Statistical Rethinking: A Bayesian Course with Examples in R and STAN (2nd edition)

Concepts in Bayesian Statistics

When using Bayesian statistics, what must a researcher explicitly specify before conducting a study?

In an approach to inferential statistics that begins by assigning initial probabilities to competing hypotheses, those probability estimates remain fixed and do not change once new data from a study are collected.

A psychology researcher wants to use a Bayesian approach to study whether mindfulness training reduces test anxiety. Arrange the following steps in the correct order as the researcher carries out this Bayesian analysis.

A psychologist uses a Bayesian approach to investigate whether a specific breathing technique reduces heart rate during public speaking. Match each component of the psychologist's research process with its corresponding role in the Bayesian framework.

A neuropsychologist is developing a new diagnostic model to determine the probability that a patient has a specific memory disorder. To construct this model using a Bayesian framework that accounts for both existing knowledge and new diagnostic data, which of the following architectures should the researcher implement?

A psychology researcher wants to understand the structure of Bayesian statistics as an alternative to traditional null hypothesis testing. Match each core concept of the Bayesian framework with the statement that best describes its role.

A researcher is critiquing the use of all-or-nothing labels (such as 'effect' or 'no effect') as being too simplistic for complex psychological research. To provide a more nuanced evaluation of evidence, the researcher advocates for a Bayesian approach because it provides a logical framework for the _____ of uncertainty.

In a Bayesian approach, the initial probability specified for a hypothesis before conducting a study is called the _____.

In Bayesian statistics, the prior probability that a researcher assigns to the null hypothesis before collecting data serves the same purpose as the alpha (α) significance level in traditional null hypothesis significance testing, because both are pre-study numerical values that determine whether the null hypothesis will ultimately be rejected.

A faculty advisor is reviewing a student's research report that claims to use a Bayesian statistical approach. To evaluate whether the student implemented and justified the Bayesian framework correctly, the advisor identifies five criteria to examine. Arrange these evaluative criteria in the logical order in which they should be addressed during the review.

Define Bayesian statistics as an approach to inferential statistics, describing the specific components a researcher must establish before conducting a study and how these components are handled after data collection.

Based on the case context, explain how Dr. Aris's Bayesian approach differs from traditional null hypothesis testing in its handling of hypothesis probabilities and uncertainty.

A developmental psychologist wants to apply a Bayesian approach to study the effect of a new reading program on children's reading comprehension. Describe the specific steps this researcher must take to implement a Bayesian statistical analysis from the start to the end of their study.