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We assume that the stochastic terms are jointly distributed following a bivariate normal distribution and therefore our model is a bivariate probit.
The CRF assigns the sequence of labels y to the observed input X. X and Y are jointly distributed, but CRFs directly model the conditional distribution p(Y| X) which takes the form: (1) p (y | x ) = 1 Z x e x p (∑ j = 1 N ∑ k = 1 K λ k f k (y j − 1, y j, x, j ) ) where Z x is the normalization factor, and f k is the feature function.
In this research, the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of the stability of infinite slopes without seepage.
In this research the jointly distributed random variables method is used for probabilistic analysis and reliability assessment of liquefaction potential based on triaxial test results.
This study highlights the interesting phenomenon whereby BSCs and PSCs are jointly distributed in opposite orientations under a canopy of patchy Achnatherum splendens grass on the alpine steppe of the Qinghai Lake watershed (Qinghai-Tibet Plateau, northwestern China).
Each of these load cases depends on combinations of at least three jointly distributed metocean parameters, the mean wind speed, the significant wave height, and the peak spectral period.
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They also learn, teach, buy products and services, collaborate on research, "acqui-hire" and jointly distribute new, innovative products — which is all well-aligned with the needs of a nascent ecosystem like Brazil's.
If X and Y are jointly normally distributed, the conditional expectation of Y given X is just a linear function of X, and hence the optimal predictor and the optimal linear predictor are the same.
Accordingly, the MI of the jointly Gaussian distributed random vector x can be formulated as [11] (17).
We assume that the vectors of unobserved attributes (v ri, v ei ) are jointly discretely distributed.
In practice, this implies that the vectors of unobserved attributes specific to each type of transition are jointly discretely distributed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com