Lesson plan
Concentration parameter
In probability theory and statistics, a concentration parameter is a special kind of numerical parameter of a parametric family of probability distributions. Concentration parameters occur in two kinds of distribution: In the Von Mises–Fisher distribution, and in conjunction with distributions whose domain is a probability distribution, such as the symmetric Dirichlet distribution and the Dirichlet process. The rest of this article focuses on the latter usage. The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution (the more it tends towards the uniform distribution). The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with most values or ranges of values having a probability near zero (in other words, the more it tends towards a distribution concentrated on a single point, the degenerate distribution defined by the Dirac delta function).
Article summary
In probability theory and statistics, a concentration parameter is a special kind of numerical parameter of a parametric family of probability distributions. Concentration parameters occur in two kinds of distribution: In the Von Mises–Fisher distribution, and in conjunction with distributions whose domain is a probability distribution, such as the symmetric Dirichlet distribution and the Dirichlet process. The rest of this article focuses on the latter usage. The larger the value of the concentration parameter, the more evenly distributed is the resulting distribution (the more it tends towards the uniform distribution). The smaller the value of the concentration parameter, the more sparsely distributed is the resulting distribution, with most values or ranges of values having a probability near zero (in other words, the more it tends towards a distribution concentrated on a single point, the degenerate distribution defined by the Dirac delta function).
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
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- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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