The random set approach to nontraditional measurements is rigorously Bayesian
In several previous publications the first author has proposed a "generalized likelihood function" (GLF) approach for processing nontraditional measurements such as attributes, features, natural-language statements, and inference rules. The GLF approach is based on random set "general...
| Main Authors: | , |
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| Format: | Conference Paper |
| Published: |
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/55323 |
| _version_ | 1848759591062470656 |
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| author | Mahler, Ronald El-Fallah, A. |
| author_facet | Mahler, Ronald El-Fallah, A. |
| author_sort | Mahler, Ronald |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In several previous publications the first author has proposed a "generalized likelihood function" (GLF) approach for processing nontraditional measurements such as attributes, features, natural-language statements, and inference rules. The GLF approach is based on random set "generalized measurement models" for nontraditional measurements. GLFs are not conventional likelihood functions, since they are not density functions and their integrals are usually infinite, rather than equal to 1. For this reason, it has been unclear whether or not the GLF approach is fully rigorous from a strict Bayesian point of view. In a recent paper, the first author demonstrated that the GLF of a specific type of nontraditional measurement - quantized measurements - is rigorously Bayesian. In this paper we show that this result can be generalized to arbitrary nontraditional measurements, thus removing any doubt that the GLF approach is rigorously Bayesian. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE). |
| first_indexed | 2025-11-14T10:02:19Z |
| format | Conference Paper |
| id | curtin-20.500.11937-55323 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:02:19Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-553232017-09-13T16:10:18Z The random set approach to nontraditional measurements is rigorously Bayesian Mahler, Ronald El-Fallah, A. In several previous publications the first author has proposed a "generalized likelihood function" (GLF) approach for processing nontraditional measurements such as attributes, features, natural-language statements, and inference rules. The GLF approach is based on random set "generalized measurement models" for nontraditional measurements. GLFs are not conventional likelihood functions, since they are not density functions and their integrals are usually infinite, rather than equal to 1. For this reason, it has been unclear whether or not the GLF approach is fully rigorous from a strict Bayesian point of view. In a recent paper, the first author demonstrated that the GLF of a specific type of nontraditional measurement - quantized measurements - is rigorously Bayesian. In this paper we show that this result can be generalized to arbitrary nontraditional measurements, thus removing any doubt that the GLF approach is rigorously Bayesian. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE). 2012 Conference Paper http://hdl.handle.net/20.500.11937/55323 10.1117/12.919824 restricted |
| spellingShingle | Mahler, Ronald El-Fallah, A. The random set approach to nontraditional measurements is rigorously Bayesian |
| title | The random set approach to nontraditional measurements is rigorously Bayesian |
| title_full | The random set approach to nontraditional measurements is rigorously Bayesian |
| title_fullStr | The random set approach to nontraditional measurements is rigorously Bayesian |
| title_full_unstemmed | The random set approach to nontraditional measurements is rigorously Bayesian |
| title_short | The random set approach to nontraditional measurements is rigorously Bayesian |
| title_sort | random set approach to nontraditional measurements is rigorously bayesian |
| url | http://hdl.handle.net/20.500.11937/55323 |