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Questions tagged [hessian]

For on-topic questions involving the Hessian matrix, a square matrix generalizing the second derivative. Please include also a statistical methods tag. For purely mathemathical questions about the Hessian it is better to ask on math.SE at https://math.stackexchange.com/.

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MLE: Does the scale of predictor variables affect whether the hessian is positive definite?

I am trying to fit a regression via maximum likelihood estimation, one of the regression terms involves $\beta_0e^{(\beta t)}$ where $t$ is measured in hours and has a range of 0 to 90 days. The ...
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How to deal with clmm warning: “hessian is numerically singular”?

I am using R's ordinal package to run a mixed regression model with an ordinal dependent variable. The data I am working with looks like this: ...
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Variance estimation of GLM coefficients

I'm having trouble understanding the relationship between the variance of the GLM coefficients and the estimated observed Hessian. In the textbook I'm using it's stated "An obvious and suitable choice ...
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Why is the Hessian of the log likelihood function in the logit model not negative *semi*definite?

The Hessian of the log likelihood function is $$\frac{\partial^2 \ln(\beta \mid x)}{\partial \beta \partial \beta'} = -\sum_{i=1}^n \underbrace{\Lambda(\beta'x_i)}_{\in(0,1)}\underbrace{\left[1-\...
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987 views

Singular Hessian/Observed information Matrix at optimal solution

I am trying to estimate the standard errors of an maximum likelihood estimate (multidimensional) in R'sfunction optim. I want to ...
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531 views

Which Hessian to use to compute standard errors

Let that I have a data vector $\textbf{x} = (x_1,x_2,x_3....x_n)$ Say these are realizations of IID random variables having a common density $f_\theta$ Likelihood computed using $i^\text{th}$ ...
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1answer
639 views

Interpretation of eigenvectors of Hessian inverse

I'm reading a paper in which they use the eigenvectors of the inverse Hessian of a continuous probability distribution to characterize dimensions along which the distribution is most and least ...
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3k views

Intuition for the “information matrix equality” result?

I am trying to understand the intuition behind the "information matrix equality" condition in the Maximum Likelihood context (perhaps this is the only context?): $$ -E[H(\theta)] = E[s(\theta) s(\...
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Name for outer product of gradient approximation of Hessian

Is there a name for approximating the Hessian as the outer product of the gradient with itself? If one is approximating the Hessian of the log-loss, then the outer product of the gradient with itself ...