  Motivation: Assigning statistical significance accurately has become
increasingly important as meta data of many types, often assembled in
hierarchies, are constructed and combined for further biological analyses.
Statistical inaccuracy of meta data at any level may propagate to downstream
analyses, undermining the validity of scientific conclusions thus drawn. From
the perspective of mass spectrometry based proteomics, even though accurate
statistics for peptide identification can now be achieved, accurate protein
level statistics remain challenging.
  Results: We have constructed a protein ID method that combines peptide
evidences of a candidate protein based on a rigorous formula derived earlier;
in this formula the database $P$-value of every peptide is weighted, prior to
the final combination, according to the number of proteins it maps to. We have
also shown that this protein ID method provides accurate protein level
$E$-value, eliminating the need of using empirical post-processing methods for
type-I error control. Using a known protein mixture, we find that this protein
ID method, when combined with the Soric formula, yields accurate values for the
proportion of false discoveries. In terms of retrieval efficacy, the results
from our method are comparable with other methods tested.
  Availability: The source code, implemented in C++ on a linux system, is
available for download at
ftp://ftp.ncbi.nlm.nih.gov/pub/qmbp/qmbp_ms/RAId/RAId_Linux_64Bit
