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Computational Statistics in Data Science. Группа авторов
Читать онлайн.Название Computational Statistics in Data Science
Год выпуска 0
isbn 9781119561088
Автор произведения Группа авторов
Жанр Математика
Издательство John Wiley & Sons Limited
The goal is to estimate the posterior mean of . We implement an MCMC algorithm to estimate the posterior mean and implement the relative‐standard deviation sequential stopping rule via effective sample size.
We sample from the posterior distribution via a componentwise random walk Metropolis–Hastings algorithm updating first and then
, with step size for both components chosen so that the acceptance probability is around 30%. Since the posterior distribution is three‐dimensional, the minimum ESS required for
and
in Equation (7) is 8123. Thus, we first run the sampler for
and obtain early estimates of
and the corresponding effective sample size. We then proceed to run the sampler until ESSn using
and
with
in Equation (4) is more than 8123.
At , ESSn was 237, and the estimated density plot is presented in Figure 3 by the dashed line. We verify the termination criteria in Equation (7) incrementally, and simulation terminates at
iterations. The final estimated density is presented in Figure 3 by the solid line.
Figure 3 Estimated density of the marginal posterior for
At termination, the estimated posterior mean is , and 80% credible intervals are
,
, and
for
,
, and
, respectively.
It is possible to run a more efficient linchpin sampler [42] by integrating out from the posterior. That is,
, where