In very simple terms, a statistical model is a set of assumptions about the probability distribution that generates some observed data.
Statistical models are the bedrock of data analysis, empowering researchers and analysts to extract meaningful insights from complex datasets. These models serve as mathematical representations of real-world phenomena, facilitating predictions, hypothesis testing, and a deeper understanding of variable relationships.
At its core, a statistical model is a structured framework that simplifies data complexities. It comprises assumptions, parameters, and mathematical equations tailored to the specific problem at hand. These models come in various forms, including linear regression, decision trees, and neural networks.
Key components of a statistical model include:
- Assumptions: Models are built on data assumptions, such as normality or linearity, which must be met for valid results.
- Parameters: These represent the variables within the model that we seek to estimate, such as coefficients in regression.
- Equations: Mathematical equations define variable relationships based on statistical theory and domain expertise.
Statistical models find applications across diverse fields, from finance and healthcare to marketing and climate science. They enable predictions, uncover hidden patterns, and drive data-informed decision-making.
List of recommended resources #
For a broad overview #
Simple statistical models can be sufficient for testing hypotheses with population time-series data
This paper proposes that although sophisticated models have been developed and applied to analyze abundance time series, they require information about species detectability that is often unavailable. In many cases, simpler models prove to be adequate for testing hypotheses
This paper by Peter McCullagh addresses two closely related questions, “What is a statistical model?” and “What is a parameter?” and argues that inference on the basis of a model is not possible unless the model admits a natural extension that includes the domain for which inference is required.
For in depth understanding #
This book by A. C. Davison gives an integrated development of the topics that blends theory and practice in statistics from topics like point processes, graphical models to Markov chain and spline regressions.
Statistical Models: Theory and Practice
This book by David A. Freedman explains the basic ideas of association and regression as well as the techniques required to build statistical models. The book focuses particularly on the applications of linear models.
Case study #
This report describes the process involved and gives a summary of the results from the pilot implementation of statistical models used for measuring the value addition to Bulgarian schools through an analysis of the national student assessment results.
This Policy research Working Paper, written as part of the Fragility, Conflict and Violence Global Theme and the Development Economics Vice Presidency, proposes a statistical forecasting method to predict food crises in advance, so that preventive measures can be taken. The results show that statistical models can effectively identify future food crises, and that using these models can help to increase the lead time for action.
References #
