Outliers can reveal critical insights or mask underlying issues, so dealing with them requires both statistical rigor and contextual awareness. In one project, outliers in customer spending data hinted at seasonal patterns previously unaccounted for, which reshaped our marketing model. When assessing outliers, I emphasize a nuanced approach: first, understanding whether they stem from measurement errors, rare events, or natural variability. I also use robust techniques like bootstrapping alongside standard methods to check if outliers disproportionately affect model accuracy. Each model should be a balance between accuracy, robustness, and interpretability, particularly in high-stakes environments like finance or healthcare.

When dealing with unexpected outliers in statistical models, it’s essential to take a methodical approach to maintain accuracy. Start by identifying and diagnosing the outliers using visual tools like boxplots or scatterplots, and statistical tests such as Grubbs' or Dixon's test. This helps determine whether the outliers are due to errors, rare events, or natural variability. Depending on the findings, you might transform the data using techniques like logarithmic or square root transformations to minimize the influence of extreme values.

If one "sees" the outliers, because they lie out, it is easy to remove them and launch the model. If one suspects the presence of outliers, one can use robust methods and/or resampling techniques to control the behavior of the parameters and their sensitivity. One may use the standard version of the model and its robust counterpart and check for differences. There are several heuristics for outlier detection, mainly if one uses numerical variables only.

If you remove the outlier be aware that you are choosing not to model some part of your sytem. That may be a measurment error, a rare event, or even some set of unknown variables converging to cause the divergence. Bootstrapping is a good check to see how much the outlier affects your model. If you want to quarentine a small number of values a Q-test is a good method for analyzing the probability the value came from a normal distribution at that point. The most important thing is being aware of why you are doing what you are doing, making choices about what you want to model and what effects you wantt o ignore.

You need to understand the origin of those outliers. Sometimes they are just falsified data that need to be corrected. Then there is no need to include those outliers in your model. If the outliers do exist, there must be a reason. A few ways to consider: (1). Can I set a cap and floor in the datasets? (2). Can I normalize the data with techniques such as z-scores? (3). Can I use the ranking of the data instead of the values? In all cases, you need to consider the rationale behind it. Data has its meaning in real life. It will be risky to do data mining blindly.