Actuarial Notes

CAS Exam MAS-II Fall 2019, Question 30

Study guide: Exam MAS-II

A parameter's posterior is sampled using an MCMC algorithm. After discarding the warmup iterations, the first 6 samples from two chains from the sampler are provided in the order they were sampled:

chain 1 = {80, 100, 90, 90, 100, 110}

chain 2 = {95, 90, 85, 80, 70, 90}

Compute the Gelman-Rubin Convergence Diagnostic, \hat{R}, of the sampler.

  • A) Less than 0.85
  • B) Greater than or equal to 0.85 but less than 0.95
  • C) Greater than or equal to 0.95 but less than 1.05
  • D) Greater than or equal to 1.05 but less than 1.15
  • E) Greater than or equal to 1.15

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