Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [bhattacharyya]

Use this tag if you are asking about the Bhattacharyya distance or the Bhattacharyya coefficient.

The Bhattacharyya coefficient $(1)$ and is the Bhattacharyya distance $(2)$ are:

\begin{align} BC(\mathbf{p},\mathbf{q}) &= \sum_{i=1}^n \sqrt{p_i q_i} \tag{1} \\[5pt] D_B(p,q) &= -\ln \left( BC(p,q) \right) \tag{2} \end{align}

The Bhattacharyya distance is a distance measure similar to Total Variation distance or Hellinger distance.

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Percentage of overlapping regions of two normal distributions

I was wondering, given two normal distributions with $\sigma_1,\ \mu_1$ and $\sigma_2, \ \mu_2$ how can I calculate the percentage of overlapping regions of two distributions? I suppose this problem has a specific name, are you aware of any…
Ali Salehi
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Differences between Bhattacharyya distance and KL divergence

I'm looking for an intuitive explanation for the following questions: In statistics and information theory, what's the difference between Bhattacharyya distance and KL divergence, as measures of the difference between two discrete probability…
JewelSue
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Intuition of the Bhattacharya Coefficient and the Bhattacharya distance?

The Bhattacharyya distance is defined as $D_B(p,q) = -\ln \left( BC(p,q) \right)$, where $BC(p,q) = \sum_{x\in X} \sqrt{p(x) q(x)}$ for discrete variables and similarly for continuous random variables. I'm trying to gain some intuition as to what…
Lucas Roberts
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distance measure of two discrete probability histograms (distance between two vectors)

I have multiple sets of discrete probability histograms(vectors) and I want to measure the distance between each histogram. I have done some research but I am in doubt. Literature suggest I could use the Bhattacharyya distance or the Hellinger…
Jasper
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Bhattacharyya distance for three histograms

There is a paper “Auto White Balance Based on the Similarity of Chromaticity Histograms” mention about automatic white balance. One of the key point of this algorithm is how to measure the similarity between three histograms (r, g, b channels). They…
StereoMatching
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Can I use the Bhattacharyya distance as an acceptance criterion for Approximate Bayesian Computation?

I am researching the spread of a disease through a population and want to capture the behavior of this disease with a model. I already have a model and patient data. The data is a value per patient that is more or less lognormally distributed. I…
user112592
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How to calculate Bhattacharya distance for singular multivariate normal distributions?

I am applying Bhattacharya distance to multivariate normal distributions $$D_{B}={1 \over 8}({\boldsymbol \mu }_{1}-{\boldsymbol \mu }_{2})^{T}{\boldsymbol \Sigma }^{{-1}}({\boldsymbol \mu }_{1}-{\boldsymbol \mu }_{2})+{1 \over 2}\ln…
Faiz Kidwai
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Thresholds for Bhattacharyya coefficient - when do the distributions differ significantly

The Bhattacharyya coefficient of two discrete probability distributions is defined as $$ BC(p,q) = \sum_{i=1}^n \sqrt{p_iq_i}. $$ This coefficient lies within the interval $[0,1]$ and if $p=q$ then it is 1 as $$ \sum_{i=1}^n \sqrt{p_i^2} =…
Richi W
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Does maximal Bhattacharyya coefficient imply mimimal total variation distance?

I'm working on numerical optimization (linear programming), on probability distributions denoted P, Q. We want to find the minimal total variation distance and maximal Bhattacharyya coefficient between P and Q. We can quite easily find the minimal…
balletpiraat
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Jeffries Matusita distance for 14 variables

I wish to perform Jeffries-Matusita distance on 14 spectral bands. Is there anyone who can help with how it is done in R?
tribalhouse49778
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Bhattacharyya Distance for Age/Gender Groups?

I'm calculating distances for groups based on Age/Gender Compositions (to rank their similarity in demographic composition.) I'm working with the following: Men 18-34, Men 35-49, Men 50-64, Men 65+, Women 18-34, Women 35-49, Women 50-64, Women…
Katherine
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Normalize vector-based integer data

I'll preface my question by saying I have a very limited knowledge of statistics, and while I've put some thought into this problem, I'm a bit stuck! Onwards... I have a collection of fixed-size vectors of the form $\overline{v} = \{ c_0,\ldots,c_n…
Bruce
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Statistical Distance Within Multivariate Distribution

Suppose you have some multivariate normal distribution $X \sim N(\mu,\Sigma)$. Is there a good way to calculate a measure of distance between an arbitrary $X_{i}$ and $X_{j}$ of $X$ (I suppose the simplest approach would be to begin with a two…
John
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How does the Bhattacharyya distance doesn't satisfy triangle inequality?

Googling doesn't seem to show many informative results. I don't know if the concept is too trivial that I should know immediately or it's an old topic. It's either article / blogs repeating the wiki or just explaining the calculation. In wiki, the…
zero heisenburg
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Bhattacharya Distance for Sets of Vectors

I have two sets of vectors and want to find a differentiable measure that can help quantify/approximate the degree of separability of the two sets. This metric might correlate well with the performance of a RF trained to separate the data. Looking…
Sauhaarda Chowdhuri
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