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| -rw-r--r-- | posts/2019-03-13-a-tail-of-two-densities.md | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/posts/2019-03-13-a-tail-of-two-densities.md b/posts/2019-03-13-a-tail-of-two-densities.md index a695af3..559215b 100644 --- a/posts/2019-03-13-a-tail-of-two-densities.md +++ b/posts/2019-03-13-a-tail-of-two-densities.md @@ -984,7 +984,7 @@ $$| X_i - X_{i - 1} | = | \log {p_i(\xi_i | \xi_{< i}) \over q_i(\xi_i | \xi_{< by Azuma\'s Inequality, -$$\prob(\log {p^k(\xi_{1 : k}) \over q^k(\xi_{1 : k})} \ge k a(\epsilon) + t) \le \exp(- {t^2 \over 2 k (\epsilon + a(\epsilon))^2}). \qquad(6.99)$$ +$$\mathbb P(\log {p^k(\xi_{1 : k}) \over q^k(\xi_{1 : k})} \ge k a(\epsilon) + t) \le \exp(- {t^2 \over 2 k (\epsilon + a(\epsilon))^2}). \qquad(6.99)$$ Let $t = \sqrt{2 k \log \beta^{-1}} (\epsilon + a(\epsilon))$ we are done. $\square$ |