Math is a subject which has always followed a constant definition theorem which proof the structure of what you are trying to study. It does not matter if it is algebraic number or an analysis the structure the arguments are the same. Statistics is born out of necessity which can work on real data. This can be messy and does not give you a clean result. Statistics in itself is a separate discipline of math which can be different from maths as it is a study of uncertainty. Many statistician services use outliers which helps you remove or keep the data which is relevant and it is your judgement call.
Some common things that statistical models assume are
- A random variable in Gaussian distribution
- Two random independent variable
- Two random variables which satisfy linear relationship
- Variance is constant
When your data is a normal distribution there are certain when you have to decide where and how to break down the data to make it useful that can be applied to your judgement.
Classical vs Statistical Algorithms
There are many proofs on the ways to be sure about you being correct in both the mathematical and statistical way.
- Non-Statistical methods use theory to justify their correctness by the mathematical means of construction and formalized runtime which behave according to their inputs.
- Non-statistical algorithms focus on primarily on worst-case analysis to even out the worst possible input with the help of mathematical means.
- A statistical method is good to help analyse the data and understand the process which can give rise to predictions which is a crucial aspect in evaluating these statistical algorithms.
Many of these approach is theoretical in nature and impractical when deciding which model works best for a dataset. There are theories which can serve as a guideline to help determine the best parameters.
Modelling the real world
- Math and statistics is used as a tool where the model is used to understand the world in different ways which creates a clear model whereas statistics is the knowledge of uncertainty which tries to make sense of the data in randomness.
- Math is good for modelling domains as the rules are logical and can be expressed with the help of equations which is just a process with a set of numbers which is easy to predict in real world. This helps create an ideal world where everything concludes with a version of reality.
- Statistics is exceptionally good when the rules of the games are uncertain where the error is embraced and every value has a confidence interval.
- The main down side of statistics is their work on sample size which requires you to collect data but maths understands system at a deeper and fundamental level.