Propriety conditions for the Bayesian autologistic model - Inference for histone modifications

Area of Science:

• Statistics
• Bioinformatics
• Genomics

Background:

• Autologistic models are used for analyzing dependent categorical data, such as spatial or sequential patterns.
• Inference in these models can be challenging when using improper priors, which are sometimes necessary for computational or theoretical reasons.
• Histone modifications, which play a key role in gene regulation, are often analyzed using models that capture spatial dependencies.

Purpose of the Study:

• To investigate the use of improper priors in autologistic models.
• To derive conditions that guarantee posterior propriety for these models.
• To provide a theoretical foundation for analyzing complex biological data like histone modifications.

Main Methods:

• We considered an improper prior for the autologistic model, motivated by applications in histone modification inference.
• Sufficient conditions for posterior propriety were derived under a constant prior on the model's coefficients.
• Established results from multinomial logistic regression were adapted to prove posterior propriety.

Main Results:

• Sufficient conditions for posterior propriety were identified for autologistic models with improper priors.
• The derived conditions are straightforward to verify in practice.
• The theoretical framework supports the use of improper priors in specific autologistic model settings.

Conclusions:

• The study provides a method to ensure proper posteriors in autologistic models, even with improper priors.
• These findings are particularly relevant for statistical inference in bioinformatics, specifically for histone modification data analysis.
• The easily verifiable conditions simplify the application of these models in complex biological data analysis.