Model Based Inference

TL;DR

• Fit a mathematical model to observed data to draw conclusions or predict outcomes.
• Can represent relationships among multiple variables (e.g., dependent vs. independent variables).
• Widely applied in fields such as economics, engineering, and biology and can give more accurate predictions than simpler statistical methods.

Definition

Model-based inference is a statistical approach that involves the use of mathematical models to make predictions or inferences about a given set of data.

Explanation

This approach builds a mathematical representation of the system or process underlying the data and estimates the model parameters by fitting the model to observed data. Once fitted, the model is used to predict values or compute probabilities for events of interest. Model-based inference can account for multiple variables and the relationships between them, allowing inference about dependent variables from one or more independent variables.

Examples

Linear regression

A linear regression model is a model-based inference example where a linear equation describes the relationship between a dependent variable and one or more independent variables. By fitting the data to this linear model, predictions about the dependent variable can be made from given values of the independent variables.

Markov chain models

Markov chain models provide another example: the model consists of equations describing the likelihood of transitions between different states in a system. Fitting data to a Markov chain model enables prediction of probabilities for certain events, for example the likelihood of a customer purchasing a product based on their previous purchases.

Use cases

• Economics
• Engineering
• Biology

Related terms

• Mathematical models
• Linear regression
• Markov chain models
• Dependent variable
• Independent variables