Bayesian vs Frequentist Analysis AI Prompt

Help me decide between a frequentist and Bayesian analysis approach for my study, and implement the chosen approach.

Study context: {{study_context}}
Prior knowledge available: {{prior_knowledge}}
Inference goal: {{inference_goal}}

1. Key conceptual differences:

   Frequentist:
   - Probability = long-run frequency of events in repeated experiments
   - Parameters are fixed (unknown) constants; data are random
   - Inference: p-value (probability of data at least as extreme as observed, given H0 is true)
   - Output: point estimate, confidence interval (if experiment repeated 100 times, 95% of CIs would contain the true value)
   - No prior knowledge formally incorporated

   Bayesian:
   - Probability = degree of belief
   - Parameters are random variables with probability distributions; data are fixed once observed
   - Inference: posterior distribution (updated beliefs after seeing data)
   - Output: posterior mean/median, credible interval (probability that parameter falls in this interval given the data)
   - Prior knowledge explicitly incorporated through prior distribution

2. When to prefer each approach:

   Prefer frequentist when:
   - Strong prior knowledge is not available or hard to justify publicly
   - Results need to be communicated to a broadly frequentist audience
   - Simple hypothesis testing with a clear alpha level is the goal
   - Regulatory context requires NHST (e.g. clinical trial primary endpoint)

   Prefer Bayesian when:
   - Informative prior knowledge exists (previous studies, domain expertise) that should influence inference
   - You want to quantify evidence for the null hypothesis (Bayes factor)
   - Sequential/adaptive designs where interim analyses are needed
   - Complex hierarchical models where priors regularize unstable estimates
   - Small samples where priors stabilize estimates
   - Direct probability statements about parameters are needed ('there is a 92% probability the effect is positive')

3. If using Bayesian analysis:
   - Specify priors: weakly informative priors (regularizing) vs strongly informative priors (based on prior studies)
   - Sensitivity analysis: show results under different prior specifications
   - Report: prior distribution, posterior distribution, posterior mean with 95% credible interval, Bayes factor if testing hypotheses
   - Software: Stan / brms (R), PyMC (Python), JASP (GUI)

4. Bayes Factor interpretation:
   - BF > 100: decisive evidence for H1
   - BF 30–100: very strong evidence for H1
   - BF 10–30: strong evidence for H1
   - BF 3–10: moderate evidence for H1
   - BF 1–3: anecdotal evidence for H1
   - BF = 1: no evidence either way
   - BF < 1/3: moderate evidence for H0

Return: recommendation with rationale, prior specification for Bayesian approach, sensitivity analysis plan, and code in R (brms) or Python (PyMC).