence intervals for a neural network (rather than prediction intervals). I'm following this paper, which treats them in the same framework as any parametric (parameter-...
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### IS $\int_{-\infty}^\infty e^{-\beta\cdot g(x)}g(x)^{\alpha-1}\text{d}x={\Gamma(\alpha)\over \beta^\alpha}\ \ ?$ [closed]

Is the following statement true: Let $g(x)$ be some non negative continuous function of $x$.We know that$$\int_{0}^\infty e^{-\beta x}x^{\alpha-1}dx={\Gamma(\alpha)\over \beta^\alpha}$$ Does ...
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### Jacobian and covariance matrix

Anyone know the Bishop's book in 2.53 they use Jacobian to convert covariance matrix x to y. $$J_{ij}=\dfrac{\partial x_i}{\partial y_i}=U_{ji} \qquad{(2.53)}$$ \int_{\bf x} f({\bf x})d{\bf x} = \...
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### Relation between Covariance matrix and Jacobian in Nonlinear Least Squares

I saw that CovB = inv(J'*J)*MSE in a MATLAB documentation here at http://www.mathworks.com/help/stats/nlinfit.html However, I cant find any sources for the ...
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### Delta method with mix of continuous and discrete variables

This is my first question on Cross Validated so please bear with me if my question is lagging in any dimension. My question regards how to evaluate a Jacobian matrix when one variable is binary. I ...
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### conditional probability, change of variable and Jacobian

I have a question, and I am guessing that the question arises due to my lack of good understanding in the change of variable technique. I would like to evaluate $f_X(x)$. When $f_Y(y)$ exists, I can ...
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### About deriving PDFs from CDFs

Suppose I have some continuous random variable $X$. Further, suppose I am interested about a transformed random variable $Y = g(X)$ where $g$ is some increasing function. If I know the CDF of $X$, I ...
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