Ville's Inequality
An inequality in probability theory concerning nonnegative supermartingales, used to construct time-uniform confidence sequences and anytime-valid bounds. It is a core tool in sequential analysis and online learning.
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An e-process is a class of nonnegative martingales or supermartingales whose expectation under the null hypothesis does not exceed 1, thereby providing anytime-valid sequential tests via Ville's inequality.
In sequential analysis, anytime-valid bounds are often implemented by constructing nonnegative supermartingales and applying Ville's inequality.
The core idea of the product betting martingale is to choose a predictable betting function such that the expectation of the product martingale does not exceed 1, and then apply Ville's inequality to obtain that the probability of exceeding 1/α is at most α.
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An e-process is a class of nonnegative martingales or supermartingales whose expectation under the null hypothesis does not exceed 1, thereby providing anytime-valid sequential tests via Ville's inequality.
50%UnverifiedIn sequential analysis, anytime-valid bounds are often implemented by constructing nonnegative supermartingales and applying Ville's inequality.
50%UnverifiedThe core idea of the product betting martingale is to choose a predictable betting function such that the expectation of the product martingale does not exceed 1, and then apply Ville's inequality to obtain that the probability of exceeding 1/α is at most α.
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