Descriptive analysis summarizes the data.
Given the daily data about fuel consumed by your car, calculating the average daily fuel consumption of your car would qualify as descriptive analysis that summarizes a feature (e.g., daily fuel consumption) of your car.
Suppose we have the daily data about number of miles traveled by your car, calculating the average daily fuel mileage of your car would also qualify as descriptive analysis. Unlike the determining the average daily fuel mileage, this analysis first combines two features to derive a new feature that further describes/characterizes your car and then summarizes the new feature.
In descriptive analysis, we focus on summarizing either original or derived features of an entity.
Inferential analysis extracts information about source entity of the data.
Continuing the previous example, suppose we also have data about the daily tire pressure of your car. Now, we can try to answer questions such as “does the tire pressure of your car influence the fuel mileage of your car?”, “Is the influence positive or negative?”, and “What is the magnitude of the influence?”
In inferential analysis, we focus on identifying relationships between features of entities.
In terms of time, inferential analysis is all about what happened in the past. So, the goal is to understand past data and answer questions about events that have occurred.
Predictive analysis predicts possible outcomes about the source entity of the data (assuming all things being equal).
Based on the previous year’s data, we know that the average fuel mileage of your car is 35 miles per gallon. Further, let’s assume we have inferred, for each psi drop in your car’s tire pressure from normal (recommended) tire pressure, your car’s fuel mileage drops by 2 miles per gallon. Now, if the tire pressure of your car is 3 psi below normal, then we can predict that you will be able to cover 290 miles with 10 gallons instead of 350 miles (independent of any previous observations of the tire pressure being 3 psi below normal).
Of course, the above prediction hinges on all things being equal. In other words, the prediction can go wrong if either the weather gets way colder or hotter than usual or the road you take is bumpier than usual or the traffic is slower than usual or any other reasons that can affect the prediction but have not been captured in the data or considered in the analysis.
In predictive analysis, assuming all things being equal, we focus on predicting the features of entities based on the inferred relationships between the features of entities. So, in some sense, predictive analysis is an extension of inferential analysis as the results of inference are used for prediction.
In terms of time, predictive analysis is kinda the dual of inferential analysis as it is all about what could have happened or can happen, i.e., both alternative past events that did not occur or possible future events. The goal is to understand past data and answer questions about events that have not occurred.
Prescriptive analysis uses the data to prescribe actions that can lead to desired outcome (assuming all things being equal).
Equipped with the results from the previous predictive analysis and the list of possible actions to increase tire pressure, we can now prescribe an action or a ranked list of actions to get good fuel mileage. So, if you mention that your fuel mileage is below (normal) 35 miles per gallon, then we can ask if the tire pressure is lower than normal? If you reply “yes, it is 24 psi instead of the normal tire pressure of 27 psi”, then we can prescribe that you increase the tire pressure by 3 psi (to 27 psi) to get normal fuel mileage.
In prescriptive analysis, we focus on prescribing actions to manipulate the features of entities to effect changes in features of entities. This aspect of manipulating the entities to effect desired future outcomes is a definitive aspect of prescriptive analysis.
In terms of time, unlike inferential analysis and predictive analysis, prescriptive analysis is all about what can happen in the future. The goal is to understand past data and prescribe actions that can lead to desired future events.
(This is minor edited version of this original post.)