Choosing between frequentist and Bayesian approaches is a major debate in the field of statistics, with a recent increase in adoption of Bayesian methods in the sciences. The number of articles referencing Bayesian statistics on sciencedirect.com in April 2024 is shown in the graph below.
The philosophical difference between these approaches is subtle, with some suggesting that even the prominent frequentist critic Fisher had Bayesian tendencies. While there are many articles exploring the differences in formulas, the practical benefits of Bayesian analysis are worth considering. This article aims to provide a practical overview of the motivation, formulation, and application of Bayesian methods.
Frequentists focus on describing the exact distributions of data, while Bayesian analysis is more subjective and allows for the incorporation of prior beliefs. This can be illustrated with a simple example of a coin flip where the probability of heads is calculated differently in a Bayesian framework.
Bayesian analysis offers benefits in situations where data is limited, allowing for the incorporation of prior beliefs to inform the analysis. However, formulating accurate prior beliefs can be challenging, and incorrect assumptions may impact the results.
Bayes’ rule forms the foundation of Bayesian inference, incorporating prior beliefs, likelihood, and observed data to calculate the posterior probability. This iterative process allows for the updating of beliefs as more data is collected, enabling more robust inferences.
While Bayesian analysis can be computationally intensive, advanced algorithms such as Metropolis-Hastings MCMC and Variational Inference have been developed to efficiently explore high-dimensional parameter spaces. Tools like STAN make Bayesian modeling more accessible by providing streamlined interfaces for popular data science languages.
In the next article, we will explore how to get started with STAN for regression models and cover the full Bayesian modeling workflow, including model specification, fitting, visualization, comparison, and interpretation. Stay tuned for more updates!
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