# Assumptions

While learning about the cause and effect relationships within causal Inference, **assumptions** play a very important role. In Machine Learning models as well, we do have assumptions. It's just that the assumptions are already embedded within the data, which we assume to be true. We usually do not have all the data on the population for the predictions, hence we need to make some strong assumptions to fill these missing values. These assumptions are about how the **Data Generating Process(DGP).**

Especially, when we are dealing with observational data (which is most of the data that we have), there is a necessity to add "**Assumptions**" for making causal conclusions from data.

**NOTE:** *If we had all the data we really need we would not need assumptions because in such case, all the assumptions about the population would be already present in the data.*

The misconception that most people have here is that statistical Inference on the selected data can be used for making conclusions. **Let's start it from the beginning!!**

**What is Population?** It is the collected data of all the existing items that are present in this world in regard to our question of interest.

**What is a Sample?** It is a random, small subset data of this population data.

Take any example and consider the definition of these again. **Example**: let's try to calculate the avg height of men in the United States. My Population here is every man (**All of them**) in the United States, that's what we need to consider for making a conclusion(decision) here. If we go and calculate the height of every man, its easy to conclude and make a very accurate conclusion on this. But this is the real world, and let's be realistic, it's not a smart approach. Now we take a sample of the population of men and make a conclusion from their height. Since calculating the real height of every man is not possible here, we make the best guess about it using statistics(we should be aware of Selection Bias here). Now if our data is of all the tall people in the US, then your assumption about the avg height of men in the US will be different from someone who had data of men with shorter height. The conclusion is different in both cases as the population considered is different!! **But the problem is that we are treating our sample as our population here**.

**Facts** :

1. The more accurate data you have more precise is your conclusion.&#x20;
2. Acknowledging the fact that we are dealing with uncertainty.&#x20;

**INFERENCE (Prediction) = DATA + ASSUMPTIONS**

* Now if we had data or facts about all the population of interest, we wouldn't need these assumptions. Now I think we can agree that in most cases we do not have the actual population data, hence we do not have the real facts with us. Which in other words mean there is a gap within what we know and what we wish we knew. Assumptions are the connecting path from our past data to making inferences about what we want to predict or infer.

***The assumption is a very important part of decision-making process!!***

When we analyze data, we assume all of it is captured without errors. The human brain also works on past data. We like something because our past experience has been positive with regards to that particular thing. It all works on past experiences or past examples or past data. But when we find bias or some misconceptions within these examples, it makes assumptions more important. **Maybe the word assumption makes it sound a little vague(hard to accept). We can consider assumptions as "teaching" or "Data Generating Rules".**

**Examples of assumptions in real life**:

1. When we are using a calculator for adding our bills, we assume that the mathematical formulas embedded in the machine are correct
2. When we drive our Tesla, we trust the company for its 5-star safety promises. We trust the company
3. When we pay our bills or transfer the money to someone, we assume the systems are secure and the transaction will go as planned in the right hands.
4. We all have been making some strong assumptions in our daily lives, which has been affecting our day to day decisions.

## **Problem**:

* People can have different assumptions which can lead to different conclusions. We see it while analyzing the data, different people come can come out with different conclusions.

## **Solution**:

1. **Domain Expert**: This is where domain experts come in, and where their domain expertise can be used to unlock the true assumptions that we need to make about the data generating process. **Example**: A researcher in the field of Healthcare or a doctor would have more knowledge about the factors affecting COVID 19 compared to others. Hence their assumptions would be a more accurate depiction of the true Causal DAG.
2. **Sensitivity Analysis**
3. **Testing and specifying Assumptions:**&#x20;

## **Conclusion**:

**We need to formalize Assumptions**. We make some assumptions, combine it with data and then make an actionable decision. Assumptions are the source for us to cope up with the facts and information that is lacking in our decision-making process.

## **Resource**:

<https://towardsdatascience.com/the-saddest-equation-in-data-science-e60e7819b63f>

<https://towardsdatascience.com/statistician-proves-that-statistics-are-boring-4fc22c95031b>
