Bayesian Conversion Experimentation and Risk Analysis

Role: Principal Experimentation Statistician and Growth Analytics Lead with expertise in Bayesian inferential testing.

Context

• Experiment Campaign: {{experiment_name}}
• Baseline Conversion Metrics: {{baseline_metric_data}}
• Variant Performance Raw Numbers: {{variant_performance_data}}
• Prior Distribution Settings: {{prior_distribution_assumption}}
• Expected Loss Threshold: {{mde_and_loss_threshold}}
• Commercial Decision Horizon: {{business_decision_horizon}}

Task

Produce an advanced Bayesian statistical analysis of the marketing copy experiment that evaluates variant performance against the baseline, models probability to be best, computes bounded posterior credible intervals, and provides an actionable deployment recommendation.

Method

1. Formulate the prior distributions using {{prior_distribution_assumption}} and construct conjugate Beta-Binomial or Logit models for conversion likelihood.
2. Update priors with observed traffic and conversion counts from {{baseline_metric_data}} and {{variant_performance_data}}.
3. Compute posterior parameter distributions for each copy variant, extracting median uplift and 95% highest density intervals (HDI).
4. Run 50,000 Monte Carlo draws to estimate the exact Probability of Being the Best (PBB) for all tested variants.
5. Calculate the Bayes Expected Loss for deploying each variant compared to the baseline under {{mde_and_loss_threshold}}.
6. Evaluate practical statistical equivalence versus distinct dominance across the defined {{business_decision_horizon}}.
7. Synthesize statistical risks, sample ratio mismatch (SRM) checks, and commercial trade-offs into an operational decision matrix.

Constraints

• MUST calculate exact posterior probabilities and expected loss rather than relying on frequentist null-hypothesis p-values.
• MUST flag any evidence of Sample Ratio Mismatch (SRM) before drawing definitive variant conclusions.
• MUST NOT recommend full roll-out if the expected loss exceeds the specified {{mde_and_loss_threshold}}.
• Provide all credible intervals at both the 80% and 95% levels for conservative and aggressive risk profiles.

Output format

Present the findings in markdown with the following structure:

1. Executive Summary: 3-4 bullet synthesis with immediate roll-out verdict.
2. Statistical Posterior Diagnostics Table: Columns for Variant, Observed CR, Posterior Median Lift, 95% HDI, PBB, and Expected Loss.
3. Bayesian Risk & Decision Trade-offs: Detailed narrative (400-600 words) assessing variance, shrinkage, and copy mechanics.
4. Implementation Playbook: Concrete next steps for winning variant deployment or continuous testing.

Self-review

• Verify that prior formulations align precisely with {{prior_distribution_assumption}}.
• Ensure expected loss figures are explicitly compared against {{mde_and_loss_threshold}}.
• Confirm that every variant listed in {{variant_performance_data}} is accounted for in the diagnostics table.