Introduction
Analytical modeling — the ability to simplify a real-world system and process it through mathematics (equations) and logical reasoning. These problems sometimes interact with one another, meaning that if they cannot be analyzed separately (like in horseracing), analysts can find it useful to break them into different components and apply mathematical principles individually for insights on making optimal decisions or optimizing systems.
Analytical modeling section
Problem Formulation:
Precise your imprecise problem clearly with objective function(s) and constraint(s).
Recognize the appropriate variables and parameters.
Model Development:
Formulate Mathematical Relationships — translate the relationships and dependencies in your problem into mathematical equations or logical expressions.
Consider uncertainty, variability and the temporal aspect.
Model Solution:
Analytic methods (solutions from calculus, linear algebra routines or optimization algorithms.)
Optional ( Step 2: Use software tools such as MATLAB, Python or special modeling software for help in the solution process).
Model Validation:
Test the model on real-world data by collecting it and comparing predictions to assess accuracy and reliability.
If, no, we then make changes to the model so that it fits better and can work its magic as a predictor of the target variable.
Model Interpretation:
Analyze the model to understand the problem and make interpretations
Present the impacts to the needs of decision makers
Types of Analytical Models
Deterministic Models:
ALL PARAMETER & VARIABLES ARE MADE KNOWN WITH CERTAINTY.
Some models include; Linear programming Network analysis Queuing theory
Stochastic Models:
Introduce the model with noise and randomness
Thoughts: Examples of these are probability theory, statistical models and simulation models.
Dynamic Models:
Systems that change over time.
Types of Models: Differential equations, difference equations, system dynamics model.
Where Analytical Modeling can be used
Engineering: Structural analysis, fluid dynamic systems, heat transfer and control system.
Economics: Predictive analysis for the economy, financial modelling and operations research.
Operations Research: Stock management, planning, and transport optimization.
Environmental Science: Climate modeling, pollution analysis & resource management
Social sciences — population dynamics, epidemiological modelling and social network analysis
