# Statistical Modeling

## Statistical Modeling Definition

Statistical modeling is the use of mathematical models and statistical assumptions to generate sample data and make predictions about the real world. A statistical model is a collection of probability distributions on a set of all possible outcomes of an experiment.

## What is Statistical Modeling?

Statistical modeling refers to the data science process of applying statistical analysis to datasets. A statistical model is a mathematical relationship between one or more random variables and other non-random variables. The application of statistical modeling to raw data helps data scientists approach data analysis in a strategic manner, providing intuitive visualizations that aid in identifying relationships between variables and making predictions.

Common data sets for statistical analysis include Internet of Things (IoT) sensors, census data, public health data, social media data, imagery data, and other public sector data that benefit from real-world predictions.

## Statistical Modeling Techniques

The first step in developing a statistical model is gathering data, which may be sourced from spreadsheets, databases, data lakes, or the cloud. The most common statistical modeling methods for analyzing this data are categorized as either supervised learning or unsupervised learning. Some popular statistical model examples include logistic regression, time-series, clustering, and decision trees.

Supervised learning techniques include regression models and classification models:

• Regression model: a type of predictive statistical model that analyzes the relationship between a dependent and an independent variable. Common regression models include logistic, polynomial, and linear regression models. Use cases include forecasting, time series modeling, and discovering the causal effect relationship between variables.
• Classification model: a type of machine learning in which an algorithm analyzes an existing, large and complex set of known data points as a means of understanding and then appropriately classifying the data; common models include models include decision trees, Naive Bayes, nearest neighbor, random forests, and neural networking models, which are typically used in Artificial Intelligence.

Unsupervised learning techniques include clustering algorithms and association rules:

• K-means clustering: aggregates a specified number of data points into a specific number of groupings based on certain similarities.
• Reinforcement learning: an area of deep learning that concerns models iterating over many attempts, rewarding moves that produce favorable outcomes and penalizing steps that produce undesired outcomes, therefore training the algorithm to learn the optimal process.

There are three main types of statistical models: parametric, nonparametric, and semiparametric:

• Parametric: a family of probability distributions that has a finite number of parameters.
• Nonparametric: models in which the number and nature of the parameters are flexible and not fixed in advance.
• Semiparametric: the parameter has both a finite-dimensional component (parametric) and an infinite-dimensional component (nonparametric).

## How to Build Statistical Models

The first step in building a statistical model is knowing how to choose a statistical model. Choosing the best statistical model is dependent upon several different variables. Is the purpose of the analysis to answer a very specific question, or solely to make predictions from a set of variables? How many explanatory and dependent variables are there? What is the shape of the relationships between dependent and explanatory variables? How many parameters will be included in the model? Once these questions are answered, the appropriate model can be selected.

Once a statistical model is selected, it must be built. Best practices for how to make a statistical model include:

• Start with univariate descriptives and graphs. Visualizing the data helps with identifying errors, understanding the variables you’re working with, how they look, how they are behaving and why.
• Build predictors in theoretically distinct sets first in order to observe how related variables work together, and then the outcome once the sets are combined.
• Next, run bivariate descriptives with graphs in order to visualize and understand how each potential predictor relates individually to every other predictor and to the outcome.
• Frequently record, compare and interpret results from models run with and without control variables.
• Eliminate non-significant interactions first; any variable involved in a significant interaction must be included in the model by itself.
• While identifying the many existing relationships between variables, and categorizing and testing every possible predictor, be sure not to lose sight of the research question.

## Statistical Modeling vs Mathematical Modeling

Much like statistical modeling, mathematical modeling translates real-world problems into tractable mathematical formulations whose analysis provides insight, results and direction useful for the originating application. However, unlike statistical modeling, mathematical modeling involves static models that represent a real-world phenomenon in mathematical form. Once a mathematical model is formulated, it does not necessitate change. Statistical models are flexible and, with the aid of machine learning, can incorporate new, emerging patterns and trends, and will adjust with the introduction of new data.

## Machine Learning vs Statistical Modeling

Machine learning is a subfield of computer science and artificial intelligence that involves building systems that can learn from data rather than explicitly programmed instructions. Machine learning models seek out patterns hidden in data independent of all assumptions, therefore predictive power is typically very strong. Machine learning requires little human input and does well with large numbers of attributes and observations.

Statistical modeling is a subfield of mathematics that seeks out relationships between variables in order to predict an outcome. Statistical models are based on coefficient estimation, are typically applied to smaller sets of data with fewer attributes, and require the human designer to understand the relationships between variables before inputting.

## Statistical Modeling Software

Statistical modeling software are specialized computer programs that help gather, organize, analyze, interpret and statistically design data. Advanced statistics software should provide data mining, data importation, analysis and reporting, automated data modeling and deployment, data visualization, multi-platform support, prediction capabilities, and an intuitive user interface with statistical features ranging from basic tabulations to multilevel models. Statistical software is available as proprietary, open-source, public domain, and freeware.

## Does HEAVY.AI a Statistical Modeling Solution?

Statistical modeling serves as one of the solutions for the data discovery challenge facing big data management systems. HEAVY.AI's Data Science Platform provides an always-on dashboard for monitoring the health of statistical models in which the user can visualize predictions alongside actual outcomes and see how predications diverge from real life.