PriorVAE: encoding spatial priors with variational autoencoders for small-area estimation.

Area of Science:

• Statistical modeling
• Machine learning
• Spatial statistics

Background:

• Gaussian processes (GPs) are widely used in small-area spatial statistical modeling for their ability to capture spatial correlations and aid interpolation.
• However, standard GPs face computational limitations, hindering their scalability and practical application.

Purpose of the Study:

• To address the computational challenges of Gaussian processes in spatial statistics.
• To develop a novel deep generative modeling approach for efficient spatial inference.

Main Methods:

• Proposed PriorVAE, a method that approximates Gaussian process priors using variational autoencoders (VAEs).
• Spatial inference is performed by replacing the GP with a trained VAE decoder within a Bayesian sampling framework.
• The VAE maps spatial data to a low-dimensional, independent latent Gaussian space, enabling efficient computation.

Main Results:

• The PriorVAE approach enables highly efficient spatial inference by leveraging the VAE decoder.
• This method provides a tractable and user-friendly way to approximate spatial priors.
• Demonstrated effectiveness on Bayesian small-area estimation tasks.

Conclusions:

• PriorVAE offers a scalable and computationally efficient alternative to traditional Gaussian processes for spatial statistical modeling.
• The VAE-based approach facilitates faster and more accessible Bayesian inference in complex spatial settings.
• This deep generative modeling strategy enhances the practical utility of GPs in applied small-area estimation.