Bayesian nonparametrics for directional statistics

Refined Pinsker’s and Reverse Pinsker’s Inequalities for Probability Distributions of Different Dimensions

“…is the convex conjugate of L, and t must be the derivative of L. We see that ( 14) and (15) solve our optimization problem. The parametrization of γ 2 The use of the augmented signed total variation is clear here; had we used the augmented total variation (as defined in Theorem 8) instead, we would have equated…”

“…Famous lower bounds are given by Pinsker's inequality [5] and Vajda's lower bound [11], while a famous upper bound is given by reverse Pinsker's inequality [3], [10]. These results are particularly useful in the optimal quantization of pm's [3] and in Bayesian nonparametrics [2].…”

Tight bounds for augmented KL divergence in terms of augmented total variation distance

“…Notorious lower bounds are given by Pinsker's inequality [5] and Vajda's lower bound [10], while a famous upper bound is given by reverse Pinsker's inequality [3,9]. These results are particularly useful in the optimal quantization of probability measures [3] and in Bayesian nonparametrics [2]. In the present work, we generalize results from [1,6] on tight upper and lower bounds to the case in which P and Q are defined on different spaces.…”