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We present two different halo-independent methods to assess the compatibilityof several direct dark matter detection data sets for a given dark matter modelusing a global likelihood consisting of at least one extended likelihood and anarbitrary number of Gaussian or Poisson likelihoods. In the first method wefind the global best fit halo function (we prove that it is a unique piecewiseconstant function with a number of down steps smaller than or equal to amaximum number that we compute) and construct a two-sided pointwise confidenceband at any desired confidence level, which can then be compared with thosederived from the extended likelihood alone to assess the joint compatibility ofthe data. In the second method we define a "constrained parametergoodness-of-fit" test statistic, whose $p$-value we then use to define a"plausibility region" (e.g. where $p \geq 10\%$). For any halo function notentirely contained within the plausibility region, the level of compatibilityof the data is very low (e.g. $p < 10 \%$). We illustrate these methods byapplying them to CDMS-II-Si and SuperCDMS data, assuming dark matter particleswith elastic spin-independent isospin-conserving interactions or exothermicspin-independent isospin-violating interactions.

Assessing Compatibility of Direct Detection Data: Halo-Independent Global Likelihood Analyses