A Bayesian Inference Algorithm for Equipment Software Price Estimation Based on Nonlinear Contribution Models

Tian Meng

doi:10.3390/a19050396

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A Bayesian Inference Algorithm for Equipment Software Price Estimation Based on Nonlinear Contribution Models

2026-05-15

Tian Meng

Jiang, Guoping *

DOI：10.3390/a19050396

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Abstract

En 中文

To address the challenges of difficult value quantification, lack of market benchmarks, and scarcity of historical data for embedded software amidst the intelligent transformation of equipment systems, this study develops a scientific price estimation method based on functional capability contribution. A nonlinear pricing model is constructed to accurately characterize the two-stage evolution of software price: diminishing marginal utility during the mature technology accumulation stage and exponential growth during the technical bottleneck breakthrough stage. To ensure the consistency of pricing logic between hardware and software, a penalty function is innovatively designed to modify the standard likelihood function, effectively transforming practical business logic into a model regularization term. Parameter estimation is achieved by employing a Bayesian inference framework integrated with operational constraints, utilizing Markov Chain Monte Carlo (MCMC) sampling to realize robust posterior inference under small-sample constraints. Empirical analysis demonstrates that the proposed method achieves superior cross-domain data transfer performance compared to traditional baseline models, with a Leave-One-Out Cross-Validation (LOOCV) Mean Absolute Percentage Error (MAPE) of 21.2%. This research provides a practical value-oriented price estimation method for embedded equipment software pricing.

Keywords:

Bayesian inference

MCMC sampling

nonlinear pricing model

functional capability contribution

regularization

small-sample estimation

embedded software