Prior Probability Estimates Research Articles

A Multifactorial Likelihood Model for MMR Gene Variant Classification Incorporating Probabilities Based on Sequence Bioinformatics and Tumor Characteristics: A Report from the Colon Cancer Family Registry

Mismatch repair (MMR) gene sequence variants of uncertain clinical significance are often identified in suspected Lynch syndrome families, and this constitutes a challenge for both researchers and clinicians. Multifactorial likelihood model approaches provide a quantitative measure of MMR variant pathogenicity, but first require input of likelihood ratios (LRs) for different MMR variation-associated characteristics from appropriate, well-characterized reference datasets. Microsatellite instability (MSI) and somatic BRAF tumor data for unselected colorectal cancer probands of known pathogenic variant status were used to derive LRs for tumor characteristics using the Colon Cancer Family Registry (CFR) resource. These tumor LRs were combined with variant segregation within families, and estimates of prior probability of pathogenicity based on sequence conservation and position, to analyze 44 unclassified variants identified initially in Australasian Colon CFR families. In addition, in vitro splicing analyses were conducted on the subset of variants based on bioinformatic splicing predictions. The LR in favor of pathogenicity was estimated to be ~12-fold for a colorectal tumor with a BRAF mutation-negative MSI-H phenotype. For 31 of the 44 variants, the posterior probabilities of pathogenicity were such that altered clinical management would be indicated. Our findings provide a working multifactorial likelihood model for classification that carefully considers mode of ascertainment for gene testing.

Wavelet Bayesian Network Image Denoising

From the perspective of the Bayesian approach, the denoising problem is essentially a prior probability modeling and estimation task. In this paper, we propose an approach that exploits a hidden Bayesian network, constructed from wavelet coefficients, to model the prior probability of the original image. Then, we use the belief propagation (BP) algorithm, which estimates a coefficient based on all the coefficients of an image, as the maximum-a-posterior (MAP) estimator to derive the denoised wavelet coefficients. We show that if the network is a spanning tree, the standard BP algorithm can perform MAP estimation efficiently. Our experiment results demonstrate that, in terms of the peak-signal-to-noise-ratio and perceptual quality, the proposed approach outperforms state-of-the-art algorithms on several images, particularly in the textured regions, with various amounts of white Gaussian noise.

A Monte Carlo simulation for the assessment of Bayesian updating in dynamic systems

The aim of this paper is to explore the effectiveness of Bayesian updating, especially in dynamic systems, where failure probability is variant in time. Through the use of Monte Carlo simulation it was tested whether (a) Bayesian updating and (b) dynamic behavior of failure probability lead to more risky behavior. The results indicate that Bayesian updating systematically lead to more risky behavior of the system, unless the prior failure probability estimates have been severely underestimated and that dynamic systems lead to more risky behavior only when Bayesian updating is applied.The main explanation is that Bayesian updating involves a feedback mechanism that leads to more extreme deviations, especially when the complexity of the underlying system is important (non-linearity, feedback, inter-dependencies, loose coupling). Bayesian updating is an unavoidable process, which is especially helpful in cases of uncertain failure probability estimates. This paper indicates its deficiencies and the factors that intensify them.

Operational Prediction of Groundwater Fluctuation in South Florida using Sequence Based Markovian Stochastic Model

The ecosystem of South Florida is characterized by a vast wetland system, karst surficial hydrogeology, and extended coastal boundary. The ecosystem is poised under risks of: ecological failure due to increased fragmentation by urbanization; groundwater flow disruption because of sinkhole formation; and intrusion of oceanic water with decreasing water table head because of drought or over pumping. It was found important to synthesize the spatiotemporal state of the groundwater hydrology and also develop a forecasting model to support the intensive management and monitoring in place. In this study, an objective was set to develop a stochastic sequence model capable of forecasting groundwater levels on a monthly span at a daily time scale. The groundwater level simulation was conceptualized as a sequence of daily fluctuating states of magnitudes and patterns that has a defined probability of occurrence. The model setup involved representation of daily fluctuation magnitudes in ten states and pattern changes in three states. The sequential occurrence of states of magnitudes and patterns at each time step was used for estimation of the transitional probabilities and employed in a hidden Markov model frame work for ensemble generation and estimation of posterior probabilities. A realization was chosen based on the highest maximum likelihood ratio of 90% and smallest root mean square error of 0.05–0.12 m against the historical data. A monthly forecasting at daily time step was done dynamically incorporating observed data at each time step and revising prior and posterior probability estimation in the hidden Markov model formulation. A case study was conducted at three well sites, which are situated at three different hydrogeologic settings. The model not only reproduced annual groundwater fluctuation patterns but also forecasted preceding monthly fluctuations at maximum likelihood ratio above 90% and root mean square error below 0.15 m. A further study was recommended first to analyze break point parametric estimation for seasonal analysis, and secondly to integrate the approach in other hydrological models for the purpose of synthetic groundwater fluctuation generation.

Bridging the gap between aggregate data and individual patient management: A Bayesian approach

The aim of this study was to explore whether Bayesian reasoning can be applied to therapeutic questions in a way that is similar to its application in diagnostics. A clinically relevant, therapeutic question was formulated in accordance with Bayesian reasoning for the clinical management of patients with newly diagnosed rheumatoid arthritis (RA). Prior probability estimates of response to drug treatment (methotrexate, MTX) were obtained from the literature. As a marker of treatment response, changes in the Health Assessment Questionnaire (HAQ) scores were assessed after three months of treatment. Likelihood ratios for this marker were calculated on the basis of data from a clinical registry, using changes in the Disease Activity Score (DAS) as gold standard. Using Bayes' theorem, prior probability and likelihood ratios were combined to estimate posterior probabilities of treatment response in individual patients. On the basis of the literature, the prior probability of response of RA patients to MTX was estimated 45 percent. At 3 months follow-up, this probability increased to 80 percent or decreased to 23 percent, depending on the changes that were observed in Health Assessment Questionnaire scores. Bayesian reasoning can be applied to therapeutic issues in a way that is conceptually fully compatible with its use in diagnostics. As such, it can be used to bridge the gap between aggregate data and individual patient management.

A level set method based on the Bayesian risk for medical image segmentation

This paper proposes an alternative criterion derived from the Bayesian risk classification error for image segmentation. The proposed model introduces a region-based force determined through the difference of the posterior image densities for the different classes, a term based on the prior probability derived from Kullback– Leibler information number, and a regularity term adopted to avoid the generation of excessively irregular and small segmented regions. Compared with other level set methods, the proposed approach relies on the optimum decision of pixel classification and the estimates of prior probabilities; thus the approach has more reliability in theory and practice. Experiments show that the proposed approach is able to extract the complicated shapes of targets and robust for various types of medical images. Moreover, the algorithm can be easily extendable for multiphase segmentation.

Acquired prior knowledge modulates audiovisual integration

Orienting responses to audiovisual events in the environment can benefit markedly by the integration of visual and auditory spatial information. However, logically, audiovisual integration would only be considered successful for stimuli that are spatially and temporally aligned, as these would be emitted by a single object in space-time. As humans do not have prior knowledge about whether novel auditory and visual events do indeed emanate from the same object, such information needs to be extracted from a variety of sources. For example, expectation about alignment or misalignment could modulate the strength of multisensory integration. If evidence from previous trials would repeatedly favour aligned audiovisual inputs, the internal state might also assume alignment for the next trial, and hence react to a new audiovisual event as if it were aligned. To test for such a strategy, subjects oriented a head-fixed pointer as fast as possible to a visual flash that was consistently paired, though not always spatially aligned, with a co-occurring broadband sound. We varied the probability of audiovisual alignment between experiments. Reaction times were consistently lower in blocks containing only aligned audiovisual stimuli than in blocks also containing pseudorandomly presented spatially disparate stimuli. Results demonstrate dynamic updating of the subject's prior expectation of audiovisual congruency. We discuss a model of prior probability estimation to explain the results.

Commentary: What's in a Name? Statistical Discrimination and Disparities Research

In this issue of Health Services Research, Maserejian, Lutfey, and McKinlay (2009) report on an experiment examining the reasons for gender differences in diagnostic decision making for coronary heart disease (CHD). The experiment utilizes actors of different genders speaking from identical scripts of a patient presenting with fairly classic CHD symptoms. The authors argue that the experimental design standardized the presentation and history available to providers, leaving two potential explanations for residual variability in diagnosis of CHD: differences due to different gender estimates of disease prevalence (a prior probability), and differences due to personal stereotypes and biases. To distinguish between these two explanations, they set out to determine whether physician estimates of prior probability of CAD explain differences in CAD diagnosis by gender.

Interpreting trial results in light of conflicting evidence: a Bayesian analysis of adjuvant chemotherapy for non-small-cell lung cancer.

When successive randomized trials contradict prior evidence, clinicians may be unsure how to evaluate them: Does accumulating evidence warrant changing practice? An increasingly popular solution, Bayesian statistics quantitatively evaluate new results in context. This study provides a clinically relevant example of Bayesian methods. Three recent non-small-cell lung cancer adjuvant chemotherapy trials were evaluated in light of prior conflicting data. Results were used from International Adjuvant Lung Trial (IALT), JBR.10, and Adjuvant Navelbine International Trialist Association (ANITA). Prior evidence was sequentially updated to calculate the probability of each survival benefit level (overall and by stage) and variance. Sensitivity analysis was performed using expert opinion and uninformed estimates of survival benefit prior probability. The probability of a 4% survival benefit increased from 33% before IALT to 64% after IALT. After sequential updating with JBR.10 and ANITA, this probability was 82% (hazard ratio = 0.84; 95% CI, 0.77 to 0.91). IALT produced the largest decrease in variance (61%) and decreased the chance of survival decrement to 0%. Sensitivity analysis did not support a survival benefit after IALT. However, sequential updating substantiated a 4% survival benefit and, for stage II and III, more than 90% probability of a 6% benefit and 50% probability of a 12% benefit. When evaluated in context with prior data, IALT did not support a 4% survival benefit. However, sequential updating with JBR.10 and ANITA did. A model for future assessments, this study demonstrates the unique ability of Bayesian analysis to evaluate results that contradict prior evidence.

Context Based Prior Probability Estimation of Object Appearance

This paper presents a method to estimate the prior probability of object appearance and position from only context information. The context is extracted from a whole image by Gabor filters. The conventional method represented the context by mixture of Gaussian distributions. The prior probabilities of object appearance and position were estimated by generative model. However, we define the probability estimation of object appearance as the binary-classification problem whether an input image contains the specific object or not. The Support Vector Machine is used to classify them, and the distance from the hyperplane is transformed to the probability using a sigmoid function. We also define the estimation problem of object position in an image from only the context as the regression problem. The position of object in an image is estimated by Support Vector Regression. Experimental results show that the proposed method outperforms the conventional method.

Methods for Causality Assessment of Adverse Drug Reactions

Numerous methods for causality assessment of adverse drug reactions (ADRs) have been published. The aim of this review is to provide an overview of these methods and discuss their strengths and weaknesses. We conducted electronic searches in MEDLINE (via PubMed), EMBASE and the Cochrane databases to find all assessment methods. Thirty-four different methods were found, falling into three broad categories: expert judgement/global introspection, algorithms and probabilistic methods (Bayesian approaches). Expert judgements are individual assessments based on previous knowledge and experience in the field using no standardized tool to arrive at conclusions regarding causality. Algorithms are sets of specific questions with associated scores for calculating the likelihood of a cause-effect relationship. Bayesian approaches use specific findings in a case to transform the prior estimate of probability into a posterior estimate of probability of drug causation. The prior probability is calculated from epidemiological information and the posterior probability combines this background information with the evidence in the individual case to come up with an estimate of causation. As a result of problems of reproducibility and validity, no single method is universally accepted. Different causality categories are adopted in each method, and the categories are assessed using different criteria. Because assessment methods are also not entirely devoid of individual judgements, inter-rater reliability can be low. In conclusion, there is still no method universally accepted for causality assessment of ADRs.

Novel Approaches to Probabilistic Neural Networks Through Bagging and Evolutionary Estimating of Prior Probabilities

In this contribution, novel approaches are proposed for the improvement of the performance of Probabilistic Neural Networks as well as the recently proposed Evolutionary Probabilistic Neural Networks. The Evolutionary Probabilistic Neural Network's matrix of spread parameters is allowed to have different values in each class of neurons, resulting in a more flexible model that fits the data better and Particle Swarm Optimization is also employed for the estimation of the Probabilistic Neural Networks's prior probabilities of each class. Moreover, the bagging technique is used to create an ensemble of Evolutionary Probabilistic Neural Networks in order to further improve the model's performance. The above approaches have been applied to several well-known and widely used benchmark problems with promising results.

Neglect as a disorder of prior probability

Subjects with spatial neglect are slower and more variable in detecting visual targets, especially on the side opposite their brain injuries. These deficits can be seen by plotting cumulative distribution functions (CDF) of response times (RT). I demonstrate that dividing RT’s by their means normalizes the RT CDF’s of neglect subjects. The motivation for this transformation comes from Carpenter’s LATER model [Carpenter, R. H. S., & Williams, M. L. L. (1995). Neural computation of log likelihood in control of saccadic eye movements. Nature, 377, 59–62]. The most direct interpretation of this result is that some symptoms of neglect reflect abnormal estimates of stimulus prior probability.

Partially Supervised classification of remote sensing images through SVM-based probability density estimation

A general problem of supervised remotely sensed image classification assumes prior knowledge to be available for all the thematic classes that are present in the considered dataset. However, the ground-truth map representing that prior knowledge usually does not really describe all the land-cover typologies in the image, and the generation of a complete training set often represents a time-consuming, difficult and expensive task. This problem affects the performances of supervised classifiers, which erroneously assign each sample drawn from an unknown class to one of the known classes. In the present paper, a classification strategy is described that allows the identification of samples drawn from unknown classes through the application of a suitable Bayesian decision rule. The proposed approach is based on support vector machines (SVMs) for the estimation of probability density functions and on a recursive procedure to generate prior probability estimates for known and unknown classes. In the experiments, both a synthetic dataset and two real datasets were used.

Policy relevance of Bayesian statistics overestimated?

The observed posterior probability distributions regarding the benefits of surgery for otitis media with effusion (OME) with expected probability distributions, using Bayes' theorem are compared. Postal questionnaires were used to assess prior and posterior probability distributions among ear-nose-throat (ENT) surgeons in the Netherlands. In their prior probability estimates, ENT surgeons were quite optimistic with respect to the effectiveness of tube insertion in the treatment of OME. The trial showed no meaningful benefit of tubes on hearing and language development. Posterior probabilities calculated on the basis of prior probability estimates and trial results differed widely from those, elicited empirically 1 year after completion of the trial and dissemination of the results. ENT surgeons did not adjust their opinion about the benefits of surgical treatment of glue ears to the extent that they should have done according to Bayes' theorem. Users of the results of Bayesian analyses, notably policy-makers, should realize that Bayes' theorem is prescriptive and not necessarily descriptively correct. Health policy decisions should not be based on the untested assumption that health-care professionals use new evidence to adjust their subjective beliefs in a Bayesian manner.

Quantifying uncertainty: physicians' estimates of infection in critically ill neonates and children.

To determine the diagnostic accuracy of physicians' prior probability estimates of serious infection in critically ill neonates and children, we conducted a prospective cohort study in 2 intensive care units. Using available clinical, laboratory, and radiographic information, 27 physicians provided 2567 probability estimates for 347 patients (follow-up rate, 92%). The median probability estimate of infection increased from 0% (i.e., no antibiotic treatment or diagnostic work-up for sepsis), to 2% on the day preceding initiation of antibiotic therapy, to 20% at initiation of antibiotic treatment (P<.001). At initiation of treatment, predictions discriminated well between episodes subsequently classified as proven infection and episodes ultimately judged unlikely to be infection (area under the curve, 0.88). Physicians also showed a good ability to predict blood culture-positive sepsis (area under the curve, 0.77). Treatment and testing thresholds were derived from the provided predictions and treatment rates. Physicians' prognoses regarding the presence of serious infection were remarkably precise. Studies investigating the value of new tests for diagnosis of sepsis should establish that they add incremental value to physicians' judgment.

Probabilistic Multiple Face Detection and Tracking Using Entropy Measures

A joint probabilistic face detection and tracking algorithm, combining likelihood estimation and a prior probability, is proposed. The likelihood estimation scheme is based on the statistical training of sets of automatically generated feature points and a mutual information tracking cue, while the prior probability estimation is based on a Gaussian temporal model. The likelihood estimation process is the core of a multiple face detection scheme used to initialize the tracking process. The resulting system has been tested on real image sequences and is robust to significant partial occlusion and illumination changes.

Improved classification of Landsat Thematic Mapper data using modified prior probabilities in large and complex landscapes

The use of modified prior probabilities to exploit ancillary data and increase classification accuracy has been proposed before. However, this method has not been widely applied because it has heavy computing requirements and because obtaining prior probability estimates has presented practical problems. This article presents a procedure that generates large sets of prior probability estimates from class frequencies modelled with ancillary data and a Mahalanobis Distance selection of previously classified pixels. The method produces a pixel sample size that is large enough to estimate class frequencies in numerous strata, which is particularly desirable for the study of large and complex landscapes. A case study is presented in which the procedure made it possible to estimate 537 sets of prior probabilities for an entire Landsat Thematic Mapper (TM) scene of central Costa Rica. After modifying the class prior probabilities, the overall classification consistency of the training sites improved from 74.6% to 91.9%, while the overall classification accuracy of sites controlled in the field by independent studies improved from 68.7% to 89.0%. The classification accuracy was most improved for spectrally similar classes. The method improves classification accuracy in large and complex landscapes with spectrally mixed land-cover categories.

"I Knew It All Along" Eventually: The Development of Hindsight Bias in Reaction to the Clinton Impeachment Verdict

Students estimated the chance that President Clinton would be convicted or acquitted in the U.S. Senate impeachment trial, at 4 points in time: (a) 22 days before the verdict (distal pretest), (b) 3 days before the verdict (proximal pretest), (c) 4 days after the verdict (immediate posttest), and (d) 11 days after the verdict (delayed posttest). Within-subjects analyses revealed that both foresight and hindsight changed over time. With respect to foresight, the perceived likelihood of conviction significantly decreased and the perceived likelihood of acquittal significantly increased between the 2 pretests. Content analyses of archived national news reports supported the notion that media predictions about the impending vote produced this temporal shift toward greater prospective accuracy. Confirming hypotheses, hindsight bias emerged for estimates of the prior probability of conviction, but not for estimates of the prior probability of acquittal. Within-subjects analyses revealed that 4 days after the ve...

Using Bayesian belief networks to evaluate fish and wildlife population viability under land management alternatives from an environmental impact statement

We developed procedures for using Bayesian belief networks (BBNs) to model habitat and population viability of selected at-risk fish and wildlife species. The BBN models represent the ecological causal web of key environmental correlates (KECs) that most influence habitat capability, potential population response for each species, and influence of habitat planning alternatives. BBN models represent site-specific KECs, habitat capability at the subwatershed level, and pattern of habitat capability across all subwatersheds. BBNs use Dirichlet prior probability distributions and standard Bayesian updating of posterior probabilities. We derived estimates of prior and conditional probabilities from a mix of empirical data and expert judgment, mostly the latter. Sensitivity analyses identified planning decisions and KECs that most influence species outcomes, and can help prioritize monitoring activities. BBN models, however, substitute for neither field studies nor empirical, quantitative population viability analyses of population demography and genetics.