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Abstract Identifying genomic adaptation is key to understanding species' evolutionary responses to environmental changes. However, current methods to identify adaptive variation have two major limitations. First, when estimating genetic variation, most methods do not account for observational uncertainty in genetic data because of finite sampling and missing genotypes. Second, many current methods use phenomenological models to partition genetic variation into adaptive and non‐adaptive components.We address these limitations by developing a hierarchical Bayesian model that explicitly accounts for observational uncertainty and underlying evolutionary processes. The first layer of the hierarchy is the data model that captures observational uncertainty by probabilistically linking RAD sequence data to genetic variation. The second layer is a process model that represents how evolutionary forces, such as local adaptation, mutation, migration and drift, maintain genetic variation. The third layer is the parameter model, which incorporates our knowledge about biological processes. For example, because most loci in the genome are expected to be neutral, the environmental sensitivity coefficients are assigned a regularized prior centred at zero. Together, the three models provide a rigorous probabilistic framework to identify local adaptation in wild organisms.Analysis of simulated RAD‐seq data shows that our statistical model can reliably infer adaptive genetic variation. To show the real‐world applicability of our method, we re‐analysed RAD‐Seq data (~105 k SNPs) from Willow Flycatchers (Empidonax traillii) in the United States. We found 30 genes close to 47 loci that showed a statistically significant association with temperature seasonality. Gene ontology suggests that several of these genes play a crucial role in egg mineralization, feather development and the ability to withstand extreme temperatures.Moreover, the data and process models can be modified to accommodate a wide range of genetic datasets (e.g. pool and low coverage genome sequencing) and demographic histories (e.g. range shifts) to study climatic adaptation in a wide range of natural systems.