Web Appendix for “ Convergence Rate of Markov Chain Methods for Genomic Motif

• w: fixed motif length. • L: length of the observed nucleotide sequence S. • M : known number of nucleotide types (typically =4 in practice). • J : number of motifs in the generative model (defined in Assumption 3.2) • p0: fixed motif frequency in the inference model (defined Section 2.1). • S = (S1, . . . , SL): observed sequence of nucleotides (defined Sec. 2.1). • A = (A1, . . . , AL/w): unknown vector of motif indicators (defined Sec. 2.1). • X = {0, 1}: space of possible values for A (defined in Sec. 2.1). • θ0: unknown length-M vector of background nucleotide frequencies (defined Sec. 2.1). • θ1:w = (θ1, . . . ,θw): unknown matrix of position-specific nucleotide frequencies within the motif, where θk has length M (defined Sec. 2.1). • N(A); N(A); N(S): length-M nucleotide count vectors defined in (2.1). • A[−i]: vector A with ith element removed; A[i,0],A[i,1]: vector A with ith element replaced by 0 or 1, respectively.