  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.
