Model-Centric Statistics: From Exploratory Analysis to Bayesian Inference

Model-Centric Statistics

Statistics is primarily about collecting, organizing, analyzing, and interpreting data. Therefore, a solid grasp of statistical fundamentals is essential for data analysis. Knowing how to write code in a language such as Python is a valuable skill for preprocessing complex real‑world data.

Exploratory Data Analysis

Data is the core component of statistics, originating from experiments, computer models, surveys, or observations. If we are the data generators or collectors, we must first define the problem and choose an appropriate method before gathering data.

Experimental design is a branch of statistics that studies how to obtain data. In the era of data abundance, data acquisition can be costly; for example, the Large Hadron Collider can generate hundreds of terabytes per day, yet its construction required years of effort.

Assuming we already have a clean dataset, the usual practice is to explore and visualize it to gain an intuitive understanding. The exploratory data analysis process can be summarized in two steps:

Descriptive statistics;

Data visualization.

Descriptive statistics use metrics such as mean, mode, standard deviation, and interquartile range to quantitatively summarize data.

Data visualization presents data in vivid forms such as histograms and scatter plots. Although exploratory analysis appears to be a preparatory step before complex analysis, it remains useful for understanding, interpreting, checking, summarizing, and communicating results, including Bayesian analyses.

Statistical Inference

Sometimes simple calculations like means are sufficient, but often we aim to draw more general conclusions, predict unseen future data, or select the most plausible explanation among many. These goals define statistical inference.

Statistical inference relies on probability models; many scientific studies and our understanding of the world are model‑based. The brain itself can be viewed as a modeling machine, as discussed in related TED talks.

A model is a simplified description of a system or process that focuses on its important aspects, not necessarily explaining the entire system.

If two models explain the same data with comparable performance, the simpler one is usually preferred—this is the principle of Occam's razor.

The Bayesian modeling workflow can be condensed into three steps:

Formulate assumptions about how the data were generated and construct a (often rough) model.

Combine the data and model using Bayesian theory to obtain a fitted model.

Assess model adequacy based on criteria such as fit to real data and prior knowledge of the research question.

Reference: Osvaldo Martin, Python Bayesian Analysis .