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On a fast consistent selection of nested models with possibly unnormalized probability densities
Journal article   Peer reviewed

On a fast consistent selection of nested models with possibly unnormalized probability densities

Rong Bian, Kung-Sik Chan, Bing Cheng and Howell Tong
Japanese journal of statistics and data science, Vol.9(3), pp.583-616
08/18/2026
DOI: 10.1007/s42081-026-00358-w

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Abstract

Models with unnormalized probability density functions are ubiquitous in statistics, artificial intelligence and many other fields. However, they face significant challenges in model selection if the normalizing constants are intractable. Existing methods to address this issue often incur high computational costs, either due to numerical approximations of normalizing constants or evaluation of bias corrections in information criteria. In this paper, we propose a novel and fast selection criterion for nested models of possibly dependent data, allowing direct data sampling from a possibly unnormalized probability density function. With a suitable multiplying factor depending only on the sample size and the model complexity, the proposed criterion gives a consistent selection under mild regularity conditions and is computationally efficient. Extensive simulation studies and real-data applications demonstrate the efficacy of this criterion in the selection of nested models with unnormalized probability densities.
 Unnormalized probability densities Gradient-based information criterion Consistent model selection Computational efficiency Nested models Markov dependent data

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