About the Bayesian Analysis Software

The Bayesian Analysis software was developed at Washington University by Dr. G. Larry Bretthorst. It contains a series of programs and macros, called packages, that implement various calculations using Bayesian probability theory. This software is fully integrated into VNMR6.1x and contains an extensive interface that allows the users to configure an analysis and then run it either under VNMR control, in background or on a remote host. Most of these calculations are implemented using Markov chain Monte Carlo. All of the programs except Bayes Analyze, an older program that was not implemented using Markov chains, are capable of fully using multiple CPUs if you have them. All of the programs can be run locally or remotely. To the user whether or not a job is running locally or remotely is fully transparent. Remote processing machines can run the programs in background or using a batch queuing system and the remote machine need not have VNMR.

The various Bayesian calculations performed by this software include:

• A time domain frequency estimation program that is fully capable of determining the number of resonances in a VNMR FID and estimating the resonance parameters.
• A common problem is to estimate the decay rate constants using data that are known to contain signals that are decaying exponentials. The sums of exponentials package estimates the exponential parameters when the number of exponentials is either known or unknown.
• Metabolic models determine the intensity of NMR resonances given a series of metabolic parameters and a resonance model. The metabolic package reads these resonance and the metabolic models and then uses Bayesian probability theory to estimate the metabolic parameters.
• In NMR it is common to have a solvent resonance that may be many hundreds of times more intense than the resonances of interest. The Big Peak/Little Peak package solves this problem by treating the solvent resonance as a nuisance and then uses Bayesian probability theory to account for the solvent while simultaneously estimating the frequencies, decay rate constants and amplitudes of the resonances of interest.

• MAS cross-polarization spin-lock contact time experiments are common in solids NMR. In this package we use Bayesian probability theory to estimate both the time constant of a spin-locked cross-polarization and the relaxation time of ¹³C polarization in the proton rotating field.
• To measure diffusion coefficients using NMR, the gradient strengths must be calibrated using a known diffusion coefficient. Unfortunately, most procedures don't take into account how uncertain one is of the calibration diffusion coefficient nor do they account for the noise in the calibration experiment itself. The diffusion package implemented in the Bayesian Analysis software does a joint calibration of the gradients strengths and an analysis of the diffusion data that self-consistently calibrates the gradients and estimates the diffusion coefficient.
• Three different two site magnetization transfer analysis are available: First, when one of the sites can be considered infinite compared to the other the solution to the two site magnetization transfer equations simplify. The package Big Magnetization transfer analyzes this type of data using Bayesian probability theory. Second, the solution to the Block-McConnell equations is used to estimate the exchange rate constants for Two Site Magnetization exchange data. Finally, the Block-McConnel equations are supplemented with the Eyring equations for the exchange rates and the kinetic package analyzes two site exchange data as a function of temperature to estimate the enthalpies and entropy of activation.
• The software also includes two packages that allow the user to build their own models. In the first case the users can enter a resonance model of an FID and then analyze it using Bayesian probability theory. These resonance models may be as simple as a series of singlets or as complicated as multiplets of multiplets of multiplets. In addition to being able to build a resonance model, sometimes the models of data are available that have not been implemented in this software. These models can be analyzed using the Enter Ascii package. In this package the user defines the parameters to be used, enters the model in either a `gcc' or Fortran function, the model is compiled and dynamically linked to the package and, finally, analyzed using Bayesian probability theory.
• There is a polynomial package that allows one to estimate the parameters associated with polynomial models for both the given and unknown models. So this package essentially allows one to determine what signal is present in the data given that one doesn't have a good model of the system.
• There is a second polynomial package that solves the so called errors-in-variables problem, i.e., fitting polynomials when there are errors in both x and y.
• Finally, there is a package that solves the Behrens-Fisher problem. The Behrens-Fisher problem is the classical medical testing problem: given two experiments that consist of repeated measurements of the same quantity where in the second measurement one has change some experiential parameter determine if the experiments are the same or if they differ.

This site is being maintained by:
Larry Bretthorst
Dept. Of Chemistry and Radiology
Washington University
St. Louis MO 63130

Phone: 314 362-9994