Table 2. Diagnostics for the Markov Chain Monte Carlo posterior samples for parameters r, k, q, σ p 2 , σ o 2 , P₁₉₉₉

Parameters	DF	Lag-1 autocorrelation	Naïve / time series	Posterior shape
r	1.04	0.00	1.03	Unimodal
k	1.02	−0.02	1.00	Unimodal
q	1.03	0.00	1.00	Unimodal
σ p 2	0.99	−0.00	1.00	Unimodal
σ o 2	0.98	−0.01	1.00	Unimodal
P1999	1.06	0.02	0.94	Unimodal

The dependence factor of Raftery-Lewis statistics (DF), lag-1 autocorrelation, ratio of naïve standard error to time series standard error, and the shape of posterior distributions were checked.