Welcome!

Welcome to the ASHE 2023 workshop, A Gentle Introduction to Bayesian Analysis with Applications to QuantCrit. This workshop will introduce quantitatively-trained researchers to the Bayesian paradigm. Participants will learn through short lecture and by implementing short example problems that focus on the unique benefits of Bayesian analysis in QuantCrit frameworks, particularly as applicable for small group inference and more readily interpretable estimates across impacted audiences.

Before the workshop, please follow the instructions on the setup page page to install the necessary software.

Tentative Schedule

1. Theoretical underpinnings

This section will introduce the concepts behind Bayesian inference. Facilitators will lead discussion using slides with opportunity for participant questions and comments.

Time: ~30-35 min

Topics

1. Conditional probability / Bayes Theorem
   Description: We will quickly derive Bayes Theorem from the decomposition of joint probability into conditional probabilities (3 lines of math. . . we promise!), focusing mostly on intuition. This is a very short bit of math that should be straightforward to those with regression training, but is easy to follow regardless.
2. Priors, likelihoods, posteriors
   Description: We will discuss the three key components of a Bayesian analysis — priors, likelihoods, and posteriors — in terms of their respective mathematical and conceptual meanings in Bayesian inference.
3. Interpretation
   Description: We will examine the key differences between Bayesian and frequentist output (parameters are random compared to data are random). Again, the discussion will be high level and mostly focused on how Bayesian results come as full distributions instead of point estimates with standard errors.

2. Example analysis

This section will guide participants through a hands-on data analysis, following the facilitator’s demonstration on their own computers. Code and data will be provided through this website created for the workshop. Extra facilitators will move throughout the room to help participants with technical issues that may arise. Work will follow the I do / we do / you do strategy and allow participants the opportunity to both work on their own computers and with each other.

Time: ~2 hours 30 min (including time for a short break)

Topics

For this analysis example, we will use publicly available data relevant to higher education. The plan will be to use a reduced version of the High School Longitudinal Study of 2009 (HSLS09) to perform increasingly complex regression analyses. We will perform various model checks and ways of presenting the results. Throughout, we will attend to the ways Bayesian analyses can support a critical approach to quantitative work.

3. Applications

This section will be primarily discussion based.

Time: ~15 min

Topics

As motivated by the example analyses, we will close the session by covering potential use cases for Bayesian analyses that make them preferable over frequentist methods in some situations. The idea is that these will be discussed during the examples, but we will conclude by reiterating these points as well as opening up the room for questions and discussion. In particular, we will focus on the promise that Bayesian analyses have in supporting QuantCrit analytic frameworks:

1. Ability to provide estimates using small data sets
2. Ability to provide estimates for small groups that otherwise might be dropped or aggregated
3. Provide estimates that are more easily interpretable by stakeholders, data owners, and participants with the purpose of supporting actionable, antiracist, social justice-oriented policy