MATLAB Implementation of Bayesian Information Criterion (BIC) for Model Selection

This MATLAB function computes the Bayesian Information Criterion (BIC), a statistical measure that evaluates model quality by balancing goodness-of-fit against model complexity. The implementation follows the standard BIC formula: BIC = -2*log-likelihood + k*log(n), where k represents the number of model parameters and n is the sample size. The code structure includes: Key computational components: 1. Likelihood function calculation using probability distributions specific to the model type 2. Parameter counting mechanism that automatically detects free parameters in the model 3. Sample size validation to ensure statistical robustness The algorithm handles both maximum likelihood estimation (MLE) and Bayesian inference scenarios. For MLE applications, the code incorporates optimization routines to find parameter values that maximize likelihood while minimizing BIC score. The implementation includes error checking for numerical stability and supports various data types including continuous, discrete, and categorical variables. This flexible implementation allows customization for different statistical models including linear regression, Gaussian mixture models, and time series analysis. The function returns both the BIC value and comparative metrics for model selection tasks. Users can easily integrate this code into machine learning pipelines, statistical modeling workflows, and automated model selection systems. The Bayesian Information Criterion serves as a crucial tool for preventing overfitting while identifying models that best capture underlying data patterns without excessive complexity.