Is the Multivariate Urn Problem Related to Discrete Distribution Theory?

In summary, the conversation revolves around a problem involving two urns with different colored balls and the desire to determine how many balls were drawn from each urn without knowing the exact origin of the balls. The suggestion is made to look into Discrete Distribution Theory and the multinomial distribution as potential solutions to this problem. References in books or journal articles on Statistics, Probability, and Discrete Distribution Theory may be helpful.
  • #1
rosa
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Hello, we are trying to solve a problem for which we would appreciate any reference that you could give us. The problem is as follows. We have two urns. Each urn contains balls in different colors. The exact number of balls of each color in each urn is known.

Imagine that we extract a number N of balls from these two urns, but we don’t know which balls have been extracted from which. We would like to know how many have been drawn from urn 1, and how many from urn 2.

We are wondering whether this is something standard in statistics, or whether it is an application that someone has solved before.

Any hints appreciated!
 
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  • #2
Thank you!This problem may have connections to a subset of statistics called Discrete Distribution Theory. In particular, it may be related to the multinomial distribution, which can be used to model the probability of drawing different numbers of balls of different colors from each urn. You may find some useful references related to this in books or journal articles on Statistics, Probability, and Discrete Distribution Theory.
 

1. What is the Multivariate urn problem?

The Multivariate urn problem is a statistical problem that involves randomly selecting objects from multiple urns with different proportions of objects. It is often used in research and data analysis to model real-world scenarios where there are multiple categories or groups.

2. How is the Multivariate urn problem different from the traditional urn problem?

The traditional urn problem involves randomly selecting objects from a single urn with a known proportion of objects. In contrast, the Multivariate urn problem involves randomly selecting objects from multiple urns with varying proportions of objects, making it a more complex problem to solve.

3. What are some real-world applications of the Multivariate urn problem?

The Multivariate urn problem has many practical applications, such as in market research to analyze consumer behavior, in genetics to study the distribution of genes in a population, and in political science to understand voting patterns in different demographic groups.

4. How is the Multivariate urn problem solved?

The Multivariate urn problem can be solved using various statistical methods, such as the maximum likelihood estimation or the Bayesian approach. These methods involve using mathematical equations and algorithms to estimate the proportions of objects in each urn based on the observed data.

5. What are some challenges associated with the Multivariate urn problem?

One of the main challenges of the Multivariate urn problem is determining the most appropriate statistical method to use, as different methods may yield different results. Additionally, the problem can become increasingly complex when there are a large number of urns or when the proportions of objects in each urn are very similar.

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