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Table 10 Bayesian inference computing the posterior probability

From: Interferon-alpha 2 but not Interferon-gamma serum levels are associated with intramuscular fat in obese patients with nonalcoholic fatty liver disease

 

Mean

Std. dev.

MCSE

Median

[95% Cred. interval]

Equal-tailed

 d.v.: IMTG

     

i.v.: IFN-alpha 2

− 0.0151632

0.004142

0.000122

− 0.0151286

− 0.0229845 to 0.0069051

  Cons

4.46095

0.5110447

0.016827

4.460191

3.442408 to 5.436929

  Sigma2

0.8045077

0.1360474

0.003159

0.7905886

0.5719823 to 1.09947

  1. Default priors are used for model parameters. Simulations introduce an additional level of uncertainty to the accuracy of the estimates. Monte Carlo standard error (MCSE), which is the standard error of the posterior mean estimate, measures the simulation accuracy
  2. Using Bayesian linear regression we asked which parts (if any) of its fit to the data was it confident about, and which parts were very uncertain (perhaps based entirely on the priors). Looking at the ratio of MCSE to Std. dev. (in this case 0.000122/0.004142 = 0.029) we have 2.9%, i.e., minus than 5% (significant auto correlation)
  3. Little of the posterior variability is due to simulation, thus the model is valid
  4. d.v. dependent variable, i.v. independent variable