While the Bayesian Information Criterion (BIC) and Akaike Information Criterion (AIC) are powerful tools for model selection in linear regression, they are built on different prior assumptions and thereby apply to different data generation scenarios. We show that their respective assumptions can be unified within an augmented model-plus-noise space and construct a prior in this space which inherits the beneficial properties of both AIC and BIC. The performance of our ‘Noncentral Information Criterion’ (NIC) matches or exceeds that of the AIC and BIC both for weak and strong signal cases. Improved Bayesian Information Criterion for Linear Regression

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