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In the case of Cramér-Rao lower bound (CRLB), the Fisher information matrix (FIM) is obtained from the K-L divergence (KLD), i.e. $D(p_\theta\|p_\theta') = \int p_\theta(x)\log\frac{p_\theta(x)}{p_{\theta'}(x)}$, by taking derivative as $$g(\theta) = -\frac{\partial}{\partial \theta}\frac{\partial}{\partial \theta'}D(p_\theta\|p_{\theta'})\Bigg|_{\theta'=\theta}.$$

In the case of Bhattacharyya bound, this reference mentions that the corresponding information matrix is $V_k$. It is also termed the Bhattacharyya matrix here.

However, I am unable to find a corresponding divergence function whose derivative would yield the Bhattacharyya matrix. Is there an analogous divergence function for Bhattacharyya bound?

-r2d2

r2d2
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