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 Creator:
 Tye, Alexander R, Wolf, Aaron S, and Niemi, Nathan A
 Description:
 Detrital zircon age distributions provide robust insights into past sedimentary systems, but these age distributions are often complex and multipeaked, with sample sizes too small to confidently resolve population distributions. This limited sampling hinders existing quantitative methods for comparing detrital zircon age distributions, which show systematic dependence on the sizes of compared samples. The proliferation of detrital zircon studies motivates the development of more robust quantitative methods. We present the first attempt, to our knowledge, to infer probability model ensembles (PMEs) for samples of detrital zircon ages using a Bayesian method. Our method infers the parent population age distribution from which a sample is drawn, using a Monte Carlo approach to aggregate a representative set of probability models that is consistent with the constraints that the sample data provide. Using the PMEs inferred from sample data, we develop a new estimate of correspondence between detrital zircon populations called Bayesian Population Correlation (BPC). Tests of BPC on synthetic and real detrital zircon age data show that it is nearly independent from sample size bias, unlike existing correspondence metrics. Robust BPC uncertainties can be readily estimated, enhancing interpretive value. When comparing two partially overlapping zircon age populations where the shared proportion of each population is independently varied, BPC results conform almost perfectly to expected values derived analytically from probability theory. This conformity of experimental and analytical results permits direct inference of the shared proportions of two detrital zircon age populations from BPC. We provide MATLAB scripts to facilitate the procedures we describe.
 Keyword:
 provenance, statistics, zircon, Bayesian, detrital, and density estimation
 Citation to related publication:
 Discipline:
 Science
 Title:
 Bayesian Population Correlation: A probabilistic approach to comparing detrital zircon age distributions

 Creator:
 Smith, Joeseph P., Gronewold, Andrew D., Read, Laura, Crooks, James L., School for Environment and Sustainability, University of Michigan, Department of Civil and Environmental Engineering, University of Michigan, and Cooperative Institute for Great Lakes Research, University of Michigan
 Description:
 Using the statistical programming package R ( https://cran.rproject.org/), and JAGS (Just Another Gibbs Sampler, http://mcmcjags.sourceforge.net/), we processed multiple estimates of the Laurentian Great Lakes water balance components  overlake precipitation, evaporation, lateral tributary runoff, connecting channel flows, and diversions  feeding them into prior distributions (using data from 1950 through 1979), and likelihood functions. The Bayesian Network is coded in the BUGS language. Water balance computations assume that monthly change in storage for a given lake is the difference between beginning of month water levels surrounding each month. For example, the change in storage for June 2015 is the difference between the beginning of month water level for July 2015 and that for June 2015., More details on the model can be found in the following summary report for the International Watersheds Initiative of the International Joint Commission, where the model was used to generate a new water balance historical record from 1950 through 2015: https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf. Large Lake Statistical Water Balance Model (L2SWBM): https://www.glerl.noaa.gov/data/WaterBalanceModel/, and This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.
 Keyword:
 Water, Balance, Great Lakes, Laurentian, Machine Learning, Machine, Learning, Lakes, Bayesian, and Network
 Citation to related publication:
 Discipline:
 Engineering and Science
 Title:
 Large Lake Statistical Water Balance Model  12 month time window  1980 through 2015 monthly summary data and model output

 Creator:
 Smith, Joeseph P., Gronewold, Andrew D., Read, Laura, Crooks, James L., School for Environment and Sustainability, University of Michigan, Department of Civil and Environmental Engineering, University of Michigan, and Cooperative Institute for Great Lakes Research
 Description:
 Using the statistical programming package R ( https://cran.rproject.org/), and JAGS (Just Another Gibbs Sampler, http://mcmcjags.sourceforge.net/), we processed multiple estimates of the Laurentian Great Lakes water balance components  overlake precipitation, evaporation, lateral tributary runoff, connecting channel flows, and diversions  feeding them into prior distributions (using data from 1950 through 1979), and likelihood functions. The Bayesian Network is coded in the BUGS language. Water balance computations assume that monthly change in storage for a given lake is the difference between beginning of month water levels surrounding each month. For example, the change in storage for June 2015 is the difference between the beginning of month water level for July 2015 and that for June 2015., More details on the model can be found in the following summary report for the International Watersheds Initiative of the International Joint Commission, where the model was used to generate a new water balance historical record from 1950 through 2015: https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf. Large Lake Statistical Water Balance Model (L2SWBM): https://www.glerl.noaa.gov/data/WaterBalanceModel/ , and This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.
 Keyword:
 Water, Balance, Great Lakes, Laurentian, Machine, Learning, Lakes, Bayesian, and Network
 Citation to related publication:
 Discipline:
 Engineering and Science
 Title:
 Large Lake Statistical Water Balance Model  Laurentian Great Lakes  6 month time window  1980 through 2015 monthly summary data and model output

 Creator:
 Smith, Joeseph P., Gronewold, Andrew D., Read, Laura, Crooks, James L., School for Environment and Sustainability, University of Michigan, Department of Civil and Environmental Engineering, University of Michigan, and Cooperative Institute for Great Lakes Research
 Description:
 Using the statistical programming package R ( https://cran.rproject.org/), and JAGS (Just Another Gibbs Sampler, http://mcmcjags.sourceforge.net/), we processed multiple estimates of the Laurentian Great Lakes water balance components  overlake precipitation, evaporation, lateral tributary runoff, connecting channel flows, and diversions  feeding them into prior distributions (using data from 1950 through 1979), and likelihood functions. The Bayesian Network is coded in the BUGS language. Water balance computations assume that monthly change in storage for a given lake is the difference between beginning of month water levels surrounding each month. For example, the change in storage for June 2015 is the difference between the beginning of month water level for July 2015 and that for June 2015., More details on the model can be found in the following summary report for the International Watersheds Initiative of the International Joint Commission, where the model was used to generate a new water balance historical record from 1950 through 2015: https://www.glerl.noaa.gov/pubs/fulltext/2018/20180021.pdf. Large Lake Statistical Water Balance Model (L2SWBM): https://www.glerl.noaa.gov/data/WaterBalanceModel/, and This data set has a shorter timespan to accommodate a prior which uses data not used in the likelihood functions.
 Keyword:
 Water, Balance, Great Lakes, Laurentian, Machine, Learning, Lakes, Bayesian, and Network
 Citation to related publication:
 Discipline:
 Engineering and Science
 Title:
 Large Lake Statistical Water Balance Model  Laurentian Great Lakes  1 month time window  1980 through 2015 monthly summary data and model output