  First principle calculation of the QCD spectral functions (SPFs) based on the
lattice QCD simulations is reviewed. Special emphasis is placed on the Bayesian
inference theory and the Maximum Entropy Method (MEM), which is a useful tool
to extract SPFs from the imaginary-time correlation functions numerically
obtained by the Monte Carlo method. Three important aspects of MEM are (i) it
does not require a priori assumptions or parametrizations of SPFs, (ii) for
given data, a unique solution is obtained if it exists, and (iii) the
statistical significance of the solution can be quantitatively analyzed.
  The ability of MEM is explicitly demonstrated by using mock data as well as
lattice QCD data. When applied to lattice data, MEM correctly reproduces the
low-energy resonances and shows the existence of high-energy continuum in
hadronic correlation functions. This opens up various possibilities for
studying hadronic properties in QCD beyond the conventional way of analyzing
the lattice data. Future problems to be studied by MEM in lattice QCD are also
summarized.
