heidel.diag is a run length control diagnostic based on a criterion of relative accuracy for the estimate of the mean. The default setting corresponds to a relative accuracy of two significant digits.

heidel.diag also implements a convergence diagnostic, and removes up to half the chain in order to ensure that the means are estimated from a chain that has converged.

Stationarity start p-value

test iteration

sigmapi_MP passed 1 0.29851

sigmapi_R failed NA 0.00127

mupi_oF passed 1 0.14574

sigmapi_oF passed 1 0.28920

diffF_1SW passed 1 0.11100

diffF_MSW passed 1 0.11554

diff1SW passed 501 0.05261

diffMSW passed 1 0.40440

pi_oD passed 1 0.13998

shape_lambda passed 1 0.89298

rate_lambda passed 1 0.89803

lambda_tot0 passed 1 0.31651

Halfwidth Mean Halfwidth

test

sigmapi_MP passed 0.3491 2.25e-02

sigmapi_R <NA> NA NA

mupi_oF passed 0.7872 3.75e-02

sigmapi_oF failed 1.1734 5.64e-01

diffF_1SW failed -0.1038 1.53e-02

diffF_MSW passed -0.8611 2.92e-02

diff1SW failed 0.5074 1.06e-01

diffMSW failed 0.9013 1.11e-01

pi_oD passed 0.2146 1.72e-02

shape_lambda passed 6.4713 3.11e-01

rate_lambda passed 0.0104 5.17e-04

lambda_tot0 passed 616.8054 2.77e+01

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Geweke's convergence diagnostic

Geweke (1992) proposed a convergence diagnostic for Markov chains based on a test for equality of the means of the first and last part of a Markov chain (by default the first 10% and the last 50%).

If the samples are drawn from the stationary distribution of the chain, the two means are equal and Geweke's statistic has an asymptotically standard normal distribution.

The test statistic is a standard Z-score: the difference between the two sample means divided by its estimated standard error. The standard error is estimated from the spectral density at zero and so takes into account any autocorrelation.

The Z-score is calculated under the assumption that the two parts of the chain are asymptotically independent, which requires that the sum of frac1 and frac2 be strictly less than 1.