Abstract
Reproducibility is regularly framed as a binary question of whether a result replicates, which oftentimes assumes exact replication. In practice, replications differ in consequential ways such as design, data, modeling assumptions, and inferential procedures, resulting in non-exactness under the idealized-experiment framework. This thesis develops a hierarchical statistical model governed by the Beta-Binomial distribution and its mean-dispersion reproducibility parameters to analyze non-exact replicability at three different levels. For a single lineage of related replication studies, heterogeneity from non-exact replications creates an asymptotic variance floor that undermines increasing replication attempts. At the field level, the framework extends to a partition of scientific attention across many lineages, where partition geometry and lineage-specific reproducibility profiles jointly shape field-wide variation. To make field structure dynamic, the thesis builds on Hoppe's urn and the Ewens sampling formula to introduce a modified urn in which successful replications reinforce their own lineage while failures redirect attention toward other extant lineages or innovation. Simulation shows that reproducibility, persistent heterogeneity, and selective reinforcement jointly shape fragmentation, consolidation, and the distribution of scientific attention over time.