Model selection in ultrasonic measurements on trabecular bone

Christian C. Anderson; Karen R. Marutyan; Keith A. Wear; Mark R. Holland; James G. Miller; G. Larry Bretthorst

doi:10.1063/1.2821280

Model selection in ultrasonic measurements on trabecular bone

Christian C. Anderson, Karen R. Marutyan, Keith A. Wear, Mark R. Holland, James G. Miller, G. Larry Bretthorst

Radiology - Radiation Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

Previous work from our laboratory showed that the widely reported decrease in phase velocity with frequency (negative dispersion) for ultrasonic waves propagating through trabecular bone can arise from the interference of two compressional waves, each of which exhibits a positive dispersion. Previous simulations suggest that Bayesian probability theory can be employed to recover the material properties linked to these two interfering waves, even when the waves overlap sufficiently that visual inspection cannot distinguish two modes. In the present study, Bayesian probability theory is applied first to simulated data and then to representative experimental bone data to determine whether one or two compressional wave modes are present. Model selection is implemented by evaluating the posterior probability for each model. The calculation is implemented by defining a model indicator and then using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for the ultrasonic parameters and the model indicator. Monte Carlo integration is used to evaluate the marginal posterior probability for each parameter given the model indicator.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Pages	337-345
Number of pages	9
DOIs	https://doi.org/10.1063/1.2821280
State	Published - 2007
Event	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 - Saratoga Springs, NY, United States Duration: Jul 8 2007 → Jul 13 2007

Publication series

Name	AIP Conference Proceedings
Volume	954
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007
Country	United States
City	Saratoga Springs, NY
Period	07/8/07 → 07/13/07

Keywords

Bayesian probability theory
Bone
Model selection
Osteoporosis
Tissue characterization
Ultrasound

Access to Document

10.1063/1.2821280

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Anderson, C. C., Marutyan, K. R., Wear, K. A., Holland, M. R., Miller, J. G., & Bretthorst, G. L. (2007). Model selection in ultrasonic measurements on trabecular bone. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007 (pp. 337-345). (AIP Conference Proceedings; Vol. 954). https://doi.org/10.1063/1.2821280

Anderson, Christian C. ; Marutyan, Karen R. ; Wear, Keith A. ; Holland, Mark R. ; Miller, James G. ; Bretthorst, G. Larry. / Model selection in ultrasonic measurements on trabecular bone. Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. pp. 337-345 (AIP Conference Proceedings).

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title = "Model selection in ultrasonic measurements on trabecular bone",

abstract = "Previous work from our laboratory showed that the widely reported decrease in phase velocity with frequency (negative dispersion) for ultrasonic waves propagating through trabecular bone can arise from the interference of two compressional waves, each of which exhibits a positive dispersion. Previous simulations suggest that Bayesian probability theory can be employed to recover the material properties linked to these two interfering waves, even when the waves overlap sufficiently that visual inspection cannot distinguish two modes. In the present study, Bayesian probability theory is applied first to simulated data and then to representative experimental bone data to determine whether one or two compressional wave modes are present. Model selection is implemented by evaluating the posterior probability for each model. The calculation is implemented by defining a model indicator and then using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for the ultrasonic parameters and the model indicator. Monte Carlo integration is used to evaluate the marginal posterior probability for each parameter given the model indicator.",

keywords = "Bayesian probability theory, Bone, Model selection, Osteoporosis, Tissue characterization, Ultrasound",

author = "Anderson, {Christian C.} and Marutyan, {Karen R.} and Wear, {Keith A.} and Holland, {Mark R.} and Miller, {James G.} and Bretthorst, {G. Larry}",

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doi = "10.1063/1.2821280",

language = "English",

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series = "AIP Conference Proceedings",

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Anderson, CC, Marutyan, KR, Wear, KA, Holland, MR, Miller, JG & Bretthorst, GL 2007, Model selection in ultrasonic measurements on trabecular bone. in Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. AIP Conference Proceedings, vol. 954, pp. 337-345, 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007, Saratoga Springs, NY, United States, 07/8/07. https://doi.org/10.1063/1.2821280

Model selection in ultrasonic measurements on trabecular bone. / Anderson, Christian C.; Marutyan, Karen R.; Wear, Keith A.; Holland, Mark R.; Miller, James G.; Bretthorst, G. Larry.

Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. p. 337-345 (AIP Conference Proceedings; Vol. 954).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Bretthorst, G. Larry

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AB - Previous work from our laboratory showed that the widely reported decrease in phase velocity with frequency (negative dispersion) for ultrasonic waves propagating through trabecular bone can arise from the interference of two compressional waves, each of which exhibits a positive dispersion. Previous simulations suggest that Bayesian probability theory can be employed to recover the material properties linked to these two interfering waves, even when the waves overlap sufficiently that visual inspection cannot distinguish two modes. In the present study, Bayesian probability theory is applied first to simulated data and then to representative experimental bone data to determine whether one or two compressional wave modes are present. Model selection is implemented by evaluating the posterior probability for each model. The calculation is implemented by defining a model indicator and then using Markov chain Monte Carlo with simulated annealing to draw samples from the joint posterior probability for the ultrasonic parameters and the model indicator. Monte Carlo integration is used to evaluate the marginal posterior probability for each parameter given the model indicator.

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Anderson CC, Marutyan KR, Wear KA, Holland MR, Miller JG, Bretthorst GL. Model selection in ultrasonic measurements on trabecular bone. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2007. 2007. p. 337-345. (AIP Conference Proceedings). https://doi.org/10.1063/1.2821280