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Table 5 Average posterior inference on herd variances from ten replicates using the bivariate Student's-t (BSt) and normal (BN) fitted models with different residual degrees of freedom (DF).

From: Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects

  

Fitted Model2

  

BS t

BN

True Parameters

True Model1

PM ± SE3

95% PPI4

ESS5

PM ± SE

95% PPI

ESS

= 1.5

BSt-4

1.71 ± 0.10

[1.07, 2.56]

12,027

1.74 ± 0.14

[1.01, 2.71]

10,437

 

BSt-12

1.82 ± 0.12

[1.19, 2.65]

16,133

1.82 ± 0.12

[1.18, 2.65]

16,802

 

BN-∞

1.71 ± 0.08

[1.12, 2.48]

17,543

1.70 ± 0.08

[1.12, 2.47]

17,537

= 6.0

BSt-4

6.33 ± 0.30

[4.47, 8.79]

24,120

6.49 ± 0.28

[4.47, 9.17]

22,810

 

BSt-12

6.69 ± 0.28

[4.77, 9.22]

27,704

6.72 ± 0.24

[4.79, 9.28]

27,956

 

BN-∞

6.33 ± 0.27

[4.55, 8.71]

29,800

6.33 ± 0.27

[4.55, 8.71]

29,881

  1. 1Used to simulate data
  2. 2Used in analysis of simulated data
  3. 3Posterior mean ± Standard Error
  4. 495% equal-tailed posterior probability interval based on the 2.5thand 97.5thpercentiles of the posterior density
  5. 5Effective sample size