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Author: Anonymous (page 4)

Multivariate Gaussian detection with  yields the LRT statist…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
Multivariate Gaussian detection with  yields the LRT statistic proportional to:
Continue reading “Multivariate Gaussian detection with  yields the LRT statist…”…

If you impose a Gaussian prior on weights in a linear-Gaussi…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
If you impose a Gaussian prior on weights in a linear-Gaussian model, the MAP estimate corresponds to:
Continue reading “If you impose a Gaussian prior on weights in a linear-Gaussi…”…

For Gaussian binary detection with equal priors and equal co…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
For Gaussian binary detection with equal priors and equal costs, the LRT threshold simplifies to
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For an inhomogeneous Poisson process with intensity , the po…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
For an inhomogeneous Poisson process with intensity , the point-process likelihood over has the form:
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Poisson-to-Gaussian approximation is most defensible when:

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
Poisson-to-Gaussian approximation is most defensible when:
Continue reading “Poisson-to-Gaussian approximation is most defensible when:”…

Under the same model, with , the decision can be written as:

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
Under the same model, with , the decision can be written as:
Continue reading “Under the same model, with , the decision can be written as:”…

The GLRT statistic for unknown amplitude (Gaussian) reduces…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
The GLRT statistic for unknown amplitude (Gaussian) reduces to a normalized matched-filter energy of the form:
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In the inhomogeneous Poisson log-likelihood ratio between a…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
In the inhomogeneous Poisson log-likelihood ratio between and , the spike-time terms appear as plus an integral “baseline correction.”
Continue reading “In the inhomogeneous Poisson log-likelihood ratio between a…”…

In Gaussian conjugate models, the posterior mean can be expr…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
In Gaussian conjugate models, the posterior mean can be expressed as a precision-weighted combination of the prior mean and the sample mean.
Continue reading “In Gaussian conjugate models, the posterior mean can be expr…”…

For univariate Gaussian detection , the false-alarm probabil…

Posted on: February 17, 2026 Last updated on: February 17, 2026 Written by: Anonymous
For univariate Gaussian detection , the false-alarm probability has the generic form:
Continue reading “For univariate Gaussian detection , the false-alarm probabil…”…
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