We propose a novel Bayesian method to analytically continue observables to real baryochemical potential $mu_B$ in finite density QCD. Taylor coefficients at $mu_B=0$ and data at imaginary chemical potential $mu_B^I$ are treated on equal footing. We consider two different constructions for the Pade approximants, the classical multipoint Pade approximation and a mixed approximation that is a slight generalization of a recent idea in Pade approximation theory. Approximants with spurious poles are excluded from the analysis. As an application, we perform a joint analysis of the available continuum extrapolated lattice data for both pseudocritical temperature $T_c$ at $mu_B^I$ from the Wuppertal-Budapest Collaboration and Taylor coefficients $kappa_2$ and $kappa_4$ from the HotQCD Collaboration. An apparent convergence of $[p/p]$ and $[p/p+1]$ sequences of rational functions is observed with increasing $p.$ We present our extrapolation up to $mu_Bapprox 600$ MeV.
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