Replicability is the cornerstone of scientific research. We study the replicability of data from high-throughput experiments, where tens of thousands of features are examined simultaneously. Existing replicability analysis methods either ignore the dependence among features or impose strong modelling assumptions, producing overly conservative or overly liberal results. Based on $p$-values from two studies, we use a four-state hidden Markov model to capture the structure of local dependence. Our method effectively borrows information from different features and studies while accounting for dependence among features and heterogeneity across studies. We show that the proposed method has better power than competing methods while controlling the false discovery rate, both empirically and theoretically. Analyzing datasets from genome-wide association studies reveals new biological insights that otherwise cannot be obtained by using existing methods.

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