This paper presents a fast Markov Chain Monte-Carlo (MCMC) method for exploring cosmological parameter space. The authors perform a joint analysis of recent CMB data and other cosmological data, including HST Key Project, 2dF galaxy redshift survey, supernovae Ia, and big-bang nucleosynthesis. They present results from 6, 9, and 11 parameter models, including constraints on the neutrino mass (m_ν < 0.3 eV), the equation of state of dark energy, and the tensor amplitude. The MCMC method allows for the rapid investigation of a large number of parameters and provides a way to compute results from new data and correct for inaccuracies in approximate methods. The authors also discuss the effect of different priors, the goodness of fit, and the use of analytic marginalization over normalization parameters. The paper describes the use of importance sampling to compute results from new data and correct for small theoretical effects. It also discusses the different ways of converting parameter samples to parameter constraints and the effect of the prior. The authors use the fast Boltzmann code CAMB to compute theoretical predictions and find that their results are limited by the accuracy of the data. They also discuss the use of the MCMC method for parameter estimation and the importance of using a proposal density that is similar in shape to the posterior distribution. The authors find that the 6-parameter model is well constrained by the data, with tight constraints on Ω_b and n_s. They also find that the 9-parameter model is well constrained by the data, with upper limits on several interesting cosmological parameters. The 11-parameter model has slightly weaker constraints, but the standard cosmology of w = -1 and Ω_K = 0 is near the peak of the posterior probability. The tensor spectral index is essentially unconstrained, as expected given that the only information comes from the large scale CMB data. The authors conclude that the MCMC method is a powerful tool for cosmological parameter estimation, allowing for the exploration of high-dimensional posterior distributions and the identification of degeneracies. They also find that the method is robust to the addition of new data and that the results are not significantly affected by the choice of prior. The authors also note that the method can be applied to future data as the number of likelihood evaluations in the MCMC method is much smaller than in other approaches.This paper presents a fast Markov Chain Monte-Carlo (MCMC) method for exploring cosmological parameter space. The authors perform a joint analysis of recent CMB data and other cosmological data, including HST Key Project, 2dF galaxy redshift survey, supernovae Ia, and big-bang nucleosynthesis. They present results from 6, 9, and 11 parameter models, including constraints on the neutrino mass (m_ν < 0.3 eV), the equation of state of dark energy, and the tensor amplitude. The MCMC method allows for the rapid investigation of a large number of parameters and provides a way to compute results from new data and correct for inaccuracies in approximate methods. The authors also discuss the effect of different priors, the goodness of fit, and the use of analytic marginalization over normalization parameters. The paper describes the use of importance sampling to compute results from new data and correct for small theoretical effects. It also discusses the different ways of converting parameter samples to parameter constraints and the effect of the prior. The authors use the fast Boltzmann code CAMB to compute theoretical predictions and find that their results are limited by the accuracy of the data. They also discuss the use of the MCMC method for parameter estimation and the importance of using a proposal density that is similar in shape to the posterior distribution. The authors find that the 6-parameter model is well constrained by the data, with tight constraints on Ω_b and n_s. They also find that the 9-parameter model is well constrained by the data, with upper limits on several interesting cosmological parameters. The 11-parameter model has slightly weaker constraints, but the standard cosmology of w = -1 and Ω_K = 0 is near the peak of the posterior probability. The tensor spectral index is essentially unconstrained, as expected given that the only information comes from the large scale CMB data. The authors conclude that the MCMC method is a powerful tool for cosmological parameter estimation, allowing for the exploration of high-dimensional posterior distributions and the identification of degeneracies. They also find that the method is robust to the addition of new data and that the results are not significantly affected by the choice of prior. The authors also note that the method can be applied to future data as the number of likelihood evaluations in the MCMC method is much smaller than in other approaches.