Electronic Communication A/B Testing with Histogram Bayesian Inference
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Solution Overview
Problem
Existing A/B testing systems are limited by the number of metrics they can use to determine a winning variation, often requiring manual characterization or user input, which is cognitively demanding and difficult for non-binary metrics like revenue, and lack flexibility in modeling arbitrary numerical metrics.
Innovation Solution
A method and system using histogram-based Bayesian inference with Dirichlet distributions and conjugate prior formulas to determine a winning arm of A/B testing, allowing for any metric without user input, by creating a histogram from historical data, computing concentration parameters, updating distributions with new data, and inferring central tendencies to construct an overall utility distribution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If traditional A/B testing systems use manual characterization or user input to determine winning variations, then the system can handle a limited subset of metrics, but the user cognitive load increases and the system cannot optimize for arbitrary metrics like revenue
Solution Approach 1:
The system automatically performs histogram-based Bayesian inference using historical data without requiring user input about expected conversion rates, minimum detectable sample sizes, or desired power. The system self-configures the statistical model by computing concentration parameters from histogram weights, eliminating the need for users to manually characterize metrics or answer complex statistical questions.
Solution Approach 2:
The histogram-based Bayesian inference framework provides a universal approach that works for any numerical metric type (binary, non-binary, revenue, etc.). By representing metric distributions as histograms with bins and weights, the system handles diverse metric types through a single unified statistical model rather than requiring separate manual configurations for each metric type.
2Measurement precision
If traditional A/B testing systems model only a subset of metrics, then the system complexity remains manageable, but the system cannot accurately determine winners for arbitrary numerical metrics like revenue
Solution Approach 1:
The system transforms the complex problem of modeling arbitrary numerical metrics into a standardized framework by changing parameters: historical data is transformed into histogram bins with weights, from which concentration parameters are computed. This parameter transformation enables accurate statistical estimation for any metric type while maintaining manageable computational complexity through the standardized histogram representation.
Solution Approach 2:
The histogram serves as an intermediary representation between raw historical data and the Bayesian statistical model. By introducing histogram bins and weights as an intermediate layer, the system simplifies the modeling process and enables accurate statistical inference for arbitrary metrics without directly confronting the full complexity of each metric type.
3Reliability
If traditional A/B testing systems solicit information from users about expected conversion rates and sample sizes, then the system can be configured for specific metrics, but the process is cognitively demanding and users cannot answer questions they may not be able to answer
Solution Approach 1:
The system automatically derives all necessary statistical parameters from historical data through histogram-based Bayesian inference. It computes concentration parameters from histogram weights and performs posterior distribution updates without requiring users to input expected conversion rates, minimum detectable sample sizes, or desired power, eliminating sources of configuration error while maintaining test reliability.
Solution Approach 2:
The system performs preliminary analysis of historical data to compute histogram concentrations before the A/B test begins. This preliminary computation of concentration parameters from historical histograms enables the system to be pre-configured with accurate statistical parameters, eliminating the need for users to provide uncertain estimates during test setup.
4Adaptability or versatility
If traditional A/B testing systems use standard statistical models, then the implementation is straightforward, but the system cannot flexibly handle non-binary metrics like revenue
Solution Approach 1:
The system achieves flexible handling of arbitrary metric types by changing the parameter representation from standard statistical distributions to histogram-based concentration parameters. This parameter transformation enables the system to model non-binary metrics like revenue while maintaining computational efficiency through closed-form posterior updates rather than requiring complex numerical integration or simulation methods.
Data Source
AI summary
Apparatuses, methods, and systems for determining winning arms of electronic testing. One method includes obtaining historical data related to the testing, creating a histogram based on the historical data, the histogram including bins and weights, creating a distribution by computing concentration parameters of the distribution from the weights of the histogram, executing the testing, receiving new data collected based on the execution of the test, allocating the new data into same bins as the bins of the histogram of the historical data yielding a new data bin count, computing a posterior distribution comprising updating the distribution using the same bins and the new data bin counts and the concentration parameters of the distribution, inferring corresponding central tendencies of samplings of a metric distribution, constructing an overall utility distribution for each arms of the test, and determining a winning arm of the testing.