Define the term 'Bayesian inference.'

Bayesian inference refers to a statistical method in which the probability of a hypothesis is updated as new evidence is encountered. This approach is rooted in Bayes' theorem, which provides a formal mechanism for incorporating prior beliefs (or initial probabilities) and modifying them based on new data. As evidence accumulates, the inference adjusts, allowing for a more accurate representation of the probability associated with a particular hypothesis.

This method is powerful because it not only allows one to make predictions but also systematically incorporates uncertainty and adjusts predictions in light of new information. As a result, it is widely applicable across various fields, including machine learning, statistics, and decision-making processes in uncertain environments.

The other options do not capture this dynamic updating process integral to Bayesian inference. While statistical methods for analyzing linear relationships, improving algorithm efficiency, and quantifying model uncertainty through sampling are important concepts in their respective domains, they do not encompass the essence of Bayesian inference, which specifically focuses on the iterative updating of probabilities as new evidence emerges.