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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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19 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(...
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58 views

Can Bhattacharyya coefficient (or distance) be used as an additive measure to compute a metric for performance?

As far as I understand, Bhattacharyya's measure(s) can be used to see similarity between two empirical distributions. Other ways to do so are nicely explained here: Similarity measure between multiple ...
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2answers
246 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}-{...
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1answer
132 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 ...
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19 views

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

I have some proof in terms of the definition explained
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356 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 $D_{kl}(p||q)=\int p(x)\log(\frac{p(x)}{q(x)})dx$. ...
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5k 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....
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720 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?
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1answer
286 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 ...
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2answers
4k 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 ...
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2answers
222 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 ...
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94 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 ...
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1answer
303 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 ...
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40 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+, ...
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2answers
10k 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 ...
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1answer
1k 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? Thank you.
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1answer
827 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 ...
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260 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 ...
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1answer
997 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 ...
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1k 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 ...
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2answers
5k 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 ...
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6answers
43k 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 ...