TY - JOUR

T1 - Bayesian analysis. II. Signal detection and model selection

AU - Bretthorst, G. Larry

PY - 1990/7

Y1 - 1990/7

N2 - In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment, and select the simplest model that "best" fits the data.

AB - In the preceding. paper, Bayesian analysis was applied to the parameter estimation problem, given quadrature NMR data. Here Bayesian analysis is extended to the problem of selecting the model which is most probable in view of the data and all the prior information. In addition to the analytic calculation, two examples are given. The first example demonstrates how to use Bayesian probability theory to detect small signals in noise. The second example uses Bayesian probability theory to compute the probability of the number of decaying exponentials in simulated T1 data. The Bayesian answer to this question is essentially a microcosm of the scientific method and a quantitative statement of Ockham's razor: theorize about possible models, compare these to experiment, and select the simplest model that "best" fits the data.

UR - http://www.scopus.com/inward/record.url?scp=0000553722&partnerID=8YFLogxK

U2 - 10.1016/0022-2364(90)90288-K

DO - 10.1016/0022-2364(90)90288-K

M3 - Article

AN - SCOPUS:0000553722

VL - 88

SP - 552

EP - 570

JO - Journal of Magnetic Resonance (1969)

JF - Journal of Magnetic Resonance (1969)

SN - 0022-2364

IS - 3

ER -