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In order to explore the mechanism for the genomic replication of classical swine fever virus (CSFV), so as to make a basis for investigating its pathogenicity, an introduction of the information theory is presented in connection with the statistical mechanics, whence small-sample statistics appears naturally as a consequence of the Bayesian approach. Furthermore, a selection rule for identifying the pattern of a recognition site for an RNA-binding protein is proposed by means of the maximum entropy principle. Based on those, the information contents of 3'-untranslated regions (3'UTRs) of genomes of 20 CSFV strains and 5'-untranslated regions (5'UTRs) of genomes of 58 CSFV strains are analyzed with a computational algorithm in a reduction mode, and the 3'UTR sites of 20 strains and 5'UTR sites of 58 strains containing important motifs are extracted from the unaligned RNA sequences of unequal lengths. These sites, which have the patterns of sequence and structure similar to the putative cis elements related to the regulation of genomic replication, would be identified as the potential recognition sites in 3'UTRs and 5'UTRs for CSFV replicase responsible for classical swine fever virus genomic replication, and to some extent, this identification is supported by experimental evidence. Finally, information analysis allows a presumption to be made about the CSFV RNA replication initiation mechanism.