Society of Actuaries (SOA) PA Practice Exam

What is the definition of bias in the context of model prediction?

1. The Expected Loss arising from model complexity

2. The Expected Loss arising from high variance

3. The Expected Loss arising from the model not being complex enough

4. The Expected Loss arising from overfitting the data

The correct answer is: The Expected Loss arising from the model not being complex enough

In the context of model prediction, bias refers to the error that is introduced by approximating a real-world problem, which may be extremely complex, by a simplified model. When a model is not complex enough to capture the underlying patterns in the data, it leads to systematic errors in predictions. This phenomenon is often referred to as high bias. Option C correctly identifies bias as the expected loss that stems from the model being overly simplistic or not complex enough. A model that is too simple may fail to learn from the data appropriately, resulting in underfitting, where the model does not perform well on either the training set or new, unseen data. The other choices represent different concepts within the bias-variance tradeoff framework. For instance, expected loss from model complexity relates more to variance, where a model's overly complex structure captures noise in the data rather than the underlying distribution. High variance contributes to overfitting, which is what those other options also address. Understanding bias helps in making informed decisions about model selection and complexity to achieve the right balance for optimal predictive performance.