What is calculated using the product of the number of parameters and the logarithm of the number of observed samples?

The Schwarz Bayesian Information Criterion, commonly known as BIC, is calculated using the product of the number of parameters in a statistical model and the logarithm of the number of observed samples. This criterion is used for model selection among a finite set of models. Specifically, it helps to identify the model that best predicts future data while penalizing for complexity, effectively balancing model fit versus the risk of overfitting.

The formula for BIC incorporates the goodness of fit of the model (often based on likelihood measures) and imposes a penalty for the number of parameters, making it particularly useful in preventing overly complex models from being favored merely because they fit the data well. This characteristic helps ensure that simpler models are preferred unless a more complex model significantly improves the fit to the data.

In contrast, other options like the Hannan-Quinn criterion are alternatives for model selection but use different formulations or combinations of parameters and samples. The log likelihood measure assesses how likely the observed data is under specific parameters but does not account for model complexity. Mean absolute error, on the other hand, is a metric for evaluating the accuracy of a model's predictions but does not involve the logarithmic function or a penalty for model complexity.