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Questions tagged [bhattacharyya]

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

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Comparing two two-dimensional probability distributions

I would like to compare two contour plots representing two probability distributions. These are not samples drawn from any known distribution, but the result of a physical calculation from a process ...
lethobentho's user avatar
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29 views

Decomposing into Gaussian components using Bhattacharya from topFishR

I am working with fishery data. I have a data vector called SFL that contains the sizes of the fish caught. Here is some sample data: ...
sermomon's user avatar
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Is there a sense in which collections of probability distributions with the same matrix of Bhattacharyya coefficients are "essentially the same"?

A popular measure of "closeness" between probability distributions $\vec{p_1}$, $\vec{p_2}$ is the Bhattacharyya coefficient $\sum_j \sqrt{p_{1,j} p_{2,j}}$. Consider two statistical models $...
user386365's user avatar
1 vote
1 answer
347 views

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 ...
zero heisenburg's user avatar
1 vote
1 answer
637 views

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 ...
Sauhaarda Chowdhuri's user avatar
3 votes
0 answers
517 views

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 ...
Richi W's user avatar
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1 answer
75 views

Convex variant of Bhattacharyya coefficient

For (discrete, finite) probability distributions $P,Q$, the Bhattacharyya coefficient is $B(P,Q) := \sum_x \sqrt{P_x Q_x}$. It can be shown that this is jointly concave in $P$ and $Q$. My question is, ...
helloworld's user avatar
1 vote
2 answers
206 views

Are Bhattacharyya coefficient and total variation distance complementary?

I was reading about total variation distance, and, as I understood it, it should measure how much two probability measures don't overlap. To be clear: in these images Bhattacharyya coefficient is ...
carlo's user avatar
  • 4,555
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0 answers
138 views

Type of logarithm in Jenson-Shannon and Bhattacharyya distance

Both Jenson-Shannon and Bhattacharyya distance can be used to measure the similarity of two probability distributions. Bhattacharyya distance between two distributions $p$ and $q$ is defined as $D_B(...
Peter B.'s user avatar
  • 111
5 votes
3 answers
2k views

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}-{...
Faiz Kidwai's user avatar
2 votes
1 answer
2k views

Comparison of two normal distribution

I have two normally distributed samples. I want to know how close or similar it is. I tried few methods to find the similarity, like z-score and bhattacharyya distance. Bhattacharyya distance didn't ...
Akhilesh's user avatar
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0 answers
42 views

Are these inequalites correct? (between variational distance and bhattacharyya distance and KL divergence) [closed]

I have some proof in terms of the definition explained
PIROOZ HOSNI ROKH's user avatar
1 vote
0 answers
617 views

Bhattacharyya distance and KL divergence show contradicting behavior

Bhattacharyya distance between two distributions $p$ and $q$ is defined as $D_B(p,q)=-\log(\int\sqrt{p(x)q(x)})dx$, The KL-divergence is defined as $D_{kl}(p||q)=\int p(x)\log(\frac{p(x)}{q(x)})dx$. ...
nomadr's user avatar
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16 votes
3 answers
15k views

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....
Lucas Roberts's user avatar
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2k views

Measuring the similarity of two distributions

What is the recommended approach to measure the similarity between two distributions of a variable—discrete and continuous? Is Bhattacharyya distance a good measure?
user3206440's user avatar
1 vote
2 answers
518 views

Is it correct to compute Bhattacharyya distance for Cauchy like, Bell shaped function?

I have the algorithm (MF (Membership function) ARTMAP Neural network). Output from this algorithm are clusters in n-dimensional feature space. Over each cluster (in n+1 dimension) there is some ...
user3635791's user avatar
7 votes
2 answers
11k views

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 ...
Jasper's user avatar
  • 73
5 votes
2 answers
377 views

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 ...
user112592's user avatar
3 votes
0 answers
148 views

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 ...
balletpiraat's user avatar
2 votes
1 answer
566 views

Bhattacharya Distance on Distributions (Matrices) with Different Number of Variables (Dimensions) [duplicate]

We have two matrices, $A$ and $B$, representing two different probability distributions, with dimensions, $m*n$ and $k*n$, respectively. How can we calculate the Bhattacharya distance or another ...
texmex's user avatar
  • 385
2 votes
0 answers
48 views

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+, ...
Katherine's user avatar
47 votes
2 answers
19k views

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 ...
JewelSue's user avatar
  • 573
4 votes
1 answer
3k views

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's user avatar
2 votes
1 answer
1k views

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 ...
Bruce's user avatar
  • 83
0 votes
0 answers
349 views

Statistical distance tests

I am using around 200 variables to compare 2 populations, group A and group B. Here's a representation of what the data looks like ...
Error404's user avatar
  • 1,431
5 votes
1 answer
1k views

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 ...
StereoMatching's user avatar
1 vote
0 answers
2k views

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 ...
John's user avatar
  • 2,287
1 vote
2 answers
6k views

Bhattacharyya distance for histograms

One of the ways to measure the similarity of two discrete probability distributions is the Bhattacharyya distance. In computer vision, for example, it is used to evaluate the degree of similarity ...
Gino Strato's user avatar
50 votes
6 answers
54k views

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 ...
Ali Salehi's user avatar