Bayesian Data-Analysis Toolbox

Release 4.23, Manual Version 3

G. Larry BretthorstBiomedical MR Laboratory

Washington University School Of Medicine,Campus Box 8227

Room 2313, East Bldg.,4525 Scott Ave.

St. Louis MO 63110http://bayes.wustl.edu

Email: gbretthorst@wustl.edu

September 18, 2018

Bibliography

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[2] G. Larry Bretthorst (1988), “Bayesian Spectrum Analysis and Parameter Estimation,” in Lec-ture Notes in Statistics, 48, J. Berger, S. Fienberg, J. Gani, K. Krickenberg, and B. Singer(eds), Springer-Verlag, New York, New York.

[3] G. Larry Bretthorst (1990), “An Introduction to Parameter Estimation Using Bayesian Prob-ability Theory,” in Maximum Entropy and Bayesian Methods, Dartmouth College 1989, P.Fougere ed., pp. 53-79, Kluwer Academic Publishers, Dordrecht the Netherlands.

[4] G. Larry Bretthorst (1990), “Bayesian Analysis I. Parameter Estimation Using QuadratureNMR Models” J. Magn. Reson., 88, pp. 533-551.

[5] G. Larry Bretthorst (1990), “Bayesian Analysis II. Signal Detection And Model Selection” J.Magn. Reson., 88, pp. 552-570.

[6] G. Larry Bretthorst (1990), “Bayesian Analysis III. Examples Relevant to NMR” J. Magn.Reson., 88, pp. 571-595.

[7] G. Larry Bretthorst (1991), “Bayesian Analysis. IV. Noise and Computing Time Considera-tions,” J. Magn. Reson., 93, pp. 369-394.

[8] G. Larry Bretthorst (1992), “Bayesian Analysis. V. Amplitude Estimation for Multiple Well-Separated Sinusoids,” J. Magn. Reson., 98, pp. 501-523.

[9] G. Larry Bretthorst (1992), “Estimating The Ratio Of Two Amplitudes In Nuclear MagneticResonance Data,” in Maximum Entropy and Bayesian Methods, C. R. Smith et al. (eds.),pp. 67-77, Kluwer Academic Publishers, the Netherlands.

[10] G. Larry Bretthorst (1993), “On The Difference In Means,” in Physics & Probability Essays inhonor of Edwin T. Jaynes, W. T. Grandy and P. W. Milonni (eds.), pp. 177-194, CambridgeUniversity Press, England.

[11] G. Larry Bretthorst (1996), “An Introduction To Model Selection Using Bayesian ProbabilityTheory,” in Maximum Entropy and Bayesian Methods, G. R. Heidbreder, ed., pp. 1-42, KluwerAcademic Publishers, Printed in the Netherlands.

479

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[12] G. Larry Bretthorst (1999), “The Near-Irrelevance of Sampling Frequency Distributions,” inMaximum Entropy and Bayesian Methods, W. von der Linden et al. (eds.), pp. 21-46, KluwerAcademic Publishers, the Netherlands.

[13] G. Larry Bretthorst (2001), “Nonuniform Sampling: Bandwidth and Aliasing,” in MaximumEntropy and Bayesian Methods in Science and Engineering, Joshua Rychert, Gary Ericksonand C. Ray Smith eds., pp. 1-28, American Institute of Physics, USA.

[14] G. Larry Bretthorst, Christopher D. Kroenke, and Jeffrey J. Neil (2004), “Characterizing WaterDiffusion In Fixed Baboon Brain,” in Bayesian Inference And Maximum Entropy Methods InScience And Engineering, Rainer Fischer, Roland Preuss and Udo von Toussaint eds., AIPconference Proceedings, 735, pp. 3-15.

[15] G. Larry Bretthorst, William C. Hutton, Joel R. Garbow, and Joseph J.H. Ackerman (2005),“Exponential parameter estimation (in NMR) using Bayesian probability theory,” Concepts inMagnetic Resonance, 27A, Issue 2, pp. 55-63.

[16] G. Larry Bretthorst, William C. Hutton, Joel R. Garbow, and Joseph J. H. Ackerman (2005),“Exponential model selection (in NMR) using Bayesian probability theory,” Concepts in Mag-netic Resonance, 27A, Issue 2, pp. 64-72.

[17] G. Larry Bretthorst, William C. Hutton, Joel R. Garbow, and Joseph J.H. Ackerman (2005),“How accurately can parameters from exponential models be estimated? A Bayesian view,”Concepts in Magnetic Resonance, 27A, Issue 2, pp. 73-83.

[18] G. Larry Bretthorst, W. C. Hutton, J. R. Garbow, and Joseph J. H. Ackerman (2008), “HighDynamic Range MRS Time-Domain Signal Analysis,” Magn. Reson. in Med., 62, pp. 1026-1035.

[19] V. Chandramouli, K. Ekberg, W. C. Schumann, S. C. Kalhan, J. Wahren, and B. R. Landau(1997), “Quantifying gluconeogenesis during fasting,” American Journal of Physiology, 273,pp. H1209-H1215.

[20] R. T. Cox (1961), “The Algebra of Probable Inference,” Johns Hopkins Univ. Press, Baltimore.

[21] Andre d’Avignon, G. Larry Bretthorst, Marilyn Emerson Holtzer, and Alfred Holtzer (1998),“Site-Specific Thermodynamics and Kinetics of a Coiled-Coil Transition by Spin InversionTransfer NMR,” Biophysical Journal, 74, pp. 3190-3197.

[22] Andre d’Avignon, G. Larry Bretthorst, Marilyn Emerson Holtzer, and Alfred Holtzer (1999),“Thermodynamics and Kinetics of a Folded-Folded Transition at Valine-9 of a GCN4-LikeLeucine Zipper,” Biophysical Journal, 76, pp. 2752-2759.

[23] David Freedman, and Persi Diaconis (1981), “On the histogram as a density estimator: L2

theory,” Zeitschrift f¨r Wahrscheinlichkeitstheorie und verwandte Gebiete, 57, 4, pp. 453-476.

[24] W. R. Gilks, S. Richardson, and D. J. Spiegelhalter (1996), “Markov Chain Monte Carlo inPractice,” Chapman & Hall, London.

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[25] Paul M. Goggans, and Ying Chi (2004), “Using Thermodynamic Integration to Calculate thePosterior Probability in Bayesian Model Selection Problems,” in Bayesian Inference and Maxi-mum Entropy Methods in Science and Engineering: 23rd International Workshop, 707, pp. 59-66.

[26] Marilyn Emerson Holtzer, G. Larry Bretthorst, D. Andre d’Avignon, Ruth Hogue Angelette,Lisa Mints, and Alfred Holtzer (2001), “Temperature Dependence of the Folding and UnfoldingKinetics of the GCN4 Leucine Lipper via 13C alpha-NMR,” Biophysical Journal, 80, pp. 939-951.

[27] E. T. Jaynes (1968), “Prior Probabilities,” IEEE Transactions on Systems Science and Cyber-netics, SSC-4, pp. 227-241; reprinted in [30].

[28] E. T. Jaynes (1978), “Where Do We Stand On Maximum Entropy?” in The Maximum EntropyFormalism, R. D. Levine and M. Tribus Eds., pp. 15-118, Cambridge: MIT Press, Reprintedin [30].

[29] E. T. Jaynes (1980), “Marginalization and Prior Probabilities,” in Bayesian Analysis inEconometrics and Statistics, A. Zellner ed., North-Holland Publishing Company, Amsterdam;reprinted in [30].

[30] E. T. Jaynes (1983), “Papers on Probability, Statistics and Statistical Physics,” a reprint col-lection, D. Reidel, Dordrecht the Netherlands; second edition Kluwer Academic Publishers,Dordrecht the Netherlands, 1989.

[31] E. T. Jaynes (1957), “How Does the Brain do Plausible Reasoning?” unpublished StanfordUniversity Microwave Laboratory Report No. 421; reprinted in Maximum-Entropy and BayesianMethods in Science and Engineering 1, pp. 1-24, G. J. Erickson and C. R. Smith Eds., 1988.

[32] E. T. Jaynes (2003), “Probability Theory—The Logic of Science,” edited by G. Larry Bretthorst,Cambridge University Press, Cambridge UK.

[33] Sir Harold Jeffreys (1939), “Theory of Probability,” Oxford Univ. Press, London; Later editions,1948, 1961.

[34] John G. Jones, Michael A. Solomon, Suzanne M. Cole, A. Dean Sherry, and Craig R. Mal-loy (2001) “An integrated 2H and 13C NMR study of gluconeogenesis and TCA cycle flux inhumans,” American Journal of Physiology, Endocrinology, and Metabolism, 281, pp. H848-H856.

[35] John Kotyk, N. G. Hoffman, W. C. Hutton, G. Larry Bretthorst, and J. J. H. Ackerman (1992),“Comparison of Fourier and Bayesian Analysis of NMR Signals. I. Well-Separated Resonances(The Single-Frequency Case),” J. Magn. Reson., 98, pp. 483–500.

[36] Pierre Simon Laplace (1814), “A Philosophical Essay on Probabilities,” John Wiley & Sons,London, Chapman & Hall, Limited 1902. Translated from the 6th edition by F. W. Truscottand F. L. Emory.

[37] N. Lartillot, and H. Philippe (2006), “Computing Bayes Factors Using Thermodynamic Inte-gration,” Systematic Biology, 55 (2), pp. 195-207.

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[38] D. Le Bihan, and E. Breton (1985), “Imagerie de diffusion in-vivo par rsonance,” Comptesrendus de l’Acadmie des Sciences (Paris), 301 (15), pp. 1109-1112.

[39] N. R. Lomb (1976), “Least-Squares Frequency Analysis of Unevenly Spaced Data,” Astrophys-ical and Space Science, 39, pp. 447-462.

[40] T. J. Loredo (1990), “From Laplace To SN 1987A: Bayesian Inference In Astrophysics,” inMaximum Entropy and Bayesian Methods, P. F. Fougere (ed), Kluwer Academic Publishers,Dordrecht, The Netherlands.

[41] Craig R. Malloy, A. Dean Sherry, and Mark Jeffrey (1988), “Evaluation of Carbon Flux andSubstrate Selection through Alternate Pathways Involving the Citric Acid Cycle of the Heartby 13C NMR Spectroscopy,” Journal of Biological Chemistry, 263 (15), pp. 6964-6971.

[42] Craig R. Malloy, Dean Sherry, and Mark Jeffrey (1990), “Analysis of tricarboxylic acid cycle ofthe heart using 13C isotope isomers,” American Journal of Physiology, 259, pp. H987-H995.

[43] Lawrence R. Mead and Nikos Papanicolaou, “Maximum entropy in the problem of moments,”J. Math. Phys. 25, 2404–2417 (1984).

[44] K. Merboldt, Wolfgang Hanicke, and Jens Frahm (1969), “Self-diffusion NMR imaging usingstimulated echoes,” Journal of Magnetic Resonance, 64 (3), pp. 479-486.

[45] Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, andEdward Teller (1953), “Equation of State Calculations by Fast Computing Machines,” Journalof Chemical Physics. The previous link is to the Americain Institute of Physics and if you donot have access to Science Sitations you many not be able to retrieve this paper.

[46] Radford M. Neal (1993), “Probabilistic Inference Using Markov Chain Monte Carlo Methods,”technical report CRG-TR-93-1, Dept. of Computer Science, University of Toronto.

[47] Jeffrey J. Neil, and G. Larry Bretthorst (1993), “On the Use of Bayesian Probability Theory forAnalysis of Exponential Decay Data: An Example Taken from Intravoxel Incoherent MotionExperiments,” Magn. Reson. in Med., 29, pp. 642–647.

[48] H. Nyquist (1924), “Certain Factors Affecting Telegraph Speed,” Bell System Technical Journal,3, pp. 324-346.

[49] H. Nyquist (1928), “Certain Topics in Telegraph Transmission Theory,” Transactions AIEE, 3,pp. 617-644.

[50] William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery (1992),“Numerical Recipes The Art of Scientific Computing Second Edition,” Cambridge UniversityPress, Cambridge UK.

[51] Emanuel Parzen (1962), “On Estimation of a Probability Density Function and Mode,” Annalsof Mathematical Statistics 33, 1065–1076

[52] Karl Pearson (1895), “Contributions to the Mathematical Theory of Evolution. II. Skew Vari-ation in Homogeneous Material,” Phil. Trans. R. Soc. A 186, 343–326.

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[53] Murray Rosenblatt, “Remarks on Some Nonparametric Estimates of a Density Function,” An-nals of Mathematical Statistics 27, 832–837 (1956).

[54] Jeffery D. Scargle (1981), “Studies in Astronomical Time Series Analysis I. Random Process InThe Time Domain,” Astrophysical Journal Supplement Series, 45, pp. 1-71.

[55] Jeffery D. Scargle (1982), “Studies in Astronomical Time Series Analysis II. Statistical Aspectsof Spectral Analysis of Unevenly Sampled Data,” Astrophysical Journal, 263, pp. 835-853.

[56] Jeffery D. Scargle (1989), “Studies in Astronomical Time Series Analysis. III. Fourier Trans-forms, Autocorrelation Functions, and Cross-correlation Functions of Unevenly Spaced Data,”Astrophysical Journal, 343, pp. 874-887.

[57] Arthur Schuster (1905), “The Periodogram and its Optical Analogy,” Proceedings of the RoyalSociety of London, 77, p. 136-140.

[58] Claude E. Shannon (1948), “A Mathematical Theory of Communication,” Bell Syst. Tech. J.,27, pp. 379-423.

[59] John E. Shore, and Rodney W. Johnson (1981), ”Properties of cross-entropy minimization,”IEEE Trans. on Information Theory, IT-27, No. 4, pp. 472-482.

[60] John E. Shore and Rodney W. Johnson (1980), “Axiomatic derivation of the principle of maxi-mum entropy and the principle of minimum cross-entropy,” IEEE Trans. on Information The-ory, IT-26 (1), pp. 26-37.

[61] Devinderjit Sivia, and John Skilling (2006), “Data Analysis: A Bayesian Tutorial,” OxfordUniversity Press, USA.

[62] Edward O. Stejskal and Tanner, J. E. (1965), “Spin Diffusion Measurements: Spin Echoesin the Presence of a Time-Dependent Field Gradient.” Journal of Chemical Physics, 42 (1),pp. 288-292.

[63] D. G. Taylor and Bushell, M. C. (1985), “The spatial mapping of translational diffusion coeffi-cients by the NMR imaging technique,” Physics in Medicine and Biology, 30 (4), pp. 345-349.

[64] Myron Tribus (1969), “Rational Descriptions, Decisions and Designs,” Pergamon Press, Oxford.

[65] P. M. Woodward (1953), “Probability and Information Theory, with Applications to Radar,”McGraw-Hill, N. Y. Second edition (1987); R. E. Krieger Pub. Co., Malabar, Florida.

[66] Arnold Zellner (1971), “An Introduction to Bayesian Inference in Econometrics,” John Wileyand Sons, New York.

Index

Ak definition, 349Hj`(ti) definition, 349λ` definition, 349gjk eigenvalue, 349

Abscissa, 437Computational, 436Generating, 427Loading, 39Multicolumn, 437Number Of Columns, 458Total Data Values, 456

Aliases, 113, 126Amplitudes orthonormal definition, 349Analyze Image Pixel Package, 411

Modification History, 413Phased Images, 397Reports

Bayes Accepted, 413Using, 413Viewers

Fortran/C Models, 411Image, 411Prior Probabilities, 413

WidgetsAbscissa File, 411Build, 411Find Outliers, 411Get Statistics, 413System, 411User, 411

Analyze Image Pixel Unique Package, 423Highlight

Abscissa, 425Data, 425

Input ImageAbscissa, 423

Data, 423Reports

Bayes Accepted, 425Console Log, 425McMC Values, 425

Using, 425Viewers

Fortran/C Models, 423Image, 423Prior Probabilities, 425

WidgetsBuild, 423Find Outliers, 423Get Statistics, 425System, 423User, 423

Ascii Data Viewer, 53Assigning Probabilities, 118

Bandwidth, 111, 127Bayes Analyze Package, 155

Levenberg-Marquardt , 171Step, 194

Algorithm, 175Amplitudes, 197, 198Bayes Model, 159, 161Bayesian Calculations, 167Bruker, 162Build BA Model, 159Covariance, 174Default Parameters Settings, 155Error Messages, 200Fid Model Viewer, 160Interface, 156Likelihood

Gaussian, 158Student’s t-distribution, 158

484

INDEX 485

Log File, 193, 195Lorentzian lineshape, 161Marking Resonances, 157ModelJo, 165Jp, 165Js, 165Amplitude, 163, 164Bessel Function, 163Constants Models, 157Correlated, 157, 162, 164Equation, 161, 164, 164First Order Phase, 157, 162, 164First Point, 162, 164Gaussian, 163Imaginary Constant, 164Multi-Exponential, 163Multiple Data Sets, 165Multiplet Order, 164Multiplet Orders, 164Multiplets, 162Multiplets of Multiplets, 164Non-Lorentzian, 163Offsets, 162Real Constant, 164Relative Amplitude, 164–166Resonance Frequency, 165Shim Order, 163Shimming, 166Shimming Order, 164Uncorrelated, 157, 162, 164Zero Order Phase, 157, 162, 164

Model Interface, 160Multiplets, 158Newton-Raphson, 171Noise File, 158Noise Standard Deviation, 158Outputs

Bayes.accepted File, 177bayes.log.nnnn File, 177, 193, 193bayes.model.nnnn File, 177, 185, 197, 197bayes.noise File, 180bayes.noise.nnnn File, 158, 180bayes.output.nnnn File, 176, 186, 186bayes.params File, 176, 177bayes.params.nnnn File, 176, 177, 177

bayes.probabilities.nnnn File, 177, 190, 190bayes.status.nnnn File, 177, 196, 200bayes.summary1.nnnn File, 177, 198, 198bayes.summary2.nnnn File, 177, 199, 199bayes.summary3.nnnn File, 177, 200, 200Global Parameters, 182, 183Model File, 184Probabilities file, 191Zero Order Phase, 182

Parameter FileActivate Shims, 180Analysis Directory, 178By Fid, 181Data Type, 180Default Model, 181Directory Organization, 180Fid Model Name, 178File Version, 178First Fid, 181First Order Phase, 180, 183Imaginary Constant, 184Last Fid, 181lb, 182Maximum Candidates, 182Maximum New Resonances, 182Model Fid Number, 181Model Name, 184Model Names, 181Model Number, 184Model Points, 181Multiplets of Multiplets, 185Noise Start, 181Numerical Parameters, 178Output Format, 180Prior Odds, 182Procpar, 178Real Constant, 184Relative Amplitude, 183Resonance Model, 185Shim Order, 182Spectrometer Frequency, 182Text Parameters, 178Total Complex Data Values, 181Total Data Values, 181Total Sampling Time, 182True Reference, 182

486 INDEX

Units, 180Use Noise StdDev, 180User Reference, 182

Prior Probabilities, 167Probabilities File, 191Product Rule, 168Relative Amplitude, 167Remove Resonances, 159Reports

Bayes Status, 155Save/Reset, 159Search, 166

Levenberg-Marquardt , 166Short Parameter Description, 195Siemens, 162Status File, 196Steepest Descents, 173Sum Rule, 168Summary File, 198Summary Reports, 176Summary2, 199Summary3, 201Units, 161Using, 157Varian/Agilent, 162Widgets, 155

By, 158, 176First Point, 157, 163From, 158, 176Imag Offset, 163Imaginary Offset, 157Mark, 159Max New Res, 157New, 159Noise, 158Phase, 157Primary, 158Real Offset, 157, 163Remove, 159Remove All, 159Reset, 159, 193Restore, 159Save, 159Secondary, 159Shim Order, 157, 163Signal, 158

To, 158, 176Bayes Find Resonances Package, 239

Bayesian Calculations, 241Current Fid, 239Model Equation, 241Number of data sets, 239Phase Model

Automatic, 239, 242Common, 239, 242Independent, 239, 242

Prior Probabilities, 243–245Reports

Bayes Accepted, 241, 246Condensed, 246Console log, 246McMC Values, 246Prob Model, 246

Using, 239, 241Viewers

Fid Data, 240Fid Model, 240, 246File, 246Plot Results, 246Text, 246

WidgetsBuild FID Model, 240, 241, 246Constant, 239, 242First Trace, 239Last Trace, 239Model Fid Number, 241Phase Model, 239, 242

Bayes Home Directory, 45, 49Bayes Manual pdf, 469Bayes Metabolite Package

WidgetsShift Left, 222Shift Right, 222

Bayes Metabolite Package, 219Aligning Resonances, 221Bayesian Calculation, 225Metabolite Locations, 221Model Equation, 223Reports

Bayes Accepted, 221, 238Condensed, 238Console log, 238

INDEX 487

McMC Values, 238Prob Model, 238

ViewersFid Data, 219Fid Model, 221, 236File, 222, 238Metabolite, 221Plot Results, 238Text, 238

WidgetsFid Model, 221Fid Model Viewer, 221Load System Metabolite File, 219Load System Resonance File, 221Load User Metabolite File, 219Load User Resonance File, 221Shift Left, 221Shift Right, 221

Bayes Model, 159, 159Bayes Test Data Package, 427

Parameters, 431Reports

Bayes Accepted, 428Condensed, 429McMC Values, 429, 431–433

ViewersFortran/C Models, 427Image, 428Prior Probabilities, 427Text Data, 430Text Results, 429

Widgets# Images, 427# Slices, 427Abscissa, 427ArrayDim, 427Build, 427Get Job, 428Max Value, 427Noise SD, 427Parameter Ranges, 428Pe, 427Ro, 427Run, 428Set (server), 428Status, 428

Bayes’ Theorem, 100, 139, 145, 153, 167, 211,226, 243, 252, 261, 269, 278, 288, 295,306, 314, 315, 317, 318, 331, 333, 343,370, 399, 407, 439

Bayes.acceptedBody, 77Header, 76

Behrens-Fisher Package, 311Bayesian Calculations

Derived Probabilities, 320Different Mean And Same Variance, 318Different Mean And Variance, 319Parameter Estimation, 321Same Mean And Different Variance, 317Same Mean And Variance, 315

Model EquationDifferent Mean And Same Variance, 318Different Mean And Variance, 319Same Mean And Different Variance, 317Same Mean And Variance, 315

Number of data sets, 311Parameter Listing, 323Prior Probabilities

Different Mean And Same Variance, 318Different Mean And Variance, 319Same Mean And Different Variance, 317Same Means And Same Variance, 315

ReportsBayes Accepted, 311, 322Condensed, 322Console Log, 322, 323McMC Values, 322, 323Prob Model, 322

Using, 311Viewers

File, 322Plot Results, 322, 324Prior Probabilities, 311Text, 322

WidgetsNone, 311

Big Endian, 471, 473Big Magnetization Transfer Package, 259

Bayesian Calculations, 259Files

Bayes Analyze, 264

488 INDEX

Fid, 263Peak Pick, 262

Model Equation, 261Number of data sets, 259Prior Probabilities, 261Reports

Bayes Accepted, 259, 262Condensed, 262Console log, 262McMC Values, 262Prob Model, 262

Using, 259Viewers

Ascii Data, 259File, 262Prior Probabilities, 259Text, 262

WidgetsFind Outliers, 259

Big Peak/Little Peak Package, 207Bayesian Calculations, 209Fid Analyzed, 207Model Equation, 210

Metabolites, 209Solvent, 210

Number of data sets, 207Prior Probabilities

Metabolite, 207Solvent, 207

Removing Resonances, 207Reports

Bayes Accepted, 209, 216Condensed, 216Console log, 216McMC Values, 216Prob Model, 216

Using, 207Viewers

File, 216Model, 209Plot Results, 216Prior Probabilities, 207Text, 216

WidgetsMetabolite, 207Solvent, 207

Binned Density Function Estimation, 355Binned Histogram Package

ReportsBayes Accepted, 357

ViewersAscii, 355

Binned Histograms PackageUsing, 357Viewers

Prior Probabilities, 355Bloch-McConnell Equations, 267, 277

Changing the Bayes Home Directory, 469Compilers, 29

CC, 29, 455Fortran, 29, 455

Correlations, 91

Diffusion Tensor Package, 247Ascii File Formats, 247, 254, 255Bayesian Calculations, 249Prior Probabilities

∆, 254Γ, 254δ, 254σ, 253Amplitudes, 253Eigenvalues, 253Euler Angles, 253Likelihood, 253Parameter, 254

ReportsBayes Accepted, 247, 255Condensed, 255Console log, 255McMC Values, 255Prob Model, 255

Symmetries, 253Using, 247Viewers

File, 247, 255Plot Results, 255Prior Probabilities, 247, 253Text, 255

WidgetsAbscissa Options, 248

INDEX 489

Find Outliers, 247Include Constant, 247, 248, 255Tensor Number, 247, 248, 255Use b Matrix, 255Use b Vectors, 255Use g Vectors, 254

Discrete Fourier Transform, 110, 113, 123

Enter Ascii Model Package, 329Bayesian Calculations, 332

Marginalization, 332No Marginalization, 331

Fortran/C Models, 330, 335Model Equation

Marginalization, 331No Marginalization, 331

Output NamesDerived, 335Parameters, 335

ReportsBayes Accepted, 331, 335Bayes Params, 335Condensed, 335Console log, 335McMC Values, 335Prob Model, 335

Using, 331Viewers

Ascii Data, 329File, 335Fortran/C Models, 329Plot Results, 335Prior Probabilities, 329Text, 335

WidgetsBuild, 329Find Outliers, 329System, 329User, 329

Enter Ascii Model Selection Package, 341Bayesian Calculations

Marginalization, 346No Marginalization, 344

Fortran/C Models, 341, 343, 353Model Equation, 343

No Marginalization, 343

With Marginalization, 347Output Names

Derived, 354Parameters, 353

ReportsBayes Accepted, 343, 353Condensed, 353Console log, 353McMC Values, 353Params File, 353Prob Model, 353

Using, 343Viewers

Ascii Data, 341File, 353Fortran/C Models, 341Plot Results, 353Prior Probabilities Not Used, 341Text, 353

WidgetsBuild Not Used, 341Find Outliers, 341System, 341User, 341

Errors In Variables Package, 303Ascii File Formats

Errors In X and Y Known, 303, 309Errors In X Known, 303, 309Errors In Y Known, 303, 309Errors Unknown, 303, 309

Bayesian Calculations, 305Data Error Bars, 303Files

Ascii, 303Bayes Analyze, 303Peak Pick, 303

Model Equation, 305Number of data sets, 303Reports

Bayes Accepted, 305, 309Condensed, 309Console log, 309McMC Values, 309Prob Model, 309

Using, 305Viewers

490 INDEX

Ascii Data, 303File, 309Plot Results, 309Text, 309

WidgetsGiven Errors In, 303Order, 303

ExponentialsGiven Package, 137Inversion Recovery Package, 151Magnetization Transfer Package, 267Unknown Number of Package, 143

Fid Data Viewer, 53Fid Model Viewer, 68File Format

Ascii, 436File Viewer, 80Files

4dfp, 59, 428, 430, 470, 471Header, 473Reading, 471

Abscissa, 39, 77, 470afh, 53ASCII, 35, 36Ascii, 53, 54, 435k-space, 437Abscissa, 435, 436, 437Data, 435Image, 436

Bayes Analyze, 36Bayes.accepted, 51, 76Bayes.params, 76, 79Bayes.prob.model, 447BayesManual.pdf, 469Condensed, 77, 78Console.log, 76, 79, 465dir.info, 470fid, 470, 470

ASCII, 36ffh, 56Model, 68, 70procpar, 470Siemens Raw, 36Siemens Rda, 36Spectroscopic, 53

Varian fid, 36Fortran/C Models, 42, 455, 457, 458, 465–

467Images

4dfp, 38Binary, 38Bruker 2dseq, 38Bruker stack, 38DICOM, 38FDF, 38Multi-Column Text, 38Siemens IMA, 38

k-spaceText, 36Varian fid, 36

mcmc.values, 76, 449Model Listing, 77prob.model, 76procpar, 470Raw, 36RDA, 36Statistics, 65System.err.txt, 469System.out.txt, 469Varian fid, 36WaterViscosityTable, 469

Fortran/C Model Viewer, 93Popup Editor, 93

Fortran/C Models, 42, 330, 335, 353, 455Abscissa, 463Body, 463

Abscissa, 457Declarations, 462Derived Parameters, 457, 459, 463Edit/Create New Model, 42, 455I/O, 464Marginalization, 464Gj(Ω, ti), 464Amplitude Range, 465Example, 465, 466Model Vectors, 465Ordering Amplitudes, 465Parameter File, 465, 467Parameter Order, 465Parameters, 465

Model Files, 455

INDEX 491

Model Selection, 464No Marginalization, 457S(ti), 455Example, 456

Parameter File, 458, 459, 465Parameters, 463Signal, 463Subroutine Interface, 460

Abscissa, 462Current Set, 460Derived Parameters, 461Maximum No Of Data Values, 461Number Of Abscissa Columns, 461Number Of Data Columns, 461Number Of Derived Parameters, 461Number Of Model Vectors, 461Number Of Parameters, 460Parameters, 461Signal, 462Total Complex Data Values, 461

Subroutines and Functions, 464Frequency Estimation, 114, 132

Given Exponential Package, 137Bayesian Calculations, 140Files

Ascii, 137Bayes Analyze, 137Peak Pick, 137

Model Equation, 139Number of data sets, 139Prior Probabilities, 139–141Reports

Bayes Accepted, 137, 141Condensed, 141Console log, 141McMC Values, 141Prob Model, 141

Symmetries, 141, 148Using, 137Viewers

File, 141Plot Results, 141Prior Probabilities, 137, 139Text, 141

Widgets

Constant, 137, 139Find Outliers, 137Given Order, 27Include Constant, 27Order, 137, 139

Given Polynomial Order Package, 285Bayesian Calculations, 288Files

Ascii, 285Bayes Analyze, 285Peak Pick, 285

Gram-Schmidt, 287Model Equation, 287Number of data sets, 285Prior Probabilities, 289Reports

Bayes Accepted, 285, 291Condensed, 291Console log, 291McMC Values, 291Prob Model, 291

Scatter Plots, 292Using, 285Viewers

File, 290Plot Results, 291Text, 290

WidgetsSet Order, 285

HistogramsBinned, 381Kernel Density, 381

Image Model Selection Package, 415Abscissa, 415Fortran/C Models, 415, 417Reports

Bayes Accepted, 417Using, 417Viewers

Fortran/C Models, 415Image, 415

WidgetsNoise SD, 415System, 415

492 INDEX

Use Gaussian, 415User, 415

Image Viewer, 59Images

FlipHorizontal, 63Vertical, 63

Grayscale, 63ImageJ, 63Original, 63

Inversion Recovery Package, 151Bayesian Calculations, 153Model Equation, 153Number of data sets, 153Prior Probabilities, 153Reports

Bayes Accepted, 151, 154Condensed, 154Console Log, 154McMC Values, 154Prob Model, 154

Using, 151Viewers

Plot Results, 154Prior Probability, 151

WidgetsFind Outliers, 151

Kernel Density Function Package, 361Ascii File Format, 361Bayesian Calculations, 369Data Requirements, 361Data, Model And Residuals, 369Kernels, 369

Biweight, 362Cosine, 362Epanechnikov, 362Exponential, 362Gaussian, 362, 370nonnegative, 361Real Valued, 361Triangular, 362Tricube, 362Triweight, 362Uniform, 362

Likelihood, 371

Number of data sets, 364Plots

Expected Density Function, 367, 368Mean Density Function, 367, 368Posterior Probability for the Kernel Type,

365Posterior Probability for the Number Of

Kernels, 366Scatter Plots of Model Averaged Density

Function, 368Standard Deviation of the Mean Density

Function, 367, 368Prior Probabilities

Kernel Center, 371Kernel Smoothing Parameter, 371Kernel Type, 370Number Of Kernels, 370

ReportsBayes Accepted, 364Condensed, 372McMC Values, 372Prob Model, 372

Using, 364Viewers

Ascii, 361Widgets

Kernel Type, 364Output Size, 364

Levenberg-Marquardt, 171Linear Phasing Package, 395, 409

Interface, 397Model Equation, 398Widgets

cf, 403Display, 403Display Array Element, 403fn, 403fn1, 403Image Type, 402Load An Image, 402np, 403nv, 403Process, 403

Load Working Directory, 33Logical Independence, 117

INDEX 493

Magnetization Transfer Kinetics Package, 275Arrhenius Plot, 281Bayesian Calculation, 278Boltzmann’s Constant, 277Eyring Equation, 275, 276, 277, 280Model Equation, 277Plank’s Constant, 277Prior Probabilities, 279Reports

Bayes Accepted, 277, 281Condensed, 281Console log, 281McMC Values, 281Prob Model, 281

Sum and Difference Variables, 280Transmission coefficient, 277Universal Gas Constant, 277Using, 277van’t Hoff Plot, 281Viewers

Ascii File, 275File, 281Prior Probabilities, 275Text, 281

WidgetsLoad, 275, 281Set, 275Uncertainty, 275

Magnetization Transfer Package, 265Bayesian Calculations, 267Files

Ascii, 265Bayes Analyze, 265Inversion Recovery, 272Peak Pick, 265

Model Equation, 267Number of data sets, 265Prior Probabilities, 265, 270Reports

Bayes Accepted, 267, 272Condensed, 272Console log, 272McMC Values, 272Prob Model, 272

Three Column Data, 265Using, 267

ViewersAscii Data, 265Fid Data, 272File, 271Plot Results, 262, 272, 281Prior Probabilities, 265Text, 271

WidgetsFind Outliers, 265

Marginalization, 100Bayes Analyze Package, 174Behrens-Fisher, 315Big Magnetization Transfer, 261Big Peak/Little Peak, 211Diffusion Tensors, 252Enter Ascii Model Package, 331Errors In Variables, 306Fortran/C Models, 464Given Exponential, 139Inversion Recovery, 153Linear Phasing, 399Magnetization Transfer, 269Magnetization Transfer Kinetics, 278Metabolic Analysis, 225Nonexhaustive Hypotheses, 101Nuisance Hypotheses, 100Nuisance Parameter, 100Unknown Number of Exponentials, 146

Markov chain Monte Carlo, 132, 439Acceptance Rate, 444Annealing Schedule, 91, 442

Dynamic, 443Linear, 442

Killing Simulations, 443Maximum Posterior Probability, 91Metropolis-Hastings, 439Mixing, 91Monte Carlo Integration, 440Multiple Simulations, 441Posterior Probability, 440Random Number Generators, 440Repeats, 91Sampling, 91Simulated Annealing, 442the Proposal, 444

494 INDEX

MaxEnt Density Function Estimation Package,373

Data Requirements, 381Plots

Contour/Scatter, 375, 379Number Of Multipliers, 375, 378

ReportsBayes Accepted, 375Console Log, 375

Using, 375Viewers

Ascii, 373Plot, 375, 378Prior Probabilities, 373

WidgetsHistogram Size, 373Order, 373

Maximum Entropy Method Of Moments, 102,377, 381

Advantages, 386Problems, 386Review, 381

Maximum Entropy Method Of Moments PackageBayesian Calculations, 387Plots

Data, Model and Residuals, 380Menus

Files, 24, 354dfp, 37, 38Abscissa, 35, 39ASCII, 35, 36Binary, 38Bruker, 37Bruker 2dseq, 38Bruker Stack, 38DICOM, 37, 38FDF, 37, 38fid, 36, 37General Binary, 37Images, 35Import Working Directories in Batch, 40Import Working Directory, 40Load Images, 36, 37, 59Load Working Directory, 35Multi-Column Text, 37, 38Save Working Directory, 35, 39

Siemens IMA, 37, 38Single-Column Text, 38Spectroscopic Fid, 35Test Data, 35, 39Text k-space, 36Text k-space fid, 37User Manual, 35, 39

Help, 24Packages, 22, 24, 33, 40Settings, 46

Add Server, 48Auto Configure Server, 48McMC Parameters, 24, 46, 48Min Annealing Steps, 48, 48Port number, 48Preferences, 49, 63Remove Server, 48, 49Repetitions, 46, 48Server Name, 48Server Setup, 24, 26, 48Set Window Size, 49Simulations, 46, 48View Server Installation Info, 48, 49

Spectroscopy fid, 36Utilities, 24, 50

Memory Monitor, 50Software Updates, 50System Information, 50

WorkDirCreating, 22, 33, 46Deleting, 22, 33, 46List, 24, 46Loading, 46Name, 46Popup, 47

Model ComparisonBig Peak/Little Peak Package, 211

model orthonormal definition, 349Mouse

Control-left, 59Fid Data Viewer

Left, 56Right, 56

Shift-left, 59Multiplets

J-Coupling

INDEX 495

Center, 159Primary, 159Secondary, 159

Newton-Raphson, 171Noise Standard Deviation, 64Non-Linear Phasing Package, 405

Calculations, 407Model Equation, 405, 407Widgets

Process, 409Write Ascii images, 409Write imaginary images, 409

Nuisance Parameter, 100, 115, 135Nyquist Critical Frequency, 111, 127

orthonormal, 349Outliers, 475

Mean Parameter, 477Model, 475Prob Number of, 476Proposal, 475Red dot, 477Weighted Average, 477

PackagesAnalyze Image Pixel Unique, 423Bayes Analyze, 20, 43, 57, 155, 200Bayes Find Resonances, 21, 239Bayes Test Data, 427Behrens-Fisher, 21, 44, 311Big Magnetization Transfer, 20, 43, 259Big Peak/Little Peak, 20, 43, 207Binned Density Function Estimation, 355Binned Histograms, 21, 44Diffusion Tensors, 20, 40, 247Enter ASCII Model, 42Enter Ascii Model, 20, 329Enter ASCII Model Selection, 42Enter Ascii Model Selection, 20, 341Errors In Variables, 21, 44, 303Find Resonances, 43Given Exponential, 20, 40, 137Given Polynomial Order, 285Image Model Selection, 415Image Pixel, 21, 45, 411

Image Pixel Model Selection, 22, 45Inversion Recovery, 20, 40, 151Kernel Density Function, 361Linear Phasing, 21, 44, 395Magnetization Transfer, 20, 42, 265Magnetization Transfer Kinetics, 20, 43, 275Maximum Entropy Method Of Moments, 21,

44, 373Metabolic Analysis, 21, 43, 219Non-Linear Image Phasing, 21, 45, 405Polynomials

of Given Order, 21, 44of Unknown Order, 21, 44

Test ASCII Model, 42Test Ascii Model, 20, 337Unknown Number of Exponentials, 20, 40,

143Unknown Polynomial Order, 293

Parameter File, 42Number Of

Abscissa, 458Data Columns, 458Model Vectors, 458Priors, 458

Prior Probability, 459Amplitude, 460High, 459Low, 459Mean, 459NonLinear, 460Ordered, 460Parameter File, 459Peak, 459Prior Type, 460Standard Deviation, 459

Phase Cycling, 162Plot Results Viewer, 71Plots

Data and Model, 81Data, Model and Residuals, 81Expected Log Likelihood, 88Logarithm of the Posterior Probability, 91Maximum Entropy Histogram, 84Maximum Entropy Histograms, 83McMC Samples, 83, 85Parameter Vs Posterior Probability, 86, 87

496 INDEX

Posterior Probability, 82Posterior Probability Vs Parameter Value,

86Residuals, 81Scatter, 88, 91

png graphics, 59Posterior Probability Vs Parameter Value, 86Power Spectrum, 112, 123, 124Prior Probabilities

Bayes Phase, 399Big Magnetization Transfer, 261Big Peak/Little Peak, 212Diffusion Tensor, 253Enter Ascii Model, 331, 333Errors In Variables, 306Magnetization Transfer, 269Magnetization Transfer Kinetics, 279Non-Linear Phasing PackageA, 408θ, 408

Prior Probability, 42, 65, 65Exponential, 67, 459Gaussian, 67, 104, 106, 459Jeffreys’, 118Normalization Constant, 67Parameter, 68, 459Positive, 68, 460Uniform, 67, 103, 118, 459

Prior Viewer, 65, 93Probabilities

Expected Log Likelihood, 453Likelihood, 453Posterior, 453Prior, 453

Product Rule, 99, 119, 344, 439

ReferencingSetting, 59

ReportsAccepted File, 76McMC Values File

General Description, 449Maximum Posterior Probability Simula-

tions, 451Mean Values, 452Prior, 450

Standard Deviations, 453Restoring An Analysis, 22, 35, 40ROI

Expanding, 63Pixels, 63Point, 62Polygon, 62Square, 62

Saving An Analysis, 35, 39Schuster Periodogram, 112, 123Screen Captures, 49Settings

httpd server, 19Software

Bayes Account, 29CC, 29Fortran, 29Installation, 29javaws, 29OS requirements, 29root requirements, 30

Start Up Window, 22, 33Steepest Descents, 173Subdirectories, 469

Bayes, 39Bayes.model.fid, 470Bayes.Predefined.Spec, 469Bayes.test.data, 39BayesAnalyzeFiles, 470BayesAsciiModels, 93, 469BayesOtherAnalysis, 35, 73, 470fid, 36, 53images, 36, 38, 39, 59, 470model.compile, 470plugins, 470Properties, 470Resources, 470Spectroscopic

fid, 470Working Directories, 470

Subroutine Names, 464Sufficient Statistics, 122

Definition, 105Location Parameter, 108

Sum Rule, 100, 119, 344, 440

INDEX 497

Test Ascii Model Package, 337Reports

Bayes Accepted, 339Mcmc Values, 339

Using, 339, 428Viewers

Ascii Data, 337Fortran/C Models, 337Prior Probabilities, 337

WidgetsBuild, 337Find Outliers, 339System, 337User, 337

Thermodynamic Integration, 445, 449

Uninstall, 49Unknown Number of Exponentials Package, 143

Bayesian Calculations, 145Model Equation, 145Reports

Bayes Accepted, 143, 148Condensed, 148Console Log, 148, 149McMC Values, 148Prob Model, 148

Using, 143Viewers

File, 148Plot Results, 149, 150Prior, 143Text, 148

WidgetsConstant, 143Find Outliers, 143Order, 143

Unknown Polynomial Order Package, 293Bayesian Calculations, 295Files

Ascii, 293Bayes Analyze, 293Peak Pick, 293

Model Equation, 295Number of data sets, 293Reports

Bayes Accepted, 293, 299

Condensed, 299Console Log, 298, 299McMC Values, 299Polynomial Order Plot , 301Prob Model, 299

Using, 293Viewers

File, 299Text, 299

WidgetsSet Order, 293, 294Unknown Order, 293, 294

Viewers, 27, 52ASCII Data, 36Ascii Data, 27, 53, 56, 63, 137, 265, 275,

285, 293, 311, 329, 337, 341Expanding Plot, 53Printing, 53Right click, 53

Bayes Model, 160Fid Data, 27, 265fid Data, 53, 53, 285, 293

Auto Range, 59Autoscale, 56Clear Cursors, 56Clear Data, 57Copy, 59Cursor, 56Data Info, 57Expand, 56fn, 57Full, 56Get Peak, 56Phase Popup, 57Print, 59Properties, 59Referencing, 59Save As, 57, 59Set Preference, 57Units, 59Zoom, 59

Fid Model, 27fid Model, 68, 186

Build BA Model, 70, 159Data, 71

498 INDEX

Horizontal, 71Model, 71Overlay, 71Report, 71Residual, 71Stacked, 71Trace, 71Vertical, 71

File, 28, 80Fortran/C Models, 93, 330Image, 27, 59, 415

Autoset Grayscale, 61Copy Selected, 62Delete All, 61Delete Selected, 61Display Full, 61Element Selection, 60Export, 62Get Statistics, 64, 65Get Threshold Statistics, 65Grayscale, 63Image Selection, 60List, 59Load Selected Pixels, 61Max, 64Mean, 64Min, 64Right Click, 61RMS, 64Save Displayed, 62Save Statistics, 65Sdev, 64Set Image Area, 62Show Histogram, 61Show Info, 62Slice, 62Slice Selection, 60Statistics, 60Value, 64View Selected Pixels, 61Viewer Settings, 62Viewing, 62X Pos, 64Y Pos, 64

Plot Results, 28, 71Prior, 27, 65

Prior Probabilities, 138, 312Text, 141, 271, 281, 290, 309, 322, 335, 353Text Results, 26, 28, 52, 74

Bayes Analyze, 176

WidgetsAnalyze Image Pixel Package

Build, 411Find Outliers, 411Get Statistics, 413System, 411User, 411

Analyze Image Pixel Unique PackageBuild, 423Find Outliers, 423Get Statistics, 425System, 423User, 423

Ascii Data ViewerDelete, 53Left-mouse, 53Right-mouse, 53

Bayes Analyze PackageBy, 158, 176First Point, 163From, 158, 176Imag Offset, 163Mark, 159Max New Res, 157New, 159Noise, 158Phase, 157Primary, 158Real Offset, 163Remove, 159Remove All, 159Reset, 159, 193Restore, 159Save, 159Secondary, 159Shim Order, 157, 163Signal, 158To, 158, 176

Bayes Find Resonances PackageBuild FID Model, 240, 241, 246Constant, 239, 242

INDEX 499

First Trace, 239Last Trace, 239Model Fid Number, 241Phase Model, 239, 242

Bayes Metabolite PackageFid Model, 221Fid Model Viewer, 221Load System Metabolite File, 219Load System Resonance File, 221Load User Metabolite File, 219Load User Resonance File, 221Shift Left, 221, 222Shift Right, 221, 222

Bayes Test Data Package# Images, 427# Slices, 427Abscissa, 427ArrayDim, 427Build, 427Get Job, 428Max Value, 427Noise SD, 427Pe, 427Ro, 427Run, 428Set (server), 428Status, 428System, 427User, 427

Big Magnetization Transfer PackageFind Outliers, 259

Big Peak/Little Peak PackageMetabolite, 207Solvent, 207

Diffusion Tensor PackageAbscissa Options, 248Find Outliers, 247Include Constant, 247, 248, 255Tensor Number, 247, 248, 255Use b Matrix, 255Use b Vectors, 254, 255Use g Vectors, 254

Enter Ascii Model PackageFind Outliers, 329System, 329User, 329

Enter Ascii Model Selection PackageFind Outliers, 341System, 341User, 341

Errors In Variables PackageGiven Errors In, 303Order, 303

Fid Data ViewerAutoscale, 56Clear Cursors, 56Cursor A, 56Cursor B, 56Delta, 56Display Type, 56Expand, 56Full, 56Get Peak, 56Left-mouse, 56Options, 57, 59Right-mouse, 56Trace, 70

Fortran/C Model ViewerAbscissa Spinner, 93Add Prior, 96Allow/Disallow Editing, 97Cancel and Exit, 96Changing Models, 94Code, 93, 94Compile Results, 97Compiling, 96Create/Edit Model, 93Data Columns Spinner, 93Derived, 96Edit/Create New Model, 93, 94High, 97Low, 97Mean, 97Model, 96Model Vectors, 93Name (parameter), 97Order, 97Parameter Type, 97Parameters button, 93, 94, 96Prior Type, 97Priors, 96Remove All (priors), 96

500 INDEX

Remove Prior, 96Remove Selected Model, 93Save and Load, 96Standard Deviation, 97

Given Exponential PackageConstant, 137, 139Find Outliers, 137Order, 137, 139

Given Polynomial Order PackageSet Order, 285

GlobalBayes Find Outliers, 27Cancel, 26, 51Edit Servers, 26Get Job, 26, 51, 137, 143, 151, 155, 209,

221, 241, 247, 259, 267, 277, 285, 293,305, 311, 331, 339, 343, 357, 364, 375,413, 417, 425, 428

Reset, 27Restore Analysis, 22Run, 26, 51, 137, 143, 151, 155, 207, 221,

241, 247, 248, 259, 267, 277, 285, 293,305, 311, 329, 337, 343, 357, 364, 373,413, 415, 425, 428

Save, 27Set (server), 26, 52, 137, 143, 151, 155,

207, 221, 239, 247, 259, 265, 277, 285,293, 305, 311, 329, 337, 343, 355, 364,373, 413, 415, 425, 428

Status, 26, 52, 137, 143, 151, 155, 207,221, 241, 247, 259, 267, 277, 285, 293,305, 311, 329, 337, 343, 355, 364, 373,413, 415, 425, 428

Image Model Selection PackageSystem, 415User, 415

Image ViewerElement Number, 62Get Statistics, 64Get Threshold Statistics, 65Grayscale, 63Save Statistics, 65Slice Number, 62Value, 64X Pos, 64Y Pos, 64

Inversion Recovery PackageFind Outliers, 151

Kernel Density Function PackageKernel Type, 364Output Size, 364

Linear Phasing Packagecf, 403Display, 403Display Array Element, 403fn, 403fn1, 403Image Type, 402Load An Image, 402np, 403nv, 403Process, 403

Magnetization Transfer Kinetics PackageLoad, 275, 281Set, 275Uncertainty, 275

Magnetization Transfer PackageFind Outliers, 265

MaxEnt Density Function Estimation Pack-age

Histogram Size, 373Order, 373

Non-Linear Phasing PackageProcess, 409Write Ascii images, 409Write imaginary images, 409

Prior ViewerHigh, 65Low, 65Mean, 65Prior Type, 67

ServerEdit, 52Name, 26, 52, 52Set (server), 48Setup, 48, 52

Test Ascii Model PackageFind Outliers, 339System, 337User, 337

Text Results ViewerCopy, 74

INDEX 501

Down arrow, 74Enable Editing, 74Print, 74Save (a copy), 74Save As, 74Settings, 74Up arrow, 74

Unknown Number of Exponentials PackageConstant, 143Find Outliers, 143Order, 143

Unknown Polynomial Order PackageSet Order, 293, 294Unknown Order, 293, 294

WorkDirCreating, 22, 33, 46Deleting, 22, 33, 46List, 24, 46Loading, 46Name, 46Popup, 47