Work Description

Title: Bayesian Population Correlation: A probabilistic approach to comparing detrital zircon age distributions Open Access Deposited

http://creativecommons.org/licenses/by-nc/4.0/
Attribute Value
Methodology
  • The files are a set of scripts for carrying out a Bayesian inference method that models a set of probability distributions from which a sample might have been drawn. These sets of probability distributions are then used to make a quantitative assessment of how similar the two populations are. The metric of this assessment is known as Bayesian Population Correlation (BPC). The datasets for which this method is primarily intended for use are U-Pb ages of detrital zircons in sedimentary rocks or modern sedimentary systems. The paper describing this method is in review (Feb. 2018) at Geochemistry, Geophysics, Geosystems under the following title and authors: Tye, A. R., Wolf, A. S., Niemi, N. A. Bayesian Population Correlation: A probabilistic approach to comparing detrital zircon age distributions.
Description
  • Detrital zircon age distributions provide robust insights into past sedimentary systems, but these age distributions are often complex and multi-peaked, 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.
Creator
Depositor
  • alextye@umich.edu
Contact information
Discipline
Funding agency
  • National Science Foundation (NSF)
Keyword
Citations to related material
  • A.R. Tye, A.S. Wolf, N.A. Niemi, Bayesian population correlation: A probabilistic approach to inferring and comparing population distributions for detrital zircon ages, Chemical Geology, Volume 518, 2019, Pages 67-78, ISSN 0009-2541, https://doi.org/10.1016/j.chemgeo.2019.03.039
Resource type
Last modified
  • 03/12/2020
Published
  • 03/01/2018
Language
DOI
  • https://doi.org/10.7302/gb3r-2j98
License
To Cite this Work:
Tye, A., Wolf, A., Niemi, N. (2018). Bayesian Population Correlation: A probabilistic approach to comparing detrital zircon age distributions [Data set]. University of Michigan - Deep Blue. https://doi.org/10.7302/gb3r-2j98

Relationships

Files (Count: 8; Size: 186 MB)

function varargout = BPCmainmenu(varargin)
% BPCMAINMENU MATLAB code for BPCmainmenu.fig
% BPCMAINMENU, by itself, creates a new BPCMAINMENU or raises the existing
% singleton*.
%
% H = BPCMAINMENU returns the handle to a new BPCMAINMENU or the handle to
% the existing singleton*.
%
% BPCMAINMENU('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in BPCMAINMENU.M with the given input arguments.
%
% BPCMAINMENU('Property','Value',...) creates a new BPCMAINMENU or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before BPCmainmenu_OpeningFcn gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to BPCmainmenu_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help BPCmainmenu

% Last Modified by GUIDE v2.5 15-Feb-2018 15:12:57

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @BPCmainmenu_OpeningFcn, ...
'gui_OutputFcn', @BPCmainmenu_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{1})
gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT

% --- Executes just before BPCmainmenu is made visible.
function BPCmainmenu_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to BPCmainmenu (see VARARGIN)

% Choose default command line output for BPCmainmenu
handles.output = hObject;

license_names = {'Optimization Toolbox\n', 'Statistics and Machine Learning Toolbox\n', 'Curve Fitting Toolbox\n', 'Parallel Computing Toolbox\n', 'Global Optimization Toolbox\n'};
installed = zeros(1,5);
installed(1) = ~isempty(ver('optim'));
installed(2) = ~isempty(ver('stats'));
installed(3) = ~isempty(ver('curvefit'));
installed(4) = ~isempty(ver('distcomp'));
installed(5) = ~isempty(ver('globaloptim'));
mess = sprintf(strcat('The following toolboxes are necessary and not installed:\n\n',license_names{find(installed==0)}));
if sum(installed) < 5
msgbox(mess);
end

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes BPCmainmenu wait for user response (see UIRESUME)
% uiwait(handles.figure1);

% --- Outputs from this function are returned to the command line.
function varargout = BPCmainmenu_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;

% --- Executes on button press in BPConeclick.
function BPConeclick_Callback(hObject, eventdata, handles)
% hObject handle to BPConeclick (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
addpath('backend');
BPConeclick_GUI

% --- Executes on button press in PMEplot.
function PMEplot_Callback(hObject, eventdata, handles)
% hObject handle to PMEplot (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
addpath('backend');
PMEplot_GUI

% --- Executes on button press in PME2CSV.
function PME2CSV_Callback(hObject, eventdata, handles)
% hObject handle to PME2CSV (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
addpath('backend');
PME2CSV_GUI

% --- Executes on button press in BPC2frac.
function BPC2frac_Callback(hObject, eventdata, handles)
% hObject handle to BPC2frac (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
addpath('backend');
BPC2frac_GUI

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