Interpreting CMB Anisotropy Observations: Trying to Tell the Truth with Statistics

A conflict has been reported between the baryon density inferred from deuterium observations and that found from recent CMB observations by BOOMERanG and MAXIMA. Despite the flurry of papers that attempt to resolve this conflict by adding new physics to the early universe, we will show that it can instead be resolved via a more careful usage of statistics. Indeed, the Bayesian analyses that produce this conflict are by their nature poorly suited for drawing this type of conclusion. A properly defined frequentist analysis can address this question directly and appears not to find a conflict. Finally, a conservative accounting of systematic uncertainties in measuring the deuterium abundance could reduce what is nominally a 3σ conflict to