Decision-theoretic Method Research Articles

Cognitive Limits and Preferences for Information

The structure of uncertainty underlying certain decision problems may be so complex as to elude decision-makers’ full understanding, curtailing their willingness to pay for payoff-relevant information — a puzzle manifesting itself in, for instance, low stock-market participation rates. I present a decision-theoretic method that enables an analyst to identify decision-makers’ information-processing abilities from observing their preferences for information. A decision-maker who is capable of understanding only those events that either almost always or almost never happen fails to attach instrumental value to any information source. On the other hand, non-trivial preferences for information allow perfect identification of the decision-maker’s mental capacity.

A multi-granulation decision-theoretic rough set method for distributed fc-decision information systems: An application in medical diagnosis

An information system is an important model in the field of artificial intelligence. A distributed fc-decision information system is an information system with distributed fuzzy data. This paper investigates a distributed fc-decision information system, proposes a multi-granulation decision-theoretic method for this system and gives an application in medical diagnosis. The fuzzy Tcos-equivalence relation, induced by an fc-decision information system by means of Gaussian kernel method, is first obtained, where Gaussian kernel is used to compute the similarity between objects in this system. Then, the approximately equal relation (for short, ae-relation) on fuzzy sets is defined and based on this ae-relation, the ae-granular structure induced by the fuzzy Tcos-equivalence relation is given. Next, a multi-granulation decision-theoretic rough set method for distributed fc-decision information systems is proposed by means of inclusion degree of sets in the viewpoint of multi-granulation. Finally, an example of medical diagnosis is employed to illustrate the effectiveness of the proposed method. These results will be helpful for dealing with distributed fuzzy data and significant for establishing a framework of multi-granulation decision-theoretic rough sets in distributed fc-decision information systems.

Rapid Spectral Cloud Screening Onboard Aircraft and Spacecraft

Next-generation orbital imaging spectrometers will generate unprecedented data volumes, demanding new methods to optimize storage and communication resources. Here, we demonstrate that onboard analysis can excise cloud-contaminated scenes, reducing data volumes while preserving science return. We calculate optimal cloud-screening parameters in advance, exploiting stable radiometric calibration and foreknowledge of illumination and viewing geometry. Channel thresholds expressed in raw instrument values can be then uploaded to the sensor where they execute in real time at gigabit-per-second (Gb/s) data rates. We present a decision theoretic method for setting these instrument parameters and characterize performance using a continuous three-year image archive from the “classic” Airborne Visible/Infrared Imaging Spectrometer (AVIRIS-C). We then simulate the system onboard the International Space Station, where it provides factor-of-two improvements in data volume with negligible false positives. Finally, we describe a real-time demonstration onboard the AVIRIS Next Generation (AVIRIS-NG) flight platform during a recent science campaign. In this blind test, cloud screening is performed without error while keeping pace with instrument data rates.

A Point Decision for Partially Identified Auction Models

This article proposes a decision-theoretic method to choose a single reserve price for partially identified auction models, such as Haile and Tamer (2003), using data on transaction prices from English auctions. The article employs Gilboa and Schmeidler (1989) for inference that is robust with respect to the prior over unidentified parameters. It is optimal to interpret the transaction price as the highest value, and maximize the posterior mean of the seller’s revenue. The Monte Carlo study shows substantial gains relative to the revenues corresponding to a random point and the midpoint in the Haile and Tamer interval.

Optimal continuous-monitoring design of single-arm phase II trial based on the simulated annealing method

Simon's two-stage design is commonly used in phase II single-arm clinical trials because of its simplicity and smaller sample size under the null hypothesis compared to the one-stage design. Some studies extend this design to accommodate more interim analyses (i.e., three-stage or four-stage designs). However, most of these studies, together with the original Simon's two-stage design, are based on the exhaustive search method, which is difficult to extend to high-dimensional, general multi-stage designs. In this study, we propose a simulated annealing (SA)-based design to optimize the early stopping boundaries and minimize the expected sample size for multi-stage or continuous monitoring single-arm trials. We compare the results of the SA method, the decision-theoretic method, the predictive probability method, and the posterior probability method. The SA method can reach the smallest expected sample sizes in all scenarios under the constraints of the same type I and type II errors. The expected sample sizes from the SA method are generally 10–20% smaller than those from the posterior probability method or the predictive probability method, and are slightly smaller than those from the decision-theoretic method in almost all scenarios. The SA method offers an excellent alternative in designing phase II trials with continuous monitoring.

PheNetic: network-based interpretation of unstructured gene lists in E. coli

At the present time, omics experiments are commonly used in wet lab practice to identify leads involved in interesting phenotypes. These omics experiments often result in unstructured gene lists, the interpretation of which in terms of pathways or the mode of action is challenging. To aid in the interpretation of such gene lists, we developed PheNetic, a decision theoretic method that exploits publicly available information, captured in a comprehensive interaction network to obtain a mechanistic view of the listed genes. PheNetic selects from an interaction network the sub-networks highlighted by these gene lists. We applied PheNetic to an Escherichia coli interaction network to reanalyse a previously published KO compendium, assessing gene expression of 27 E. coli knock-out mutants under mild acidic conditions. Being able to unveil previously described mechanisms involved in acid resistance demonstrated both the performance of our method and the added value of our integrated E. coli network. PheNetic is available at .

A Point Decision for Partially Identified Auction Models

This paper proposes a decision theoretic method to choose a single reserve price for partially identified auction models, such as [Haile and Tamer, 2003], using data on transaction prices from English auctions. The paper employs [Gilboa and Schmeidler, 1989] for inference that is robust with respect to the prior over unidentified parameters. It is optimal to interpret the transaction price as the highest value, and maximize the posterior mean of the seller’s revenue. The Monte Carlo study shows sub- stantial gains relative to the revenues corresponding to a random point and the midpoint in the Haile and Tamer interval.

A decision-theoretic method for surrogate model selection

The use of surrogate models to approximate computationally expensive simulation models, e.g., large comprehensive finite element models, is widespread. Typical uses of surrogate models include design, optimization, sensitivity analysis and/or uncertainty quantification. A surrogate model is defined by a postulated functional form, and values for the surrogate model parameters are estimated using results from a limited number of solutions to the comprehensive model. In general, there may be multiple surrogate models, each defined by possibly a different functional form, consistent with the limited data from the comprehensive model. We refer to each as a candidate surrogate model. Methods are developed and applied to select the optimal surrogate model from the collection of candidate surrogate models. One approach is to select the surrogate model that best fits the data provided by the comprehensive model, regardless of its intended use. The proposed approach applies techniques from decision theory, where postulated utility functions are used to account for the model use within the selection process. Three applications are presented to illustrate the methods. These include surrogate model selection for the purpose of: (1) estimating the minimum of a deterministic function, (2) the design under uncertainty of a simple oscillator, and (3) the uncertainty quantification of a complex engineering system subject to a severe shock and vibration environment.

Model Selection in Applied Science and Engineering: A Decision-Theoretic Approach

Mathematical models are developed and used to study the properties of complex systems in just about every area of applied science and engineering. Information on the system being modeled is, in general, incomplete, so that there may be two or more models consistent with the available information. The collection of these models is called the class of candidate models. A decision-theoretic method is developed for selecting the optimal member from the collection. The optimal model depends on the available information, the class of candidate models, and the model use. The candidate models may be deterministic or random. Classical methods for model selection, including the method of maximum likelihood and Bayesian methods, are briefly reviewed. These methods ignore model use and require data to be available. In addition, examples are used to show that classical methods for model selection can be unreliable in the sense that they can deliver unsatisfactory models when data is limited. The proposed decision-theo...

Implementing a decision‐theoretic design in clinical trials: Why and how?

This paper addresses two main questions: first, why should Bayesian and other innovative, data-dependent design models be put into practice and, secondly, given the past dearth of actual applications, how might one example of such a design be implemented in a genuine example trial? Clinical trials amalgamate theory, practice and ethics, but this last point has become relegated to the background, rather than taking often a more appropriate primary role. Trial practice has evolved but has its roots in R. A. Fisher's randomized agricultural field trials of the 1920s. Reasons for, and consequences of, this are discussed from an ethical standpoint, drawing on an under-used dichotomy introduced by French authors Lellouch and Schwartz (Int. Statist. Rev. 1971; 39:27-36). Plenty of ethically motivated designs for trials, including Bayesian designs have been proposed, but have found little application thus far. One reason for this is a lack of awareness of such alternative designs among trialists, while another reason is a lack of user-friendly software to allow study simulations. To encourage implementation, a new C++ program called 'Daniel' is introduced, offering much potential to assist the design of today's randomized controlled trials. Daniel evaluates a particular decision-theoretic method suitable for coping with either two or three Bernoulli response treatments with input features allowing user-specified choices of: patient horizon (number to be treated before and after the comparative stages of the trial); an arbitrary fixed trial truncation size (to allow ready comparison with traditional designs or to cope with practical constraints); anticipated success rates and a measure of their uncertainty (a matter ignored in standard power calculations); and clinically relevant, and irrelevant, differences in treatment effect sizes. Error probabilities and expected trial durations can be thoroughly explored via simulation, it being better by far to harm 'computer patients' instead of real ones. Suppose the objective in a clinical trial is to select between two treatments using a maximum horizon of 500 patients, when the truly superior treatment is expected to yield a 40 per cent success rate, but is believed to really range between 20 and 60 per cent. Simulation studies show that to detect a clinically relevant, absolute difference of 10 per cent between treatments, simulation studies show the decision-theoretic procedure would treat a mean 68 pairs of patients (SD 37) before correctly identifying the better treatment 96.7 per cent of the time, an error rate of 3.3 per cent. Having made a recommendation based on these patients, the remaining, on average 364 individuals, could either be given the indicated treatment, knowing its choice is optimal for the chosen horizon, or, alternatively, they could be entered into another, separate clinical trial. For comparison, a fixed sample size trial, with standard 5 per cent level of significance and 80 per cent power to detect a 10 per cent difference, requires treating over 700 patients in two groups, with the half allocated to inferior treatment considerably outnumbering the 68 expected under the decision-theoretic design, and the overall number simply too high for realistic application. In brief, the keys to answering the above 'why?' and 'how?' questions are ethics and software, respectively. Wider implications, both pros and cons, of implementing the particular method described will be discussed, with the overall conclusion that, where appropriate, clinical trials are now ready to undergo modernization from the agricultural age to the information age.

Morphological correlates to cognitive dysfunction in schizophrenia as studied with Bayesian regression

BackgroundRelationships between cognitive deficits and brain morphological changes observed in schizophrenia are alternately explained by less gray matter in the brain cerebral cortex, by alterations in neural circuitry involving the basal ganglia, and by alteration in cerebellar structures and related neural circuitry. This work explored a model encompassing all of these possibilities to identify the strongest morphological relationships to cognitive skill in schizophrenia.MethodsSeventy-one patients with schizophrenia and sixty-five healthy control subjects were characterized by neuropsychological tests covering six functional domains. Measures of sixteen brain morphological structures were taken using semi-automatic and fully manual tracing of MRI images, with the full set of measures completed on thirty of the patients and twenty controls. Group differences were calculated. A Bayesian decision-theoretic method identified those morphological features, which best explained neuropsychological test scores in the context of a multivariate response linear model with interactions.ResultsPatients performed significantly worse on all neuropsychological tests except some regarding executive function. The most prominent morphological observations were enlarged ventricles, reduced posterior superior vermis gray matter volumes, and increased putamen gray matter volumes in the patients.The Bayesian method associated putamen volumes with verbal learning, vigilance, and (to a lesser extent) executive function, while caudate volumes were associated with working memory. Vermis regions were associated with vigilance, executive function, and, less strongly, visuo-motor speed. Ventricular volume was strongly associated with visuo-motor speed, vocabulary, and executive function. Those neuropsychological tests, which were strongly associated to ventricular volume, showed only weak association to diagnosis, possibly because ventricular volume was regarded a proxy for diagnosis. Diagnosis was strongly associated with the other neuropsychological tests, implying that the morphological associations for these tasks reflected morphological effects and not merely group volumetric differences. Interaction effects were rarely associated, indicating that volumetric relationships to neuropsychological performance were similar for both patients and controls.ConclusionThe association of subcortical and cerebellar structures to verbal learning, vigilance, and working memory supports the importance of neural connectivity to these functions. The finding that a morphological indicator of diagnosis (ventricular volume) provided more explanatory power than diagnosis itself for visuo-motor speed, vocabulary, and executive function suggests that volumetric abnormalities in the disease are more important for cognition than non-morphological features.

Estimating reference fishing mortality rates from noisy spawner–recruit data

We review and evaluate methods of estimating reference fishing mortality rates from spawner–recruit (SR) data to obtain maximum sustainable yield. Using Monte Carlo simulations, we found that a reference fishing mortality rate derived from the maximum likelihood estimates of the SR parameters was less biased than reference fishing mortality rates obtained using the mode of the marginal probability distribution for the maximum rate that spawners produce recruits or by finding the fishing mortality rate that maximizes the expected yield. However, the maximum likelihood method produced the most variable estimates, at times leading to substantial under- or over-exploitation of the population. In contrast, the decision theoretic method of maximizing the expected yield exhibited less variability, produced higher yields, and substantially reduced the risk of overexploiting the population. We show how these methods can be extended to include information from other populations. Bayesian priors for the SR parameters, obtained through meta-analyses of population dynamics at some higher organizational level (e.g., the species), may be used to assess the plausibility of parameter estimates obtained for a single population or combined with the data for the population of interest. Reference fishing mortality rates are then estimated from the resulting joint posterior distribution.

Multiple-testing strategy for analyzing cDNA array data on gene expression.

An objective of many functional genomics studies is to estimate treatment-induced changes in gene expression. cDNA arrays interrogate each tissue sample for the levels of mRNA for hundreds to tens of thousands of genes, and the use of this technology leads to a multitude of treatment contrasts. By-gene hypotheses tests evaluate the evidence supporting no effect, but selecting a significance level requires dealing with the multitude of comparisons. The p-values from these tests order the genes such that a p-value cutoff divides the genes into two sets. Ideally one set would contain the affected genes and the other would contain the unaffected genes. However, the set of genes selected as affected will have false positives, i.e., genes that are not affected by treatment. Likewise, the other set of genes, selected as unaffected, will contain false negatives, i.e., genes that are affected. A plot of the observed p-values (1 - p) versus their expectation under a uniform [0, 1] distribution allows one to estimate the number of true null hypotheses. With this estimate, the false positive rates and false negative rates associated with any p-value cutoff can be estimated. When computed for a range of cutoffs, these rates summarize the ability of the study to resolve effects. In our work, we are more interested in selecting most of the affected genes rather than protecting against a few false positives. An optimum cutoff, i.e., the best set given the data, depends upon the relative cost of falsely classifying a gene as affected versus the cost of falsely classifying a gene as unaffected. We select the cutoff by a decision-theoretic method analogous to methods developed for receiver operating characteristic curves. In addition, we estimate the false discovery rate and the false nondiscovery rate associated with any cutoff value. Two functional genomics studies that were designed to assess a treatment effect are used to illustrate how the methods allowed the investigators to determine a cutoff to suit their research goals.

Troubleshooting using probabilistic networks and value of information

We develop a decision-theoretic method that yields approximate, low cost troubleshooting plans by making more relevant observations and devoting more time to generate a plan. The method is tested against other methods on three different problems in an experimental setting. Sensitivity analysis of the parameters is also carried out. The method yields low cost troubleshooting plans by spending substantially more computation time. The method turns out to be robust with respect to changes in observation and repair costs.

Bayesian Estimation and Model Choice in Item Response Models

Item response models are essential tools for analyzing results from many educational and psychological tests. Such models are used to quantify the probability of correct response as a function of unobserved examinee ability and other parameters explaining the difficulty and the discriminatory power of the questions in the test. Some of these models also incorporate a threshold parameter for the probability of the correct response to account for the effect of guessing the correct answer in multiple choice type tests. In this article we consider fitting of such models using the Gibbs sampler. A data augmentation method to analyze a normal-ogive model incorporating a threshold guessing parameter is introduced and compared with a Metropolis-Hastings sampling method. The proposed method is an order of magnitude more efficient than the existing method. Another objective of this paper is to develop Bayesian model choice techniques for model discrimination. A predictive approach based on a variant of the Bayes factor is used and compared with another decision theoretic method which minimizes an expected loss function on the predictive space. A classical model choice technique based on a modified likelihood ratio test statistic is shown as one component of the second criterion. As a consequence the Bayesian methods proposed in this paper are contrasted with the classical approach based on the likelihood ratio test. Several examples are given to illustrate the methods.

A Decision-Theoretic Method for Assessing a Change in the Rate of Non-Acceptable Inpatient Claims

A health care measure that assesses the occurrence or non-occurrence of an event may be costly to obtain. For instance, measuring whether an inpatient hospital stay was necessary according to accepted clinical protocols is a relevant, though expensive analysis. Prior research (Rosenberg, 1998; Rosenberg, et al., 1999; Rosenberg and Griffith, 2000) has shown that a Bayesian logistic regression model is an excellent tool to predict the rate of Non-Acceptable inpatient hospital Claims (NACs). This paper describes a decision-theoretic approach to determine whether a change in the NAC rate warrants investigation. The Bayesian model is used to estimate, by principal discharge diagnosis, the posterior distribution of the NAC rate for a group of claims at the time of the audit (defined as time 0). This distribution of the NAC rate is compared against another posterior distribution of the NAC rate obtained at a later time (without further audit). Claim and investigation costs are included in the assessment of whether an investigation of a change in the NAC rate should be undertaken. This approach provides an inexpensive, supplemental level of control between audits for monitoring the level of the NAC rate. The methodology is also applicable to other health care measurements.

Computation of lower bounds for switching activity using decision theory

Accurate switching-activity estimation is crucial for power budgeting. It is impractical to obtain an accurate estimate by simulating the circuit for all possible inputs. An alternate approach would be to compute tight bounds for the switching activity. In this paper, we propose a nonsimulative decision theoretic method to compute the lower bound for switching activity. First, we show that the switching activity can be modeled as the decision error of an abstract two-class problem. It is shown that the Bayes error L* is a lower bound for the switching activity. Further, we improve L* to obtain a tighter bound L/sub 1/, which is based on the one-nearest neighbor classification error. The proposed lower bounds are used for switching-activity characterization at the register transfer (RT) level. Experimental results for the RT-level switching-activity estimates for ISCAS'85 circuits are presented. This technique is simple and fast and produces accurate estimates.

Timing medical examinations via intensity functions

SUMMARY This paper studies a decision theoretic method for timing medical examinations. The specific model is motivated by screening asymptomatic individuals for hidden disease or risk-increasing conditions. Ideas and strategies may be applied more broadly to problems in which a stochastic process is monitored over time with a costly and possibly faulty data collection procedure. The decision space is modelled as a space of functions, termed screening intensity functions. Results include explicit rules for deciding whether or not an individual of given age and risk factors should be screened for a disease, and for deciding when an individual examined today should be examined again. Breast cancer screening

A spectral attentional mechanism tuned to object configurations

This paper describes an attentional mechanism based on the interpretation of spectral signatures for detecting regular object configurations in areas of an image delineated using context information. The proposed global operator relies on the spectral analysis of edge structure and exploits spatial as well as frequency-domain constraints derived from known geometrical models of monitored objects. A decision theoretic method for learning acceptance detection regions is presented. Applications of this attentional mechanism are demonstrated for several aerial image interpretation tasks for attentional as well as recognition purposes. Specific examples are described for detecting vehicle formations (such as convoys), qualifying the geometry of detected formations, or monitoring the occupancy of regions of interest (such as parking areas, roads, or open areas). Experiments and sensitivity analysis results are reported.

Automatic recognition of liquids and glides

This study describes a new algorithm to recognize liquids (/l/, /r/) and glides (/w/, /y/) spoken by a number of speakers. To make the recognition problem more general, /i/ and /u/, the closest vowels to the glides, are also included in the study. We consider the sequence of time samples of each phoneme as an auto-regressive (AR) process of order r. These r coefficients (estimated by a least-square technique) and signal-to-noise ratio of this process will be taken as raw features for the phoneme under consideration. These raw features contain most of the information (speaker-dependent, speaker-independent, and noise, etc. ) that was contained in the phoneme. Clearly, only the speaker-independent information is required to carry out the above task. To extract the speaker-independent information and reduce the dimension of the raw feature space, we perform a linear transformation. The resulting features (in the lower-dimensional space) are then used for classifying the phonemes by a decision theoretic method, namely, the nearest-mean classification rule. Each of the six phonemes was spoken 10 times by each of the four speakers (two male and two female). We chose r as 8. The correct classification rate of about 85% was observed.