The correct answer is: All of the mentioned.
A deterministic set of equations is a set of equations that have a unique solution for each set of initial conditions. This means that if you know the initial conditions of a system, you can use the deterministic set of equations to predict the future state of the system.
Predictive analysis is the use of data and statistical models to make predictions about future events. Causal analysis is the study of the relationships between cause and effect. Mechanistic analysis is the study of the underlying mechanisms that cause things to happen.
All of these types of analysis can be modeled by deterministic set of equations. For example, you could use a deterministic set of equations to predict the future price of a stock, to study the relationship between smoking and lung cancer, or to understand the mechanism by which a drug works.
Deterministic set of equations are often used in predictive analysis because they can provide accurate predictions. However, they can also be used in causal analysis and mechanistic analysis. In causal analysis, deterministic set of equations can be used to identify the cause of an event. In mechanistic analysis, deterministic set of equations can be used to understand the underlying mechanisms that cause things to happen.
Deterministic set of equations are a powerful tool that can be used to understand and predict the future.