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The optimality of Kalman filtering

It is known that the Kalman filter estimates the state of the following system recursively. $$x_{k+1}=Ax_k+w_k, \ \ w_k \sim \mathcal{N}(0,Q)$$ $$y_k=Cx_k+v_k, \ \ v_k \sim \mathcal{N}(0,W)$$ In the ...
Jing Zhou's user avatar
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Calculate sample mean confidence interval of noisy logistical distribution

I have $n$ samples which follow a logistic distribution with unknown $u$ and $s$; it is affected by a Gaussian noise with 0 mean. I would like to estimate its average $u$ with a confidence interval (...
Dallatorre's user avatar
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Maximum-likelihood estimation for univariate responses from multivariate data

I am new in the field of machine learning, so I hope I will be able to formulate my question in a clear way... I have some data represented by vectors $\mathbf{x}_1,\mathbf{x}_2,\ldots,\mathbf{x}_n \...
guigux's user avatar
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Distances between up and down crosses in Gaussian Processes

Given a gaussian process $g := \mathcal{GP}\left(\mu, \Sigma \right)$, where $\mu$ is the mean and $\Sigma$ is the covariance function, I am interested in estimating the mean value $L_m$ of the ...
Kikolo's user avatar
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