Results - NIG Priors Sample Clauses

Results - NIG Priors. Normal-inverse-gamma priors are first employed in the Bayesian Armitage-Doll model to obtain the posterior estimate for the parameter of number of stages. The NIG priors are σ2 ∼ IG(a, d) and β|σ2 ∼ N (m, σ2 V ), where a and d are set as .001 and the prior for m is defined as (5, 5)r. I let V as 1000I and I is 2 by 2 identity matrix. As discussed previously, the posterior estimate of β which is E(β|y) = m∗ can be written Table 3.2: Fit of NIG priors in the Bayesian Armitage-Doll Model Cancer Estimate SD MCSE HPD Geweke Diagnostics pvalue Esophagus 6.27 0.57 .008 (5.14, 7.42) .89 Colon 4.99 0.28 .004 (4.44, 5.54) .35 Pancreas 6.33 0.34 .005 (5.64, 7.08) .28 Lung 6.84 0.36 .005 (6.13, 7.57) .05 Breast 3.94 0.40 .02 (3.11, 4.73) .80 Bladder 5.78 0.36 .005 (5.11, 6.53) .85 Stomach 4.51 .25 .003 (4.03, 5.00) .11 Overy 3.67 .25 .003 (3.17, 4.15) .86 Rectum 4.37 0.26 .004 (3.87, 4.89) .49 Cervix Uteri 0.56 0.22 .01 (0.15, 1.02) .82 as m∗ = (V —1 + XrX)—1(V —1m + XrXβˆ) = (I − A)m + Aβˆ, where A = (V —1 + XrX)—1XrX. The assumption for the above formulation is that XrX is non-singular matrix. In the log-normal Armitage-Doll model, I have  Σ logti (XrX)—1 = ,. n —1  Σ . logti