Exploring the Overestimation of Conjunctive Probabilities

Predicting space object conjunctions is inherently probabilistic due to initial state and orbit model uncertainty. A commonly considered Monte Carlo estimator of the conjunction probability is the ’all-to-all’ estimator. Given independent random samples of the trajectories of both objects, the estimator is the percentage of all pairs of trajectories that result in a conjunction. Intuitively, the all-to-all estimator is the best possible estimator of the conjunction probability since it considers all pairs of Monte Carlo samples. However, its distribution is not available in closed-form, which limits its use in practice and makes this intuition difficult to make rigorous. In this paper, the all-to-all estimator is identified as a U-statistic, which implies that it has several favorable properties. Specifically, the estimator is the minimum variance unbiased estimator of the conjunction probability and is asymptotically Gaussian distributed. An approximate confidence interval for the conjunction probability is obtained from an estimate of the asymptotic Gaussian distribution. We show how to efficiently compute the confidence interval and demonstrate that the interval has the nominal coverage level. The confidence intervals are also seen to be narrower than those based on the commonly-used each-to-each estimator. Furthermore, the all-to-all estimator is shown to allow different Monte Carlo sample sizes, whereas the each-to-each estimator requires equal sample sizes.

The accuracy of a logistic prediction model is degraded when it is transported to populations with outcome prevalences different from that of the population used to derive the model. The resultant errors can have major clinical implications. Accordingly, the authors developed a logistic prediction model with respect to the noninvasive diagnosis of coronary disease based on 1,824 patients who underwent exercise testing and coronary angiography, varied the prevalence of disease in various "test" populations by random sampling of the original "derivation" population, and determined the accuracy of the logistic prediction model before and after the application of a mathematical algorithm designed to adjust only for these differences in prevalence. The accuracy of each prediction model was quantified in terms of receiver operating characteristic (ROC) curve area (discrimination) and chi-square goodness-of-fit (calibration). As the prevalence of the test population diverged from the prevalence of the derivation population, discrimination improved (ROC-curve areas increased from 0.82 +/- 0.02 to 0.87 +/- 0.03; p < 0.05), and calibration deteriorated (chi-square goodness-of-fit statistics increased from 9 to 154; p < 0.05). Following adjustment of the logistic intercept for differences in prevalence, discrimination was unchanged and calibration improved (maximum chi-square goodness-of-fit fell from 154 to 16). When the adjusted algorithm was applied to three geographically remote populations with prevalences that differed from that of the derivation population, calibration improved 87%, while discrimination fell by 1%. Thus, prevalence differences produce statistically significant and potentially clinically important errors in the accuracy of logistic prediction models. These errors can potentially be mitigated by use of a relatively simple mathematical correction algorithm.

Summary Production forecasting is usually performed by applying a single model from a classical statistical standpoint (point estimation). This approach neglects: (a) model uncertainty and (b) quantification of uncertainty of the model’s estimates. This work evaluates the predictive accuracy of rate-time models to forecast production from tight-oil wells using Bayesian methods. We apply Bayesian leave-one-out (LOO) and leave-future-out (LFO) cross-validation (CV) using an accuracy metric that evaluates the uncertainty of the models’ estimates: the expected log predictive density (elpd). We illustrate the application of the procedure to tight-oil wells of west Texas. This work assesses the predictive accuracy of rate-time models to forecast production of tight-oil wells. We use two empirical models, the Arps hyperbolic and logistic growth models, and two physics-based models: scaled slightly compressible single-phase and scaled two-phase (oil and gas) solutions of the diffusivity equation. First, we perform Bayesian inference to generate probabilistic production forecasts for each model using a Bayesian workflow in which we assess the convergence of the Markov chain Monte Carlo (MCMC) algorithm, calibrate, and evaluate the robustness of the models’ inferences. Second, we evaluate the predictive accuracy of the models using the elpd accuracy metric. This metric provides a measure of out-of-sample predictive performance. We apply two different CV techniques: LOO and LFO. The results of this study are the following. First, we evaluate the predictive performance of the models using the elpd accuracy metric, which accounts for the uncertainty of the models’ estimates assessing distributions instead of point estimates. Second, we perform fast CV calculations using an important sampling technique to evaluate and compare the results of the application of two CV techniques: leave-one-out cross-validation (LOO-CV) and leave-future-out cross-validation (LFO-CV). While the goal of LOO-CV is to evaluate the models’ ability to accurately resemble the structure of the production data, LFO-CV aims to assess the models’ capacity to predict future-time production (honoring the time-dependent structure of the data). Despite the difference in their prediction goals, both methods yield similar results on the set of tight-oil wells under study. The logistic growth model yields the best predictive performance for most of the wells in the data set, followed by the two-phase physics-based flow model. This work shows the application of new tools to evaluate the predictive accuracy of models used to forecast production of tight-oil wells using: (a) an accuracy metric that accounts for the uncertainty of the models’ estimates and (b) fast computation of two CV techniques, LOO-CV and LFO-CV. To our knowledge, the proposed approach is novel and suitable to evaluate and eventually select the rate-time model(s) with the best predictive accuracy of models to forecast hydrocarbon production.

Prediction of lung tumour position based on spirometry and on abdominal displacement: Accuracy and reproducibility

BackgroundGenomic prediction of purebred animals for crossbred performance can be based on a model that estimates effects of single nucleotide polymorphisms (SNPs) in purebreds on crossbred performance. For crossbred performance, SNP effects might be breed-specific due to differences between breeds in allele frequencies and linkage disequilibrium patterns between SNPs and quantitative trait loci. Accurately tracing the breed-of-origin of alleles (BOA) in three-way crosses is possible with a recently developed procedure called BOA. A model that accounts for breed-specific SNP effects (BOA model), has never been tested empirically on a three-way crossbreeding scheme. Therefore, the objectives of this study were to evaluate the estimates of variance components and the predictive accuracy of the BOA model compared to models in which SNP effects for crossbred performance were assumed to be the same across breeds, using either breed-specific allele frequencies ({text{G}}_{text{A}} model) or allele frequencies averaged across breeds ({text{G}}_{text{B}} model). In this study, we used data from purebred and three-way crossbred pigs on average daily gain (ADG), back fat thickness (BF), and loin depth (LD).ResultsEstimates of variance components for crossbred performance from the BOA model were mostly similar to estimates from models {text{G}}_{text{A}} and {text{G}}_{text{B}}. Heritabilities for crossbred performance ranged from 0.24 to 0.46 between traits. Genetic correlations between purebred and crossbred performance ({text{r}}_{text{pc}}) across breeds ranged from 0.30 to 0.62 for ADG and from 0.53 to 0.74 for BF and LD. For ADG, prediction accuracies of the BOA model were higher than those of the {text{G}}_{text{A}} and {text{G}}_{text{B}} models, with significantly higher accuracies only for one maternal breed. For BF and LD, prediction accuracies of models {text{G}}_{text{A}} and {text{G}}_{text{B}} were higher than those of the BOA model, with no significant differences. Across all traits, models {text{G}}_{text{A}} and {text{G}}_{text{B}} yielded similar predictions.ConclusionsThe BOA model yielded a higher prediction accuracy for ADG in one maternal breed, which had the lowest {text{r}}_{text{pc}} (0.30). Using the BOA model was especially relevant for traits with a low {text{r}}_{text{pc}}. In all other cases, the use of crossbred information in models {text{G}}_{text{A}} and {text{G}}_{text{B}}, does not jeopardize predictions and these models are more easily implemented than the BOA model.

The aim was to investigate the predictive accuracy of maternal cardiovascular variables for predicting operative delivery due to presumed fetal compromise in women undergoing induction of labour (IOL). This was a prospective cohort study conducted at St. George's University Hospital in London. Women undergoing IOL were invited to participate in the study. A USCOM-1A monitor was used for the cardiovascular evaluation of eligible women. Cardiac output (CO), cardiac index (CI), stroke volume (SV), stroke volume index (SVI), systemic vascular resistance (SVR) were assessed. Women who delivered via either caesarean or instrumental delivery with an abnormal cardiotocography tracing were evaluated in the operative delivery due to presumed fetal compromise group. A total of 99 women were recruited and four women were later excluded due to elective Caesarean (n=2) and failed IOL (n=2). In the univariate analysis, a CI < 2.9 L/minute (p = 0.043), SV < 65 mL (p = .027), stroke volume index (SVI) < 36 ml/m2 (p = 0.014), SVR > 7.2 logs (p = .020) and SVRI > 7.7 logs (p = 0.023) were significantly associated with the risk of operative delivery. Multiparity was the only maternal risk factor that showed a significant association with the risk of operative delivery in univariate regression model. The baseline model (parity) showed poor predictive accuracy with an area under the curve (AUC) value of 0.67 (95% CI: 0.58-0.77). The addition of SVI < 36 ml/m2, SVR>7.2 logs and SVRI>7.7 logs significantly improved the baseline model (p = 0.012, p = 0.026 and p = 0.012, respectively). The predictive accuracy of models had AUC values of 0.73 (95% CI: 0.64-0.82), 0.73 (95% CI: 0.63-0.84), 0.73 (95% CI: 0.64-0.82) for the combined models with SV, SVR and SVRI respectively. We demonstrated that maternal cardiovascular assessment could be useful for assessing the risk of intrapartum fetal compromise necessitating operative delivery. The addition of SV, SVR and SVRI significantly improved the predictive accuracy of the baseline antenatal model in women undergoing IOL. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Probability estimation is an essential cognitive function in perception, motor control, and decision making. Many studies have shown that when making decisions in a stochastic operant conditioning task, people and animals behave as if they underestimate the probability of rare events. It is commonly assumed that this behavior is a natural consequence of estimating a probability from a small sample, also known as sampling bias. The objective of this article is to challenge this common lore. We show that, in fact, probabilities estimated from a small sample can lead to behaviors that will be interpreted as underestimating or as overestimating the probability of rare events, depending on the cognitive strategy used. Moreover, this sampling bias hypothesis makes an implausible prediction that minute differences in the values of the sample size or the underlying probability will determine whether rare events will be underweighted or overweighed. We discuss the implications of this sensitivity for the design and interpretation of experiments. Finally, we propose an alternative sequential learning model with a resetting of initial conditions for probability estimation and show that this model predicts the experimentally observed robust underweighting of rare events.

Purpose: To make a preliminary estimate of the probability of adverse events for various critical anatomical structures for stereotactic body radiation therapy (SBRT). Method and Materials: An extensive literature search has uncovered a collection of more than 500 published dose tolerance limits for various anatomical critical structures for one to five fractions of SBRT. We have not found any TD5/5 or TD50/5 adverse event probabilities for SBRT yet, and an appreciable number of the authors do not even present minimum dosimetric information for the adverse events they report. We compiled a database from the available published data and performed statistical analysis to obtain a preliminary estimate of probability of adverse events. Results: Sixty five of the 500 dose tolerance limits correspond to a reported adverse event. For nineteen of these cases, the authors reported the number of patients exceeding the stated dose tolerance limit. For brain tumors, details of adverse events were reported in optic chiasm and optic nerve, and for lung tumors details of adverse events were reported in bronchi, lungs, and ribs. For these critical structures we can estimate the adverse event probability, although in some cases the number of data points is quite limited. Conclusion: It would be quite helpful for the future if more authors would present dosimetric data corresponding to the adverse events they report. At a minimum, it would be helpful to report the maximum dose received by the involved critical structure, the doses received by a few selected volumes, and the number of patients that received these dose levels. In the meantime, this work provides preliminary estimates of adverse event probability for selected anatomical critical structures from the sparse data available.

The purpose of this study is to investigate the relationship between data skewness in the output variable and the accuracy of artificial neural network predictive model. The artificial neural network predictive model is built using multilayer perceptron and consist of one output variable and six input variable, and the algorithm used is back propagation. Data used in this study is generated by conducting the simulations in 1000 cycles. Three categories of skewness used in the output variables are positive skewness, neutral, and negative skewness. The results show that data skewness does not have a significant effect on the accuracy of the artificial neural network predictive model. These results imply that artificial neural network predictive model has a higher capability to cope with skewed data due to its complexity in the hidden layer.

Muth’s Rational Expectations Hypothesis, That “…The Subjective Probability Distributions Are Distributed Around an Objective Probability Distribution, for a given Information Set…” is an Oxymoron. It Can Be Corrected by Amending It to Read “…The Subjective Probability Distributions Are Distributed Around a Subjective Consensus Probability Distribution, for a given Information Set…”

Due to the high pour point of the oil products transported in the long-distance high wax crude oil pipeline, in order to ensure the operation safety, it is necessary to adopt heating transmission technology, so as to ensure that the oil temperature along the pipeline is 3–5 °C higher than the pour point, that is to say, the oil temperature is the most important operation parameter of the long-distance hot oil pipeline, and the accurate prediction and control of the oil temperature is the premise of the pipeline safety optimization. Aiming at the problems of large prediction error and poor applicability of the previous theoretical formula, this paper studies the establishment of oil temperature prediction model by using data mining algorithms such as Back Propagation (BP) neural network, and improves the prediction efficiency and accuracy of the model by using Genetic Algorithm (GA) optimization. The correlation coefficient formula is used to calculate the influence coefficient of oil temperature, ground temperature, pipeline transportation and other parameters on the inlet oil temperature of the downstream station, so as to obtain the input parameters of the model. The actual production data training model is downloaded through SCADA system, and the prediction accuracy of the control model is ±0.5 °C. Compared with BP model and other theoretical formulas, the accuracy and efficiency of GA-BP oil temperature prediction model are greatly improved, and the adaptability is better. The GA-BP oil temperature prediction model trained according to the actual production data can be effectively applied to the future pipeline big data platform, which lays a theoretical foundation for the intelligent control of the pipeline.

In the Wason selection task, subjects show a tendency towards counter-logical behaviour. Evidence gained from this experiment raises questions about the role that deductive logic plays in human reasoning. A prominent explanation of the effect uses an information-gain model. Rather than reasoning deductively, it is argued that subjects seek to reduce uncertainty. The bias that is observed is seen to stem from maximizing information gain in this adaptively rational way. This theoretical article shows that a Boolean generalization of the information-gain model is potentially considered the normative foundation of reasoning, in which case several inferences traditionally considered errors are found to be valid. The article examines how this affects inferences involving both over-extension of logical implication and overestimation of conjunctive probability. • Proposes a hybrid, logic/probability calculus. • Derives this as a generalization of the pre-existing information-gain model. • Connects reasoning to information acquisition. • Shows that several inferences traditionally classified as errors change their status under this hybrid form of normativity.

To develop a machine-learning (ML) model for prediction of shoulder dystocia (ShD) and to externally validate the model's predictive accuracy and potential clinical efficacy in optimizing the use of Cesarean delivery in the context of suspected macrosomia. We used electronic health records (EHR) from the Sheba Medical Center in Israel to develop the model (derivation cohort) and EHR from the University of California San Francisco Medical Center to validate the model's accuracy and clinical efficacy (validation cohort). Subsequent to application of inclusion and exclusion criteria, the derivation cohort included 686 singleton vaginal deliveries, of which 131 were complicated by ShD, and the validation cohort included 2584 deliveries, of which 31 were complicated by ShD. For each of these deliveries, we collected maternal and neonatal delivery outcomes coupled with maternal demographics, obstetric clinical data and sonographic fetal biometry. Biometric measurements and their derived estimated fetal weight were adjusted (aEFW) according to gestational age at delivery. A ML pipeline was utilized to develop the model. In the derivation cohort, the ML model provided significantly better prediction than did the current clinical paradigm based on fetal weight and maternal diabetes: using nested cross-validation, the area under the receiver-operating-characteristics curve (AUC) of the model was 0.793 ± 0.041, outperforming aEFW combined with diabetes (AUC = 0.745 ± 0.044, P = 1e-16 ). The following risk modifiers had a positive beta that was > 0.02, i.e. they increased the risk of ShD: aEFW (beta = 0.164), pregestational diabetes (beta = 0.047), prior ShD (beta = 0.04), female fetal sex (beta = 0.04) and adjusted abdominal circumference (beta = 0.03). The following risk modifiers had a negative beta that was < -0.02, i.e. they were protective of ShD: adjusted biparietal diameter (beta = -0.08) and maternal height (beta = -0.03). In the validation cohort, the model outperformed aEFW combined with diabetes (AUC = 0.866 vs 0.784, P = 0.00007). Additionally, in the validation cohort, among the subgroup of 273 women carrying a fetus with aEFW ≥ 4000 g, the aEFW had no predictive power (AUC = 0.548), and the model performed significantly better (0.775, P = 0.0002). A risk-score threshold of 0.5 stratified 42.9% of deliveries to the high-risk group, which included 90.9% of ShD cases and all cases accompanied by maternal or newborn complications. A more specific threshold of 0.7 stratified only 27.5% of the deliveries to the high-risk group, which included 63.6% of ShD cases and all those accompanied by newborn complications. We developed a ML model for prediction of ShD and, in a different cohort, externally validated its performance. The model predicted ShD better than did estimated fetal weight either alone or combined with maternal diabetes, and was able to stratify the risk of ShD and neonatal injury in the context of suspected macrosomia. Copyright © 2019 ISUOG. Published by John Wiley & Sons Ltd.

Memory is a complex phenomenon due to a large number of potential interactions that are associated with the organization of memory at the psychological and neural system level. In this review article a tripartite, multiple attribute, multiple process memory model with different forms of memory and its neurobiological underpinnings is represented in terms of the nature, structure or content of information representation as a set of different attributes including language, time, place, response, reward value (affect) and visual object as an example of sensory-perception. For each attribute, information is processed in the event-based, knowledge-based, and rule-based memory systems through multiple operations that involve multiple neural underpinnings. Of the many processes associated with the event-based memory system, the emphasis will be placed on short-term or working memory and pattern separation. Of the many processes associated with the knowledgebased memory system, the emphasis will be placed on perceptual processes. Of the many processes associated with the rule-based memory system the emphasis will be on short-term or working memory and paired associate learning. For all three systems data will be presented to demonstrate differential neuroanatomical mediation and where available parallel results will be presented in rodents, monkeys and humans.

The variability of soil is well known to affect the geotechnical performance of structures. As probabilistic design methods become more commonly used, the ability to measure the variability of soil becomes more important. However, by using only the point statistics of soil parameters in design (e.g. the mean and standard deviation), typically an over-estimation of failure probabilities occurs, leading to over-conservative designs. By looking at the spatial correlation (e.g. scales of fluctuation) a more accurate representation can be achieved. This paper presents a method to use vertical Cone Penetration Tests (CPTs) to detect both the vertical and horizontal scales of fluctuation. An extensive numerical and experimental investigation has been undertaken to understand how spatial variation can be estimated and to quantify the accuracy in that estimation. The impact of being able to quantify the uncertainty is illustrated via a simple slope stability example.