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CRM Analytics · Bayesian Inference · Decision ScienceIndividual academic project

Bayesian Conversion Rate Estimation for Bank Telemarketing Campaigns

Binomial–Beta model applied to commercial-campaign conversion to estimate uncertainty, update evidence, and support marketing decisions.

Type

Individual academic project

Area

CRM Analytics · Bayesian Inference · Decision Science

Tools

FirstBayes · Excel · UCI Bank Marketing dataset

Techniques

Binomial-Beta model · Posterior update · Prior sensitivity · Predictive distribution · Uncertainty intervals

Output

Probabilistic conversion model

Value

Individual project where I estimated bank telemarketing conversion using Binomial-Beta Bayesian inference and predictive distributions to translate uncertainty into operational marketing expectations.

4.521

Contacts analysed

521

Observed conversions

11,5 %

Estimated conversion rate

6–18

Plausible range per 100 contacts

17,7 %

Probability of 15+ conversions

Executive summary

A useful marketing analytics case because it shifts the conversation from “what was the observed conversion” to “what range of conversion is plausible and with what probability”. That logic helps decisions without overreacting to noise.

Business context

In marketing, it is not enough to know the observed conversion. We need to distinguish normal variability from real performance changes. Bayesian inference allows beliefs to be updated as evidence arrives and helps estimate plausible ranges for decisions.

My role

Individual academic project in Business Management with External Information. I framed the problem, interpreted the dataset, compared informative and non-informative priors, applied two-stage Binomial-Beta sequential learning, and translated the predictive distribution into operating expectations.

Data & methods

  • UCI Bank Marketing dataset, bank.csv file with 4,521 contacts.
  • Binary conversion variable: term-deposit subscription yes/no.
  • Non-informative Beta(1,1) prior and weak informative Beta(2.48, 17.52) prior based on Moro et al. (2014).
  • Sequential learning in two blocks: 500 initial contacts and 4,021 later contacts.
  • Posterior update, 95% HDI, probability of exceeding a 12% threshold, and Beta-Binomial predictive distribution for 100 contacts.
  • FirstBayes and Excel.

Process

  1. 01Define the decision problem.
  2. 02Interpret the dataset and conversion variable.
  3. 03Select informative and non-informative priors.
  4. 04Update to the posterior with STAGE1 and use that posterior as the STAGE2 prior.
  5. 05Compare result sensitivity to the prior.
  6. 06Build the predictive distribution for 100 future contacts.
  7. 07Translate probabilities into operating expectations.

Key findings

  • The sample contains 521 conversions out of 4,521 contacts, with an observed rate of 11.52%.
  • Estimated conversion rate close to 11.5%.
  • The informative and non-informative priors converge to almost the same final result: sample evidence dominates the inference.
  • The posterior probability of exceeding 12% falls to ~16–17% after incorporating all evidence.
  • Operational expectation: 11–12 conversions for every 100 contacts.
  • Plausible range: 6–18 conversions per 100 contacts.
  • Approximate 17.7% probability of reaching 15 or more conversions.

Business implications

  • It allows campaigns to be planned with uncertainty ranges.
  • It prevents overreaction to normal variation.
  • It helps define realistic conversion expectations.

Limitations

  • External dataset.
  • Univariate model for global conversion rate.
  • It does not incorporate individual predictors.
  • The unit of analysis is the campaign contact, not necessarily a unique customer.
  • It does not replace a scoring or uplift model.

What I would do next

  • Incorporate customer variables.
  • Compare segments.
  • Build a predictive model.
  • Use machine learning for propensity scoring.
  • Create a budget-based conversion simulator.

Assets

View summaryComing soonView notebookComing soonNotebook pending publication with reproducible logic.

Suggested visuals

Prior/posterior chart.

Predictive distribution.

Conversion probability cards.

Expected conversions per 100 contacts chart.

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