Intuitively, the marginal probability of " X " is computed by examining the conditional probability of " X " given a particular value of " Y ", and then averaging this conditional probability over the distribution of all values of " Y ".
22.
On the other hand, one can also show that under such models the proportions a, b, c and d are not equal to the product of the marginals probabilities ( a + b ) / 2n, ( c + d ) / 2n and ( a + c ) / 2n, ( b + d ) / 2n.
23.
Due to the exceedingly high impact on public health of widely used medications, such as hormonal contraception and hormone replacement therapy, which may affect millions of users, even marginal probabilities of adverse effects of a severe nature, such as breast cancer, have led to public outcry and changes in medical therapy, although its benefits largely surpassed the statistical risks.
24.
A smooth function should change slowly where the input data are dense; that is, the gradient \ nabla _ { M } f ( x ) should be small where the " marginal probability density " \ mathcal { P } _ X ( x ), the probability density of a randomly drawn data point appearing at x, is large.
25.
Where p ( v _ i ) is the prior probability of feature variable F _ a adopting value v _ i, p ( c _ j ) is the marginal probability of category variable C adopting value c _ j, and p ( v _ i, c _ j ) is the joint probability of variables F _ a and C simultaneously adopting those respective values.
26.
The term p ( f _ { ik } ) \ designates the marginal probability that feature f _ i \ takes on value k \, and the term p ( f _ { ik } | c _ j ) \ designates the category-conditional probability that feature f _ i \ takes on value k \ " given " that the object in question belongs to category c _ j \.
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