An experimental approach to medical decision problems

We have previously described how imaging systems and image reconstruction algorithms can be evaluated on the basis of how well binary-discrimination tasks can be performed by a machine algorithm that `views' the reconstructions. Algorithms used in these investigations have been based on approximations to the ideal observer of Bayesian statistical decision theory. The present work examines the performance of an extended family of such algorithmic observers viewing tomographic images reconstructed from a small number of views using the Cambridge Maximum Entropy software, MEMSYS 3. We investigate the effects on the performance of these observers due to varying the parameter (alpha) ; this parameter controls the stopping point of the iterative reconstruction technique and effectively determines the smoothness of the reconstruction. For the detection task considered here, performance is maximum at the lowest values of (alpha) studied; these values are encountered as one moves toward the limit of maximum likelihood estimation while maintaining the positivity constraint intrinsic to entropic priors. A breakdown in the validity of a Gaussian approximation used by one of the machine algorithms (the posterior probability) was observed in this region. Measurements on human observers performing the same task show that they perform comparably to the best machine observers in the region of highest machine scores, i.e., smallest values of (alpha) . For increasing values of (alpha) , both human and machine observer performance degrade. The falloff in human performance is more rapid than that of the machine observer at the largest values of (alpha) (lowest performance) studied. This behavior is common to all such studies of the so-called psychometric function.

There are many applications of Bayesian decision theory in computer science and mathematical modeling. Because of how it works, the algorithm can evaluate possible outcomes and choose a course of action. Decisions are made in the face of ambiguity and incomplete information in every area of human activity. When making a choice, it is common for the outcomes and their worth to the decision maker to rely on factors outside their control. Bayesian decision theory is devoted to solving these sorts of decision-making difficulties. Using Bayesian decision theory has benefited engineering, economics, business, public policy, and even AI. Examining recent literature in the field, this study delves into how Bayesian decision theory might be used for tasks including mistake detection, risk assessment, and route planning. The study’s findings demonstrate the value and utility of using Bayesian decision theory, and the authors hope that its presentation will stimulate the use of a similar approach in the future.

Classical and Bayesian statistical decision theory

-3 HHE work of several writers appears largely to have succeeded in mak..Ling disreputable the once fashionable practice of crediting public investment activities in the development of water resources, in particular, with substantial "secondary" or "indirect" benefits.2 Secondary benefits in one guise or another still appear to be much in style, however, in dealing with the benefits of investments in highways and other transportation facilities. Among the benefits of highway investment to which reference is commonly made are those presumed to accrue to property owners. More specifically, many studies have demonstrated that land values tend to increase sometimes dramatically-in the vicinity of newly improved highways.3 Since these increases are independent of the extent to which the affected property owners use the highway facilities involved, such gains are quite properly labeled "non-user benefits." They are, furthermore, commonly regarded as benefits over and above those that accrue to highway users. That is to say, they are regarded as benefits that must in some way be added to those arising directly from highway use if total highway benefits are to be estimated accurately. Although widely accepted (particularly among highway planners), this final conclusion is, as it happens, fallacious. That property values increase in the vicinity of highway improvements does reflect the existence of highway benefits. Careful analysis of highwayland value relationships can yield valuable information on the magnitude of these benefits. Increases in land value are not in themselves net highway benefits, however. Rather, they reflect an actual or potential transfer of benefits derived from highways from one population group to another. Furthermore, the fact that land values generally do increase in the vicinity of highway improvements by no means guarantees that a net effect of these improvements is to increase land values as a whole. The primary goal of this paper is to demonstrate these assertions by exploring the relationship between land values on the one hand and transportation costs and reductions in them on the other. More specifically, Section I demonstrates the effects of certain types of transporta1 I am indebted to Robert Clower, William Garrison, William Pendleton, and Stephen Sobotka for much helpful advice. Richard Morrill undertook one of the preliminary analyses underlying the material reported in Section II, while Harold Williamson, Jr., directed most of the statistical work entailed in this section. The work reported here was undertaken as part of a larger study of the nature and measurement of highway benefits carried out with the support of the Bureau of Public Roads. My views do not necessarily reflect those of the Bureau, however.

In assessing structural safety, the state of knowledge is imperfect when uncertainties arise from estimation error or model imperfection. The nature of these uncertainties is fundamentally different from those arising from inherent variabilities. A reliability index under such conditions is a point estimator of safety. Motivated by needs in structural code development, a set of fundamental requirements on the point-estimator reliability index are formulated. Existing definitions of the reliability index are examined in this light and are found to be deficient in satisfying one or more of the requirements. Based on the concepts from Bayesian statistical decision theory, a new reliability index is introduced which satisfies all the stipulated requirements. The index recognizes the fundamental difference between the sources of uncertainty and provides a rational basis for the assessment of structural safety and for development of reliability-based codes under arbitrary states of knowledge. Methods are also developed for quantifying the uncertainty in the measure of safety arising from the imperfect state of knowledge. Existing reliability methods can be used to compute the probability distribution or variance of the safety measure. A simple example illustrates the main concepts of the paper.

In this final chapter we consider several fuzzy algorithms that effect partitions of feature space ℝ p , enabling classification of unlabeled (future) observations, based on the decision functions which characterize the classifier. S25 describes the general problem in terms of a canonical classifier, and briefly discusses Bayesian statistical decision theory. In S26 estimation of the parameters of a mixed multivariate normal distribution via statistical (maximum likelihood) and fuzzy (c-means) methods is illustrated. Both methods generate very similar estimates of the optimal Bayesian classifier. S27 considers the utilization of the prototypical means generated by (A11.1) for characterization of a (single) nearest prototype classifier, and compares its empirical performance to the well-known k-nearest-neighbor family of deterministic classifiers. In S28, an implicit classifier design based on Ruspini’s algorithm is discussed and exemplified.

An overview of Bayesian statistical decision theory is presented in the tutorial spirit. A section on fundamental principles is followed by selected applications of the Bayesian approach to parameter estimation, pattern recognition, image processing, computer-aided medical diagnosis, optimal diagnostic test selection, and radiotherapy treatment planning.

BackgroundTranslating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made.ResultsWe compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogenous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations.ConclusionWe present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

This research work is based on the location prediction of wireless nodes with the terrains/clutters considerations. Multi-condition Bayesian decision theory is applied for precision in selected locations. Currecnt research is the continution of our previous research work in which twelve terrains were proposed based on the atmospharic atteunation. In the first phase of paper, basic parameters such as receive signal strength and available signal strength are calculated by using terrain/clutter considerations. Secondly, geomatric approach is used to calculate angle of arrival. Finally, multi-condition bayesian decision theory is used to precise the calculated results. Three posterior probabilities, the angle error rate (e), overlapping coverage area (Ω) and the terrains/clutters error rate (Ć) are used with the Bayesian decision theory for the most probable location of wireless node. Results show that 60%- 80% accuracy could be achived if proper terrain defination and multi-condition bayesian decision theory is followed.

Bayesian statistical theory is a convenient way of taking a priori information into consideration when inference is made from images. In Bayesian image segmentation, the a priori distribution should capture the knowledge about objects. Taking inspiration from (Alvarez et al., 1999), we design a prior density that penalizes the area of homogeneous parts in images. The segmentation problem is further formulated as the estimation of the set of curves that maximizes the posterior distribution. In this paper, we explore a posterior distribution model for which its maximal mode is given by a subset of level curves, that is the boundaries of image level sets. For the completeness of the paper, we present a stepwise greedy algorithm for computing partitions with connected components.

The artificial neural network began in 1940, which is an important part of artificial intelligence. At present, it has become a hot topic in the fields of neuroscience, computer science, brain science, mathematics, and psychology. Thomas Bayes firstly reported the Bayesian theory in 1763. After the development in the twentieth century, it has been widespread in all areas of statistics. In recent years, due to the solution of the problem of high-dimensional integral calculation, Bayesian Statistics has been improved theoretically, which solved many problems that cannot be solved by classical statistics and is also applied to the interdisciplinary fields. In this paper, the related concepts and principles of the artificial neural network are introduced. It also summarizes the basic content and principle of Bayesian Statistics, and combines the artificial neural network technology and Bayesian decision theory and implement them in all aspects of image recognition, such as enhanced face detection method based on neural network and Bayesian decision, as well as the image classification based on the Bayesian decision. It can be seen that the combination of artificial intelligence and statistical algorithms has always been the hot research topic.

Problem statement: The study and research of survival or reliability or life time belong to the same area of study but they may belong to a different area of application. In survival analysis one can use several life time distribution, exponential distribution with mean life time θ is one of them. To estimate this parameter and survival function we must be used estimation procedures with less MSE and MPE. Approach: The only statistical theory that combined modeling inherent uncertainty and statistical uncertainty is Bayesian statistics. The theorem of Bayes provided a solution to how learn from data. Bayes theorem was depending on prior and posterior distribution and standard Bayes estimator depends on Jeffery prior information. In this study we annexed Jeffery prior information to get the modify Bayes estimator and then compared it with standard Bayes estimator and maximum likelihood estimator to find the best (less MSE and MPE). Results: when we derived Bayesian and Maximum likelihood of the scale parameter and survival functions. Simulation study was used to compare between estimators and Mean Square Error (MSE) and Mean Percentage Error (MPE) of estimators are computed. Conclusion: The new proposed estimator of modify Bayes estimator in parameter and survival function was the best estimator (less MSE and MPE) when we compared it with standard Bayes and maximum likelihood estimator.

The quality of in situ data is key to calculating resistance factor of bored piles. However, it is difficult to summarize accuracy data due to various uncertainties in engineering. This paper employs the Bayesian method and mathematical statistics theory to put forward an estimation method for updating in situ data. A testing database (33 tests in noncohesive soils and 53 tests in cohesive soils) of bored piles is summarized. The model factor of bored piles is quantified as the ratio of the measured capacity to the calculated capacity. The proposed method is used to classify summarized data into three categories, which are “good data,” “general data,” and “bad data.” The “bad data” are discarded because of bad contribution to calculation, and Bayesian theory is incorporated into updating the model factor statistics. Three methods are used to calculate the reliability index and resistance factor of bored piles, and the results show that the reliability index and resistance factor are sensitive to the quality of data. Finally, the available values of resistance factors are proposed based on resistance factor design for bridge design specification, which can offer references to revision relevant specifications. The proposed method can be used to update other geotechnical data.

Are spatially specific agricultural input use recommendations more profitable to smallholder farmers than broad recommendations? This paper provides a theoretical and empirical modeling procedure for determining the optimal spatial scale at which agricultural researchers can make soil fertility recommendations. Theoretically, the use of Bayesian decision theory in the spatial economic optimization model allows the complete characterization of the posterior distribution functions of profits thereby taking into account spatial heterogeneity and uncertainty in the decision making process. By applying first order spatial scale stochastic dominance and Jensen’s inequality; theoretically and empirically, this paper makes the case that spatially specific agricultural input use recommendations will always stochastically dominate broad recommendations for all non-decreasing profit functions ignoring the quasi-fixed cost differentials in the decision itself. These findings are consistent with many economic studies that find precision agriculture technologies to be more profitable than conventional fertilizer (regional or national recommendations based) application approaches. The modeling approach used in this study however provides an elegant theoretical justification for such results. In addition, seasonal heterogeneity in maize responses was evident in our results. This demonstrates that broad recommendations may not only be wrong spatially but also seasonally. Further research on the empirical aspects of spatio-temporal instability of crop responses to fertilizer application using multi-location and multi-season data is needed to fully address the question posed initially. The decision making theory developed here can however be extended to incorporate spatio-temporal heterogeneity and alternative risk preferences.

The concept of shrinking bet size in Kelly betting to minimize estimated frequentist risk has recently been mooted. This rescaling appears to conflict with Bayesian decision theory through the likelihood principle and the complete class theorem; the Bayesian solution should already be optimal. We show theoretically and through examples that when the modeldetermining the likelihood function is correct, the prior distribution (if not dominated by data) is `correct' in a frequentist sense, and the posterior distribution is proper, then no further rescaling is required. However, if the model or the prior distribution is incorrect, or the posterior distribution improper, frequentist risk minimization can be a useful technique. We discuss how it might best be exploited. Another example, from maintenance, is used to show the wider applicability of the methodology; these conclusionsapply generally to decision-making.