How to characterize mathematical models for comparison

In summary, the conversation discussed the need to characterize mathematical models in order to compare them and weigh their advantages and disadvantages in a specific realm of wildlife biology. The speaker mentioned being unsure of essential model aspects and provided examples such as statistical vs dynamical, linear or nonlinear, and data requirements. They also referenced the complexity of creating a list of differential equations and applications and the need for valuable descriptions of both. Finally, the conversation ended with a question about the important advantages and disadvantages in the field of study.
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tez369
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TL;DR Summary
identifying components of a model
I am reviewing and comparing a wide range of mathematical models that are being applied to a specific realm of wildlife biology. For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model. As I do not yet have a great amount of experience working with models I am unsure of essential model aspects that can be used to characterize them. Examples that I have thought of are statistical vs dynamical, linear or nonlinear, heavy or low data requirement...
Can you provide a list of aspects you would use to characterize a model, to be used for comparison?
 
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  • #2
Any model is probably a system of differential equations. To list them is basically impossible as there are so many. Famous examples are Lotka-Volterra for predator prey models, or the SIR model for epidemics.
 
  • #3
There are a great many aspects to model and you have not specified what is being modeled. You might start with this article and the links in it and go from there to the specific type of model that you are interested in.
 
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  • #4
FactChecker said:
There are a great many aspects to model and you have not specified what is being modeled.
I remember a thread in which someone asked about a list of differential equations vs. applications, like a lexicon. I started and searched a few on the internet only to find out, that - if added valuable descriptions of both, model and application - this would turn into a job of decades! But it would certainly be of value.
 
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  • #5
tez369 said:
For the comparison of these models, and to weigh advantages/disadvantages of different aspects with regard to application, I need to characterize each model.

Specifically, what "advantages/disadvantages" are important "with regard to application" in your field of study?
 

1. What is the purpose of characterizing mathematical models for comparison?

The purpose of characterizing mathematical models for comparison is to understand the similarities and differences between different models and to determine which model is the most accurate or appropriate for a given situation. This allows for better decision making and prediction in various fields such as economics, biology, and physics.

2. How do you determine the complexity of a mathematical model?

The complexity of a mathematical model can be determined by looking at the number of variables, equations, and parameters used in the model. A more complex model will have a higher number of these elements, making it more difficult to understand and analyze.

3. What are the key factors to consider when comparing mathematical models?

The key factors to consider when comparing mathematical models include the assumptions made, the level of detail and accuracy, the predictive power, and the ability to explain real-world data. Other factors may include the computational efficiency and the simplicity of the model.

4. How do you validate a mathematical model?

A mathematical model can be validated by comparing its predictions to real-world data and observing how closely they match. This can be done through statistical analysis and hypothesis testing. Additionally, the model can be tested against different scenarios or conditions to see if it accurately predicts the outcomes.

5. What are the limitations of characterizing mathematical models for comparison?

One limitation of characterizing mathematical models for comparison is that it may not always be possible to accurately compare models due to differences in assumptions, data, or variables. Additionally, the complexity of some models may make it difficult to fully understand and compare them. It is also important to note that a model may be suitable for one situation but not for another, so it is important to consider the context when comparing models.

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