Forensic Error Probability Calculation via Convolution
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Solution Overview
Problem
Current methods for determining the probability of error in forensic identification, such as DNA matching, often rely on approximate calculations and fail to provide precise error rates, especially for large datasets, leading to potential misidentification and incorrect conclusions.
Innovation Solution
A method involving the convolution of independent factor distributions to form a joint distribution, allowing for the accurate calculation of tail probabilities and reporting exact error rates, using a computer program to process prior and posterior probability distributions from multiple tests.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If approximate error calculation methods are used, then calculation speed is improved, but measurement precision of error rates deteriorates
Solution Approach 1:
The patent segments the complex error calculation into multiple independent test components, where each test contributes a factor distribution. By dividing the overall error probability calculation into separate test-level calculations and then combining them through convolution, the method achieves both computational efficiency and precision for large datasets
Solution Approach 2:
The patent replaces traditional mechanical or manual error calculation methods with computer-based convolution algorithms. The computer automatically performs the complex mathematical operations of convolving factor distributions and calculating tail probabilities, achieving high precision error rates while maintaining rapid calculation speed
2Measurement precision
If exact error rates are calculated for large datasets, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The patent performs preliminary actions by obtaining prior and posterior probability distributions from multiple independent tests before conducting the final error calculation. By pre-processing the data into factor distributions and organizing them, the subsequent convolution and tail probability calculation can be executed rapidly with high precision, avoiding time loss during the critical calculation phase
3Loss of information
If likelihood ratio is used to quantify evidence strength, then information concentration is improved, but ease of operation for non-statisticians deteriorates
Solution Approach 1:
The patent introduces false match probability (FMP) as an intermediary metric that bridges the gap between the technical likelihood ratio and non-technical interpretation. The FMP translates the concentrated evidence information into a more intuitive error probability format that is easier for non-statisticians to understand and apply in decision-making
Solution Approach 2:
The patent transforms the likelihood ratio parameter into a false match probability parameter through mathematical conversion. This parameter change converts an abstract evidence strength metric into a concrete error probability that is more directly relevant to decision-making and easier for non-experts to comprehend
Data Source
AI summary
An apparatus for determining probability of error in identifying evidence includes a computer. The apparatus includes a non-transitory memory in communication with the computer in which is stored a software program, and prior and posterior probability distributions from a plurality of independent tests conducted on an item of evidence. For each test, the computer forms a factor distribution from the test's probability distributions using the software program stored in the non-transitory memory of the computer. The computer convolves the independent factor distributions to form a joint factor distribution using the software program. The computer calculates a tail probability from the joint factor distribution using the software program to determine a probability of error in identifying the evidence. The computer stores the probability of error in the non-transitory memory. A method. A computer program.