My Personal Blog - De Finetti’s theorem

Theorem: A sequence of random variables \((x_1, x_2, \dots)\) is infinitely exchangeable iff, for all n, \[ p(x_1, x_2, \dots, x_n) = \int \prod^{n}_{i=1} p(x_i|\theta) P(d\theta), \] for some measure \(P\) on \(\theta\).

(See Jordan and Broderick 2010)

References

Jordan, Michael I, and Tamara Broderick. 2010. “Lecture 1: History and De Finetti’s Theorem.” 2010. https://people.eecs.berkeley.edu/~jordan/courses/260-spring10/lectures/lecture1.pdf.

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Citation

BibTeX citation:

@online{li2023,
  author = {Li, Chengkun},
  title = {De {Finetti’s} Theorem},
  date = {2023-06-11},
  url = {https://pipme.github.io/posts/2023-06-11-De-Finetti-theorem/index-gist.html},
  langid = {en}
}

For attribution, please cite this work as:

Li, Chengkun. 2023. “De Finetti’s Theorem.” June 11, 2023. https://pipme.github.io/posts/2023-06-11-De-Finetti-theorem/index-gist.html.