Incorporating prior knowledge improves detection of differences in bacterial growth rate

BACKGROUND: Robust statistical detection of differences in the bacterial growth rate can be challenging, particularly when dealing with small differences or noisy data. The Bayesian approach provides a consistent framework for inferring model parameters and comparing hypotheses. The method captures the full uncertainty of parameter values, whilst making effective use of prior knowledge about a given system to improve estimation. RESULTS: We demonstrated the application of Bayesian analysis to bacterial growth curve comparison. Following extensive testing of the method, the analysis was applied to the large dataset of bacterial responses which are freely available at the web-resource, ComBase. Detection was found to be improved by using prior knowledge from clusters of previously analysed experimental results at similar environmental conditions. A comparison was also made to a more traditional statistical testing method, the F-test, and Bayesian analysis was found to perform more conclusively and to be capable of attributing significance to more subtle differences in growth rate. CONCLUSIONS: We have demonstrated that by making use of existing experimental knowledge, it is possible to significantly improve detection of differences in bacterial growth rate

Repeatability of IVIM biomarkers from diffusion-weighted MRI in head and neck:Bayesian probability versus neural network

Purpose: The intravoxel incoherent motion (IVIM) model for DWI might provide useful biomarkers for disease management in head and neck cancer. This study compared the repeatability of three IVIM fitting methods to the conventional nonlinear least-squares regression: Bayesian probability estimation, a recently introduced neural network approach, IVIM-NET, and a version of the neural network modified to increase consistency, IVIM-NETmod. Methods: Ten healthy volunteers underwent two imaging sessions of the neck, two weeks apart, with two DWI acquisitions per session. Model parameters (ADC, diffusion coefficient (Formula presented.), perfusion fraction (Formula presented.), and pseudo-diffusion coefficient (Formula presented.)) from each fit method were determined in the tonsils and in the pterygoid muscles. Within-subject coefficients of variation (wCV) were calculated to assess repeatability. Training of the neural network was repeated 100 times with random initialization to investigate consistency, quantified by the coefficient of variance. Results: The Bayesian and neural network approaches outperformed nonlinear regression in terms of wCV. Intersession wCV of (Formula presented.) in the tonsils was 23.4% for nonlinear regression, 9.7% for Bayesian estimation, 9.4% for IVIM-NET, and 11.2% for IVIM-NETmod. However, results from repeated training of the neural network on the same data set showed differences in parameter estimates: The coefficient of variances over the 100 repetitions for IVIM-NET were 15% for both (Formula presented.) and (Formula presented.), and 94% for (Formula presented.); for IVIM-NETmod, these values improved to 5%, 9%, and 62%, respectively. Conclusion: Repeatabilities from the Bayesian and neural network approaches are superior to that of nonlinear regression for estimating IVIM parameters in the head and neck

An Introduction to Parameter Estimation Using Bayesian Probability Theory

. Bayesian probability theory does not define a probability as a frequency of occurrence; rather it defines it as a reasonable degree of belief. Because it does not define a probability as a frequency of occurrence, it is possible to assign probabilities to propositions such as "The probability that the frequency had value ! when the data were taken," or "The probability that hypothesis x is a better description of the data than hypothesis y." Problems of the first type are parameter estimation problems, they implicitly assume the correct model. Problems of the second type are more general, they are model selections problems and do not assume the model. Both types of problems are straight forward applications of the rules of Bayesian probability theory. This paper is a tutorial on parameter estimation. The basic rules for manipulating and assigning probabilities are given and an example, the estimation of a single stationary sinusoidal frequency, is worked in detail. This example is su..

Bayesian Analysis of Linear Phased-Array Radar

. A number of methods have been developed to analyze the response of the linear phased array radar. These perform remarkably well when the number of sources is known, but in cases where a determination of this number is required, problems are often encountered. These problems can be resolved by a Bayesian approach. Here, a linear phased-array consisting of equally spaced elements is considered. Analytic expressions for the posterior probability distribution over source positions and amplitudes, and the corresponding Hessians are derived. These are integrated to give the evidence for each model order. Tests using model data showed that performance at the second level of inference is critically determined by the accuracy of position estimation. If adequate parameter optimization is available, the Bayesian approach is demonstrated to work well, even in extreme circumstances. A commonly employed method of source location, noise subspace eigenanalysis of the correlation matrix, was tried an..

From Laplace to supernova SN 1987a: Bayesian Inference In Astrophysics

The Bayesian approach to probability theory is presented as an alternative to the currently used long-run relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to well-posed statistical problems, and is historically the original approach to statistics. The reasons for earlier rejection of Bayesian methods are discussed, and it is noted that the work of Cox, Jaynes, and others answers earlier objections, giving Bayesian inference a firm logical and mathematical foundation as the correct mathematical language for quantifying uncertainty. The Bayesian approaches to parameter estimation and model comparison are outlined and illustrated by application to a simple problem based on the gaussian distribution. As further illustrations of the Bayesian paradigm, Bayesian solutions to two interesting astrophysical problems are outlined: the measurement of weak signals in a strong background, and the analysis of the neutrinos detected from supernova SN 1987A. A brief bibliography of astrophysically interestin

Clearing Up Mysteries - The Original Goal

: We show how the character of a scientific theory depends on one's attitude toward probability. Many circumstances seem mysterious or paradoxical to one who thinks that probabilities are real physical properties existing in Nature. But when we adopt the "Bayesian Inference" viewpoint of Harold Jeffreys, paradoxes often become simple platitudes and we have a more powerful tool for useful calculations. This is illustrated by three examples from widely different fields: diffusion in kinetic theory, the Einstein--Podolsky--Rosen (EPR) paradox in quantum theory, and the second law of thermodynamics in biology. INTRODUCTORY REMARKS 2 THE MOTIVATION 2 DIFFUSION 3 DISCUSSION 6 THE MIND PROJECTION FALLACY 7 BACKGROUND OF EPR 7 CONFRONTATION OR RECONCILIATION? 8 EPR 9 THE BELL INEQUALITIES 10 BERNOULLI'S URN REVISITED 13 OTHER HIDDEN--VARIABLE THEORIES 14 THE SECOND LAW IN BIOLOGY 15 GENERALISED EFFICIENCY FORMULA 17 THE REASON FOR IT 18 QUANTITATIVE DERIVATION 20 A CHECK 23 CONCLUSION 24 REFER..