Computational Statistics in Data Science. Группа авторов

Gamma left-parenthesis StartFraction n Over 2 EndFraction comma one half sigma-summation Underscript i equals 1 Overscript 8 Endscripts left-parenthesis y Subscript i Baseline minus beta 1 left-parenthesis 1 minus e Superscript minus beta 2 x Super Subscript i Superscript Baseline right-parenthesis right-parenthesis squared right-parenthesis"/>

      and

The sampler then proceeds to implement a random walk Metropolis–Hastings step to update , and a draw from yields a joint MCMC draw from the posterior. We empirically note that this linchpin variable sampler yields lower marginal autocorrelation in as illustrated by Figure 4.

      Repeating the previous procedure with the linchpin sampler, we have an estimated ESS at of 652, and the sequential stopping rule terminates at . The resulting estimates of posterior mean and quantiles are similar. Thus, using a more efficient sampler requires substantially fewer iterations to obtain estimates of similar quality.

Figure 4 Estimated autocorrelations for nonlinchpin sampler (a) and linchpin sampler (b).

      Note

1 For constructing simultaneous confidence intervals with approximately correct coverage, see Robertson et al. [10].

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