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High-dimensional categorical data models, often with inadequately large sample sizes, crop up in many fields of application. The SARS epidemic, originating in southern China in 2002, had an identified single-stranded and positive-sense RNA virus with large genome size and moderate mutation rate. The present genomic study is used as a prime illustration for motivating appropriate statistical methodology for comprehending the genomic variation in such high-dimensional categorical data models. Because of underlying restraints, a pseudomarginal approach based on Hamming distance is considered in a constrained statistical inference setup. The union-intersection principle and jackknifing methods are incorporated in exploring appropriate statistical procedures. [ABSTRACT FROM AUTHOR]