Estimates Of Conditional Probabilities Research Articles

Risk estimation using probability machines

BackgroundLogistic regression has been the de facto, and often the only, model used in the description and analysis of relationships between a binary outcome and observed features. It is widely used to obtain the conditional probabilities of the outcome given predictors, as well as predictor effect size estimates using conditional odds ratios.ResultsWe show how statistical learning machines for binary outcomes, provably consistent for the nonparametric regression problem, can be used to provide both consistent conditional probability estimation and conditional effect size estimates. Effect size estimates from learning machines leverage our understanding of counterfactual arguments central to the interpretation of such estimates. We show that, if the data generating model is logistic, we can recover accurate probability predictions and effect size estimates with nearly the same efficiency as a correct logistic model, both for main effects and interactions. We also propose a method using learning machines to scan for possible interaction effects quickly and efficiently. Simulations using random forest probability machines are presented.ConclusionsThe models we propose make no assumptions about the data structure, and capture the patterns in the data by just specifying the predictors involved and not any particular model structure. So they do not run the same risks of model mis-specification and the resultant estimation biases as a logistic model. This methodology, which we call a “risk machine”, will share properties from the statistical machine that it is derived from.

Bayesian network based semantic image classification with attributed relational graph

Semantic image classification is a hot issue of image mining. Information of spatial relations between objects in an image is one of the important semantic information of an image. However, the previous researches have not made full use of the spatial relations for image modeling and classification. In addition, to classify the images with Bayesian network, the accuracy of conditional probability estimation may be insufficient, because the learning methods of spatial contextual models have usually used a limited number of training samples. In this work, the semantic image modeling based on attributed relational graph has been proposed, in which the distance measure method between images was presented, therefore the object information and spatial relational information could be fully utilized. Then, the semantic distance between images based on attributed relational graph could be calculated for the support vector machine to obtain the joint conditional probability distribution of Bayesian network. Therefore the probabilistic estimation problem under the sparse training samples could be solved, and the accuracy of semantic image classification with Bayesian network was improved. Experimental results show the validity and reliability of this proposed method.

An efficient model-free estimation of multiclass conditional probability

Conventional multiclass conditional probability estimation methods, such as Fisher's discriminate analysis and logistic regression, often require restrictive distributional model assumption. In this paper, a model-free estimation method is proposed to estimate multiclass conditional probability through a series of conditional quantile regression functions. Specifically, the conditional class probability is formulated as a difference of corresponding cumulative distribution functions, where the cumulative distribution functions can be converted from the estimated conditional quantile regression functions. The proposed estimation method is also efficient as its computation cost does not increase exponentially with the number of classes. The theoretical and numerical studies demonstrate that the proposed estimation method is highly competitive against the existing competitors, especially when the number of classes is relatively large.

The relationship between smoking, quitting smoking and obesity in Australia: a seemingly unrelated probit approach

Smoking and obesity are two leading causes of preventable death. Further understanding of the relationship between these two risk factors can assist in reducing avoidable morbidity and mortality. This study investigates the empirical association between obesity and the propensity to smoke and to quit smoking, using a Seemingly Unrelated (SUR) probit approach that takes into consideration the potential for reverse causality and unobserved heterogeneity. Using Australian health survey data, this article demonstrates the usefulness of the SUR probit approach in generating information on the relationship between unobserved factors influencing both smoking behaviour and obesity, and in providing estimates of the conditional probabilities of each risk factor. Results suggest the two risk factors are not independent. The presence, size and direction of correlation between the unobserved factors are found to vary by smoking behaviour and by gender. Estimates of conditional probabilities demonstrate smokers have a lower probability of obesity, particularly among females, and ex-smokers have a higher probability of obesity, particularly among males. These findings suggest that health policies targeted at one risk factor may have unintended implications for the other.

A semi-empirical method for predicting hydrological drought magnitudes in the Canadian prairies

A hydrological drought magnitude (M T ) expressed in standardized terms is predicted on annual, monthly and weekly time scales for a sampling period of T years in streamflow data from the Canadian prairies. The drought episodes are considered to follow the Poisson law of probability and, when coupled with the gamma probability distribution function (pdf) of drought magnitude (M) in the extreme number theorem, culminate in a relationship capable of evaluating the expected value, E(M T ). The parameters of the underlying pdf of M are determined based on the assumption that the drought intensity follows a truncated normal pdf. The E(M T ) can be evaluated using only standard deviation (σ), lag-1 autocorrelation (ρ) of the standardized hydrological index (SHI) sequence, and a weighting parameter Φ (ranging from 0 to 1) to account for the extreme drought duration (L T ), as well as the mean drought duration (Lm ), in a characteristic drought length (Lc ). The SHI is treated as standard normal variate, equivalent to the commonly-used standardized precipitation index. A closed-form relationship can be used for the estimation of first-order conditional probabilities, which can also be estimated from historical streamflow records. For all rivers, at the annual time scale, the value of Φ was found equal to 0.5, but it tends to vary (in the range 0 to 1) from river to river at monthly and weekly time scales. However, for a particular river, the Φ value was nearly constant at monthly and weekly time scales. The proposed method estimates E(M T ) satisfactorily comparable to the observed counterpart. At the annual time scale, the assumption of a normal pdf for drought magnitude tends to yield results in close proximity to that of a gamma pdf. The M T , when transformed into deficit-volume, can form a basis for designing water storage facilities and for planning water management strategies during drought periods. Editor D. Koutsoyiannis; Associate editor C. Onof Citation Sharma, T.C. and Panu, U.S., 2013. A semi-empirical method for predicting hydrological drought magnitudes in the Canadian prairies. Hydrological Sciences Journal, 58 (3), 549–569.

Judge‐Jury Agreement in Criminal Cases: The First Three Years of the Korean Jury System

This study examined jury trials conducted during the first three years since the introduction of a new jury system in South Korea. Case information from all jury trials held during the time was collected and empirically analyzed with a focus on judge‐jury agreement. The statistical analyses were guided by previous studies (Eisenberg et al. ; Spencer ). Results indicated that judges and juries agreed on the verdict 91.4 percent of the time (70.3 percent for conviction and 21.1 percent for acquittal). When they disagreed, juries had a greater tendency to acquit than did judges (7.4 percent and 1.2 percent, respectively). Neither evidentiary strength nor complexity had any systematic impact on agreement rates. Judges were more likely than juries to convict across all levels of evidentiary strength. The accuracy and error rates of jury verdicts were assessed by estimates of conditional probability.

Quality Perceptions and Dynamic Brand Choice

A simple model of dynamic brand choice that takes into account the uncertainty faced by the consumer and the consequent information value associated with choice is developed in this paper. The model is developed using the Neumann-Morgenstern expected utility framework. The consumer, on each occasion, chooses from the brands available so as to maximize his expected utility over a finite horizon based on preferences that are dynamically updated with consumption experience. The dependence of current choice on past choices is hypothesized as being due to learning effects. Brands are allowed to vary in their ability to influence long term preferences with consumption experience. The dynamic model is estimated on scanner panel data using the conditional choice probability (CCP) estimation procedure, proposed by Hotz and Miller [1993], that is computationally simple compared to the extant methods of estimating dynamic models. Results support the hypothesis that the consumer is not perfectly informed and is forward looking. Models that explicitly take such effects into account fit the data better than reduced form approaches.

410O - Conditional Probability of Survival in Patients with Glioblastoma Multiforme in the Temozolomide Treatment Era

ABSTRACT Introduction Glioblastoma multiforme (GBM) is the most aggressive of gliomas. With standard treatment consisting of surgery followed by radiotherapy (RT) with concurrent and adjuvant temozolomide (TMZ), median survival is approximately 14.6 mo. These estimates are not as informative to patients (pts) who have survived for some time after diagnosis. Aim: To retrospectively review outcomes and report conditional probability estimates in the TMZ treatment era of pts who presented to a multidisciplinary team at the tertiary referral center PrincessMargaretHospital, Toronto, with a diagnosis of GBM. Methods 892 pts were followed from 01/04 – 08/10. Complete demographics, performance status (PS), GBM localization, extent of surgery, percent receiving RT +/- TMZ, overall survival (OS) and conditional probability were analyzed. Results The cohort includes 548 (61%) males with median age 62 (5-93). Baseline PS was 0-1 in 600 (67%), 2-3 in 251 (28%) pts. 205 (23%) had frontal lobe tumors. Extent of surgery; 26% biopsy, 68% partial/subtotal resection, 6% unknown. 516 (58%) received concurrent RT/TMZ +/- adjuvant TMZ. Survival was similar for those with frontal lobe tumors vs other locations (10.2 vs 9.7 mo, Logrank test p = 0.28). OS for biopsy pts was 4.5 mo (3.5 – 6.2), and partial/subtotal resection pts; 11.6 mo (10.3 – 12.5) (p Time Overall Survival (%) 95% CI Conditional Probability of Survival (%) 95% CI 1 Year 43.1 39.8 – 46.4 41.4 35.9 – 47.0 2 Year 17.9 15.2 – 20.7 57.4 47.5 – 67.4 3 Year 10.3 8.0 – 12.8 80.6 68.4 – 92.8 4 Year 8.3 6.1 – 10.9 85.6 71.1 – 100 5 Year 7.1 5.0 – 9.7 81.5 60.9 – 100 Conclusion The conditional probability of surviving an additional yr after survival to 2 yrs post diagnosis exceeds the 1 yr survival rate, indicating that the future prognosis of a pt who has survived for 2 yrs may be as good as those recently diagnosed. Conditional probabilities of survival in this general disease population in the era of TMZ therapy may provide more accurate life expectancy predictions for survivors of GBM. Disclosure All authors have declared no conflicts of interest.

Latent Class Modeling for Site- and Non-Site-Specific Classification Accuracy Assessment Without Ground Data

Accuracy assessment should be a fundamental component of an image classification analysis and is typically undertaken following either a non-site- or a site-specific methodology. The assessment of classification accuracy is, however, often difficult, with many challenges associated with the ground data typically required. Using a series of classifications of two test sites, this paper shows that accuracy assessment from both perspectives is possible through the use of a latent class modeling approach in the absence of ground data. This is possible because the parameters of a latent class model that explains the observed associations in class labeling made by a series of classifications provide estimates of class cover and conditional probabilities of class membership that equate to popular non-site- and site-specific (producer's accuracy) measures of accuracy, respectively. Additionally, the latent class model provides a new classification that could be evaluated by traditional means if ground data are available. The classification of each test site derived from the latent class model was accurate, being of equivalent accuracy to a conventional ensemble classification that was based on the same series of classifications for a site. The ability to derive a highly accurate classification and yield estimates of classification accuracy without ground data to form a testing set indicates the considerable promise of the method and a means to reduce demands for costly ground data that may also be a source of error due to imperfections.

Risk assessment for structural design criteria of FPSO systems. Part II: Consequence models and applications to determination of target reliabilities

The paper presents applications of the framework for generic risk assessment for FPSO systems described in a companion paper [1]. Consequence models for structural risk assessment are developed for failure of hull girder sections, hull components and mooring lines using Bayesian Probabilistic Networks (BPN). The estimation of conditional probabilities required in the BPN models, such as the probability of a combined failure of several components and system failure conditional on components failure, are discussed. The risk assessment framework is applied for decision making on target reliabilities for ULS design of mooring lines. The target reliabilities are found by optimizing expected life-cycle costs and verifying compliance with risk acceptance criteria developed according to the Life Quality Index (LQI) principle. It is shown that the optimal reliability index, which minimizes total expected costs, may not always lead to an acceptable solution from the point-of-view of the LQI criterion.

Statistical models and learning algorithms for ordinal regression problems

In this study, we propose a learning algorithm for ordinal regression problems. In most existing learning algorithms, the threshold or location model is assumed to be the statistical model. For estimation of conditional probability of labels for a given covariate vector, we extended the location model to apply ordinal regressions. We present this learning algorithm using the squared-loss function with the location-scale models for estimating conditional probability. We prove that the estimated conditional probability satisfies the monotonicity of the distribution function. Furthermore, we have conducted numerical experiments to compare these proposed methods with existing approaches. We found that, in its ability to predict labels, our method may not have an advantage over existing approaches. However, for estimating conditional probabilities, it does outperform the learning algorithm using location models.

Dynamic-Model-Based Seasonal Prediction of Meteorological Drought over the Contiguous United States

Abstract A simple method was developed to forecast 3- and 6-month standardized precipitation indices (SPIs) for the prediction of meteorological drought over the contiguous United States based on precipitation seasonal forecasts from the NCEP Climate Forecast System (CFS). Before predicting SPI, the precipitation (P) forecasts from the coarse-resolution CFS global model were bias corrected and downscaled to a regional grid of 50 km. The downscaled CFS P forecasts, out to 9 months, were appended to the P analyses to form an extended P dataset. The SPIs were calculated from this new time series. Five downscaling methods were tested: 1) bilinear interpolation; 2) a bias correction and spatial downscaling (BCSD) method based on the probability distribution functions; 3) a conditional probability estimation approach using the mean P ensemble forecasts developed by J. Schaake, 4) a Bayesian approach that bias corrects and downscales P using all ensemble forecast members, as developed by the Princeton University group; and 5) multimethod ensemble as the equally weighted mean of the BCSD, Schaake, and Bayesian forecasts. For initial conditions from April to May, statistical downscaling methods were compared with dynamic downscaling based on the NCEP regional spectral model and forecasts from a high-resolution CFS T382 model. The skill is regionally and seasonally dependent. Overall, the 6-month SPI is skillful out to 3–4 months. For the first 3-month lead times, forecast skill comes from the P analyses prior to the forecast time. After 3 months, the multimethod ensemble has small advantages, but forecast skill may be too low to be useful in practice.

Semantic Coherence and Inconsistency in Estimating Conditional Probabilities

ABSTRACTTwo studies examined semantic coherence and internal inconsistency fallacies in conditional probability estimation. Problems reflected five distinct relationships between two sets: identical sets, mutually exclusive sets, subsets, overlapping sets, and independent sets (a special case of overlapping sets). Participants estimated P(A), P(B), P(A|B), and P(B|A). Inconsistency occurs when this constellation of estimates does not conform to Bayes' theorem. Semantic coherence occurs when this constellation of estimates is consistent with the depicted relationship among sets. Fuzzy‐trace theory predicts that people have difficulty with overlapping sets and subsets because they require class‐inclusion reasoning. On these problems, people are vulnerable to denominator neglect, the tendency to ignore relevant denominators, making the gist more difficult to discern. Independent sets are simplified by the gist understanding that P(A) provides no information about P(B), and thus, P(A|B) = P(A). The gist for identical sets is that P(A|B) = 1.0, and the gist of mutually exclusive sets is that P(A|B) = 0. In Study 1, identical, mutually exclusive, and independent sets yielded superior performance (in internal inconsistency and semantic coherence) than subsets and overlapping sets. For subsets and overlapping sets, interventions clarifying appropriate denominators generally improved semantic coherence and inconsistency, including teaching people to use Euler diagrams, 2 × 2 tables, or relative frequencies. In Study 2, with problems about breast cancer and BRCA mutations, there was a strong correlation between inconsistency in conditional probability estimation and conjunction fallacies of joint probability estimation, suggesting that similar fallacious reasoning processes produce these errors. Copyright © 2012 John Wiley & Sons, Ltd.

Methodology for estimation of conditional probability of stagnation channel break for PHWRs

A methodology to estimate the conditional probability of a break in inlet feeder being the stagnation channel break in Pressurized Heavy Water Reactors is presented in this paper. According to AERB Safety Guide AERB/SG/D-5, rupture at any location of PHT system up to size of double ended largest feeder pipe belongs to category-2 events which are events of moderate frequency. For a particular range of break sizes in inlet feeder, the flow in the corresponding reactor channel reduces almost immediately to stagnant/very low flow conditions and remains sustained due to high flow inertia of PHWR pipe structure. As it is a single channel event out of hundreds of channels, the signal for reactor trip is generated very late. Consequently the fuel temperature rises sharply and fuel failure may occur. The probability of break in a feeder leading to flow stagnation conditions in the corresponding channel is low but needs to be estimated. In this paper the conditional probability of stagnation channel break for feeder pipe is estimated deterministically for a reactor similar to Indian PHWR. In this work, the stagnation channel break is identified if minimum critical heat flux ratio (MCHFR) is sustained lower than one anywhere in the corresponding reactor channel. It leads to sudden rise in fuel clad temperature due to sudden significant reduction in heat removal. There is a range of break sizes for which the clad surface temperature rises above fuel failure limits. Depending on this range and break locations in the feeder, the conditional probability is estimated. It is assumed that conditional probability depends on the range of break sizes leading to stagnation. It is observed from the calculations that the conditional probability of stagnation channel break is significant. The analysis has been carried out using thermal hydraulic code RELAP5/Mod 3.4.

Adaptive Context-Tree-Based Statistical Filtering for Raster Map Image Denoising

Filtering of raster map images is chosen as a case study of a more general class of palette-indexed images for the denoising problem of images with a discrete number of output colors. Statistical features of local context are analyzed to avoid damage to pixel-level patterns, which is frequently caused by conventional filters. We apply a universal statistical filter using context-tree modeling via a selective context expansion capturing those pixel combinations that are present in the image. The selective context expansion makes it possible to use a much larger spatial neighborhood, with a feasible time and memory complexity, than fixed-size templates. We improve the existing context-tree approaches in two aspects: Firstly, in order to circumvent the context contamination problem, a context-merging strategy is applied where multiple similar contexts are considered in the conditional probability estimation procedure. Secondly, we study a specific continuous-input-finite-output problem in which the map images are corrupted by additive Gaussian noise. Performance comparisons with competitive filters demonstrate that the proposed algorithm provides robust noise filtering performance and good structure preservation in all test cases without any a priori information on the statistical properties of the noise.

Statistical analysis of kernel-based least-squares density-ratio estimation

The ratio of two probability densities can be used for solving various machine learning tasks such as covariate shift adaptation (importance sampling), outlier detection (likelihood-ratio test), feature selection (mutual information), and conditional probability estimation. Several methods of directly estimating the density ratio have recently been developed, e.g., moment matching estimation, maximum-likelihood density-ratio estimation, and least-squares density-ratio fitting. In this paper, we propose a kernelized variant of the least-squares method for density-ratio estimation, which is called kernel unconstrained least-squares importance fitting (KuLSIF). We investigate its fundamental statistical properties including a non-parametric convergence rate, an analytic-form solution, and a leave-one-out cross-validation score. We further study its relation to other kernel-based density-ratio estimators. In experiments, we numerically compare various kernel-based density-ratio estimation methods, and show that KuLSIF compares favorably with other approaches.

Conditional Probability Estimation for Significant Tornadoes Based on Rapid Update Cycle (RUC) Profiles

Abstract Recent literature has identified several supercell/tornado forecast parameters in common use that are operationally beneficial in assessing environments supportive of supercell tornadoes. These parameters are utilized in the computation of tornado forecast guidance such as the significant tornado parameter (STP), a dimensionless parameter developed at the Storm Prediction Center (SPC) that applies a subjectively chosen scale. The goal of this research is to determine if useful logistic regression equations can be developed to estimate the conditional probability of supercell tornadoes that are categorized as level 2 or stronger on the enhanced Fujita scale (EF) when a similar set of environmental background parameters is applied as variables. A large database of Rapid Update Cycle (RUC) analysis soundings in proximity to a representative sample of tornadic and nontornadic supercells over the central and eastern United States, a number of which were associated with EF2 or stronger tornadoes, was used to compute supercell tornado forecast parameters similar to those in the original version of STP. Three logistic regression equations were developed from this database, two of which are described and analyzed in detail. Statistical verification for both equations was accomplished using independent data from 2008 in proximity to supercell storms identified by staff at SPC. A recent version of the STP was utilized as a comparison diagnostic to accomplish part of the statistical verification. The results of this research suggest that output from both logistic regression equations can provide valuable guidance in a probabilistic sense, when adjustments are made for the ongoing convective mode. Case studies presented also suggest that this guidance can provide information complementary to STP in severe weather situations with potential for supercell tornadoes.

Practical Methods for Estimation of Dynamic Discrete Choice Models

Many discrete decisions are made with an eye toward how they will affect future outcomes. Formulating and estimating the underlying models that generate these decisions is difficult. Conditional choice probability (CCP) estimators often provide simpler ways to estimate dynamic discrete choice problems. Recent work shows how to frame dynamic discrete choice problems in a way that is conducive to CCP estimation and demonstrates that CCP estimators can be adapted to handle rich patterns of unobserved state variables.

Direct Density-Ratio Estimation with Dimensionality Reduction via Hetero-Distributional Subspace Analysis

Methods for estimating the ratio of two probability density functions have been actively explored recently since they can be used for various data processing tasks such as non-stationarity adaptation, outlier detection, feature selection, and conditional probability estimation. In this paper, we propose a new density-ratio estimator which incorporates dimensionality reduction into the density-ratio estimation procedure. Through experiments, the proposed method is shown to compare favorably with existing density-ratio estimators in terms of both accuracy and computational costs.

Experts, Bayesian Belief Networks, rare events and aviation risk estimates

Bayesian Belief Networks (BBN) are conceptually sensible models for aviation risk assessment. The aim here is to examine the ability of BBN-based techniques to make accurate aviation risk predictions. BBNs consist of a framework of causal factors linked by conditional probabilities. BBN conditional probabilities are elicited from aviation experts. The issue is that experts are not being asked about their expertise but about others’ failure rates. A simple model of expertise, which incorporates the main features proposed by researchers, implies that a best-expert’s estimates of failure rates are based on accessible quantitative data on accidents, incidents, etc. Best-expert estimates will use the best available and accessible data. Depending on the frequency of occurrence, this will be data on similar events, on similar types of event, or general mental rules about event frequencies. These considerations, plus the need to be cautious about statistical fluctuations, limit the accuracy of conditional probability estimates. The BBN framework assumes what is known as the Causal Markov Condition. In the present context, this assumes that there are no hidden common causes for sequences of failure events. Examples are given from safety regulation comparisons and serious accident investigations to indicate that common causes may be frequent occurrences in aviation. This is because some States/airlines have safety cultures that do not meet ‘best practice’. BBN accuracy might be improved by using data from controlled experiments. Aviation risk assessment is now very difficult, so further work on resilience engineering could be a better way of achieving safety improvements.