We have extended the analysis of Jaffe et al . ( 13 , 15 ) to a complete Markov chain Monte Carlo ( MCMC ) parameter space study of the Bianchi type { VII _ { h } } models including a dark energy density , using Wilkinson Microwave Anisotropy Probe ( WMAP ) cosmic microwave background ( CMB ) data from the 1-year and 3-year releases . Since we perform the analysis in a Bayesian framework our entire inference is contained in the multidimensional posterior distribution from which we can extract marginalised parameter constraints and the comparative Bayesian evidence . Treating the left-handed Bianchi CMB anisotropy as a template centred upon the ‘ cold-spot ’ in the southern hemisphere , the parameter estimates derived for the total energy density , ‘ tightness ’ and vorticity from 3-year data are found to be : \Omega _ { tot } = 0.43 \pm 0.04 , h = 0.32 ^ { +0.02 } _ { -0.13 } , \omega = 9.7 ^ { +1.6 } _ { -1.5 } \times 10 ^ { -10 } with orientation \gamma = { 337 ^ { \circ } } ^ { +17 } _ { -23 } ) . This template is preferred by a factor of roughly unity in log-evidence over a concordance cosmology alone . A Bianchi type template is supported by the data only if its position on the sky is heavily restricted . All other Bianchi { VII _ { h } } templates including all right handed models , are disfavoured . The low total energy density of the preferred template , implies a geometry that is incompatible with cosmologies inferred from recent CMB observations . Jaffe et al . ( 14 ) found that extending the Bianchi model to include a term in \Omega _ { \Lambda } creates a degeneracy in the \Omega _ { m } - \Omega _ { \Lambda } plane . We explore this region fully by MCMC and find that the degenerate likelihood contours do not intersect areas of parameter space that 1 or 3 year WMAP data would prefer at any significance above 2 \sigma . Thus we can confirm the conclusion that a physical Bianchi { VII _ { h } } model is not responsible for this signature , which we have treated in our analysis as merely a template .