# Mathematical Modelling

Mathematical modelling is the art of turning a business problem into a clear mathematical formulation. This abstraction and its subsequent algorithmic implementation generate insights, answers, and understanding in order to enable knowledge- and data-driven decision-making.

## Start with the use case, not the data

We use mathematical modelling to put your business problems squarely into focus. This method can be applied to anything from the strategic allocation of your advertising budget across marketing channels to technical IoT issues. You could, for example, use forecasting to determine the optimal operational mode for a physical or machine process for which you already have a great deal of domain-specific knowledge.

## Modelling means understanding

We begin by talking to your domain experts in order to fully understand the use case in question. We then use the insights gained to analyse the existing data and formulate a comprehensive mathematical model. This model covers everything from the cost functions (KPIs) to be optimised to the use case’s underlying mechanisms and relationships.

As simple as possible, as complex as necessary.

We use your data to validate model-based hypotheses and then to calibrate the model’s parameters. Mathematical modelling is very similar to machine learning, in that data is used to train the model for a specific use case. The big difference, however, is that mathematical modelling does not rely on universal, one-size-fits-all approximation methods. Instead, it uses existing domain knowledge to choose the method that best suits each case. Our approach is “As simple as possible, as complex as necessary”.

### Causality trumps correlation

Mathematical modelling is particularly suited for supporting use cases which require the understanding of causal mechanisms, such as generating recommendations for marketing activities. Our models allow us to go beyond mere predictions to provide practical (prescriptive) insights for action. This method adds a great deal of value compared to machine learning methods, which are often based on pure correlation.

### Data efficiency is crucial — even for big data

As mathematical models rely heavily on domain knowledge, they are significantly more data-efficient than other types of models. Even though we live in the big-data era, labelled data is often scarce. Especially in industrial use cases, data is often highly imbalanced or has low variance. We can use specialised methods to represent and consistently estimate hierarchically structured data, as well as censored, truncated, or zero-inflated distributions.

This is in contrast to traditional machine-learning approaches, which learn these structures solely from the data fed to the model (without the benefit of domain-specific knowledge) and which are, therefore, much more data-greedy.

### Transparent, interpretable, and explainable

By design, mathematical models focus on interpretability and explainability. The models’ mechanics are therefore transparent, allowing for much easier detection of biases and discrimination. This becomes particularly important when we want to use a model to support high-stakes decisions in sensitive areas, such as medicine, justice, security, or vehicle-related applications. Mathematical models also outperform machine-learning methods when it comes to extrapolation tasks, such as predicting behaviour outside the range of the data already observed.

## Partnering with inovex

Choosing inovex as your partner enables you to benefit from our broad experience in different fields of mathematical modelling, such as causal modelling, hierarchical modelling, Bayesian methods or uncertainty quantification.

We would recommend beginning our collaboration with one of our workshops, where we can discuss your use case and available data in order to determine the appropriate approach.

Get in touch!

### Florian Wilhelm

Head of Data Science, Contact for Data Management & Analytics