Use Of Conditional Probabilities Research Articles

OLYMPUS-POPGEN: A synthetic population generation model to represent urban populations for assessing exposure to air quality.

With the new individual- and activity-based approaches to simulating exposure to air pollutants, exposure models must now provide synthetic populations that realistically reflect the demographic profiles of individuals in an urban territory. Demographic profiles condition the behavior of individuals in urban space (activities, mobility) and determine the resulting risks of exposure and environmental inequalities. In this context, there is a strong need to determine the relevance of the population modeling methods to reproduce the combinations of socio-demographic parameters in a population from the existing databases. The difficulty of accessing complete, high-resolution databases indeed proves to be very limiting for the ambitions of the different approaches. This work proposes to evaluate the potential of a statistical approach for the numerical modeling of synthetic populations, at the scale of dwellings and including the representation of coherent socio-demographic profiles. The approach is based on and validated against the existing open databases. The ambition is to be able to build upon such synthetic populations to produce a comprehensive assessment of the risk of environmental exposure that can be cross-referenced with lifestyles, indicators of social, professional or demographic category, and even health vulnerability data. The approach implemented here is based on the use of conditional probabilities to model the socio-demographic properties of individuals, via the deployment of a Monte Carlo Markov Chain (MCMC) simulation. Households are assigned to housing according to income and house price classes. The resulting population generation model was tested in the Paris region (Ile de France) for the year 2010, and applied to a population of almost 12 million individuals. The approach is based on the use of census and survey databases. Validation, carried out by comparison with regional census data, shows that the model accurately reproduces the demographic attributes of individuals (age, gender, professional category, income) as well as their combination, at both regional and sub-municipal levels. Notably, population distribution at the scale of the model buildings remains consistent with observed data patterns. The outcomes of this work demonstrate the ability of our approach to create, from public data, a coherent synthetic population with broad socio-demographic profiles. They give confidence for the use of this approach in an activity-based air quality exposure study, and thus for exploring the interrelations between social determinants and environmental risks. The non-specific nature of this work allows us to consider its extension to broader demographic profiles, including health indicators, and to different study regions.

Teaching the Difficult Past of Statistics to Improve the Future

In recent years, the discipline of statistics has begun reckoning with its difficult history. Institutions are reconsidering names that have honored key historical figures in statistics who have deep ties to eugenics movements and racial and class prejudice. These names, however, continue to appear in our classrooms, where we teach the methods created by these individuals, raising the question of how instructors should address their legacies. Three examples of famous statisticians and their work—Francis Galton’s use of conditional probabilities to demonstrate “hereditary talent,” Karl Pearson’s attempt to quantify the intelligence of Jewish immigrant students, and Ronald A. Fisher’s creation of the analysis of variance to de-emphasize environment in human development—highlight the intimate ties between statistics and eugenics. These examples, along with a discussion of the context of these men, eugenics movements, and the statisticians and scientists who opposed their eugenic programs, can humanize the field for students, teach them about the challenges in accurate and unbiased data collection and analysis, and connect historical mistakes to contemporary ethical issues. Confronting this history in the classroom can both improve the teaching of the statistical methodologies themselves and begin a broader conversation about the role of statistics in the world. Supplementary materials for this article are available online.

Estimation of the Conditional Probability Using a Stochastic Gradient Process

The use of conditional probabilities has gained in popularity in various fields such as medicine, finance, and imaging processing. This has occurred especially with the availability of large datasets that allow us to extract the full potential of the available estimation algorithms. Nevertheless, such a large volume of data is often accompanied by a significant need for computational capacity as well as a consequent compilation time. In this article, we propose a low-cost estimation method: we first demonstrate analytically the convergence of our method to the desired probability and then we perform a simulation to support our point.

Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach

We revisit the calculation of quantum-gravitational corrections to the power spectra of scalar and tensor perturbations in the Born-Oppenheimer approach to quantum gravity. We focus on the issue of the definition of the inner product of the theory and the unitarity of the corrections to the dynamics of the cosmological perturbations. We argue that the correction terms are unitary, provided the inner product is defined in a suitable way, which can be related to a notion of gauge-fixing the time variable and the use of conditional probabilities in quantum cosmology. We compare the corrections obtained within this framework to earlier results in the literature and we conclude with some remarks on the physical interpretation of the correction terms.

A Dynamic Bayesian Network Structure for Joint Diagnostics and Prognostics of Complex Engineering Systems

Dynamic Bayesian networks (DBNs) represent complex time-dependent causal relationships through the use of conditional probabilities and directed acyclic graph models. DBNs enable the forward and backward inference of system states, diagnosing current system health, and forecasting future system prognosis within the same modeling framework. As a result, there has been growing interest in using DBNs for reliability engineering problems and applications in risk assessment. However, there are open questions about how they can be used to support diagnostics and prognostic health monitoring of a complex engineering system (CES), e.g., power plants, processing facilities and maritime vessels. These systems’ tightly integrated human, hardware, and software components and dynamic operational environments have previously been difficult to model. As part of the growing literature advancing the understanding of how DBNs can be used to improve the risk assessments and health monitoring of CESs, this paper shows the prognostic and diagnostic inference capabilities that are possible to encapsulate within a single DBN model. Using simulated accident sequence data from a model sodium fast nuclear reactor as a case study, a DBN is designed, quantified, and verified based on evidence associated with a transient overpower. The results indicate that a joint prognostic and diagnostic model that is responsive to new system evidence can be generated from operating data to represent CES health. Such a model can therefore serve as another training tool for CES operators to better prepare for accident scenarios.

A risk evaluation method for deformation monitoring systems

In this contribution, we propose a method for statistically evaluating the risk in a deformation monitoring system. When the structure under monitoring moves beyond tolerance, the monitor system should issue an alert. Only a very small probability is acceptable of the system telling us that no change beyond a critical threshold has taken place, while in reality it has. This probability is referred to as integrity risk. We provide a formulation of integrity risk where the interaction between estimation and testing is taken into account, implying the use of conditional probabilities. In doing so, we assumed different scenarios with the alerts being dependent on both the identified hypothesis and the threat that the estimated size of deformations entails. It is hereby highlighted that a correct risk evaluation requires estimation and testing being considered together, as they are typically intimately linked. In practice, one may, however, find it simpler computation-wise to neglect the estimation–testing link. For this case, we provide an approximation of the integrity risk. This approximation may provide a too optimistic or pessimistic description of the integrity risk depending on the testing procedure and tolerances of the structure at hand. Monitoring systems, besides issuing timely alerts, are also required to provide threat estimates together with their corresponding probabilistic properties. As the testing outcome determines how the threat gets estimated, the threat estimator will then inherit the statistical properties of both estimation and testing. We derive the threat estimator bar{b}_{j} and its probability density function, taking the contributions from combined estimation and testing into account. It is highlighted that although the threat estimator under the identified hypothesis {mathcal {H}}_{j}, i.e., hat{b}_{j}, is normally distributed, the estimator bar{b}_{j} is not. It is explained that working with hat{b}_{j} instead of bar{b}_{j}, thus ignoring the estimation–testing link, may provide a too optimistic description of the threat estimator’s quality. The presented method is illustrated by means of two simple deformation examples.

Interventionist decision theory

Jim Joyce has argued that David Lewis’s formulation of causal decision theory is inadequate because it fails to apply to the “small world” decisions that people face in real life. Meanwhile, several authors have argued that causal decision theory should be developed such that it integrates the interventionist approach to causal modeling because of the expressive power afforded by the language of causal models, but, as of now, there has been little work towards this end. In this paper, I propose a variant of Lewis’s causal decision theory that is intended to meet both of these demands. Specifically, I argue that Lewis’s causal decision theory can be rendered applicable to small world decisions if one analyzes his dependency hypotheses as causal hypotheses that depend on the interventionist causal modeling framework for their semantics. I then argue that this interventionist variant of Lewis’s causal decision theory is preferable to interventionist causal decision theories that purportedly generalize Lewis’s through the use of conditional probabilities. This is because Lewisian interventionist decision theory captures the causal decision theorist’s conviction that any correlation between what the agent does and cannot cause should be irrelevant to the agent’s choice, while purported generalizations do not.

A Recurrent Solution of PH/M/c/N-Like and PH/M/c-Like Queues

We propose an efficient semi-numerical approach to compute the steady-state probability distribution for the number of requests at arbitrary and at arrival time instants in PH/M/c-like systems with homogeneous servers in which the inter-arrival time distribution is represented by an acyclic set of memoryless phases. Our method is based on conditional probabilities and results in a simple computationally stable recurrence. It avoids the explicit manipulation of potentially large matrices and involves no iteration. Owing to the use of conditional probabilities, it delays the onset of numerical issues related to floating-point underflow as the number of servers and/or phases increases. For generalized Coxian distributions, the computational complexity of the proposed approach grows linearly with the number of phases in the distribution.

A Recurrent Solution of PH/M/c/N-Like and PH/M/c-Like Queues

We propose an efficient semi-numerical approach to compute the steady-state probability distribution for the number of requests at arbitrary and at arrival time instants in PH/M/c-like systems with homogeneous servers in which the inter-arrival time distribution is represented by an acyclic set of memoryless phases. Our method is based on conditional probabilities and results in a simple computationally stable recurrence. It avoids the explicit manipulation of potentially large matrices and involves no iteration. Owing to the use of conditional probabilities, it delays the onset of numerical issues related to floating-point underflow as the number of servers and/or phases increases. For generalized Coxian distributions, the computational complexity of the proposed approach grows linearly with the number of phases in the distribution.

Fast reliability analysis of combinatorial logic circuits using conditional probabilities

Probabilistic reliability analysis is a common approach in logic circuit reliability analysis. Existing methods suffer from accuracy or scalability problems for large circuits because of combinatorial explosion. In this work we show how the use of conditional probabilities can overcome scalability problems while maintaining accurate reliability estimation. The source of accuracy and scalability problems in these approaches is the presence of reconverging signals. An efficient use of conditional probabilities used to decorrelate signals allows for fast and accurate reliability analysis.

Quantum mechanics from classical statistics

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a "purity constraint". Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Input Effects Within a Constructionist Framework

Constructionist approaches to language hypothesize that grammar can be learned from the input using domain‐general mechanisms. This emphasis has engendered a great deal of research—exemplified in the present issue—that seeks to illuminate the ways in which input‐related factors can both drive and constrain constructional acquisition. In this commentary piece, we situate results reported by contributors to the present issue within the larger body of acquisition work in the constructionist framework. We address the importance of both type frequency and skewed input samples in the development of constructional categories and we compare different ways that the association between verbs and constructions can be measured, including through the use of conditional probabilities, lexical biases, and introspective judgments.

Benefit and Risk of Mammography Screening – Considerations from an Epidemiological Viewpoint: Inaccurate Estimation of Everyday Risks

Conditional probabilities versus absolute frequencies: what is this really all about? We know from psychological research that the manner in which facts are presented has a major influence on the thoughts and actions of the persons affected by them. Facts are assessed differently if they are presented as a potential gain or a potential loss. This is the central point: whoever controls the manner in which study data are presented will essentially determine whether a proposed screening program will be accepted. The authors object to presenting the benefit of screening with absolute frequencies and advocate using conditional probabilities instead. They postulate that the general population is well versed in the use of conditional probabilities because certain risks that are permanently present in everyday life require constant assessment (e.g., building insurance). I do not share this opinion. Many studies in social psychology have shown that most people generally estimate everyday risks inaccurately. Gigerenzer (1) has shown in several studies that neither laypersons nor experts can draw correct conclusions from conditional probabilities. This being known, the authors’ argument that the general acceptance of building insurance reflects a correct understanding of conditional probabilities seems rather weak. It is, furthermore, good scientific practice to express study data in terms of frequencies. No critically thinking physician would assess a drug trial, for example, on the basis of relative risk reduction alone; rather, the actual benefits and potential risks would need to be assessed in the light of the frequency parameters NNT (number needed to treat) and NNH (number needed to harm). Why should this be any less obvious when a screening test comes under scrutiny?

Determining the Duration of Antidepressant Treatment: Application of Signal Detection Methodology and the Need for Duration Adaptive Designs (DAD)

With remission now the treatment goal, antidepressant trial duration has increased. However, most patients do not remit and are exposed to prolonged, ineffective treatment. Conditional probabilities and signal detection methodology were contrasted in early detection of nonremitters in three comparator, 12-week antidepressant trials conducted in late- or mid-life depression. The mid- and late-life samples did not differ in rates or time-to-onset of remission or accuracy of early identification of nonremission. Using conditional probabilities, there were marked differences in predictive power depending on the remission criterion. With signal detection methods, sensitivity and specificity of early identification were uniform across the differing medication conditions, remission criteria, and the three studies. By week 6, > or = 60% of ultimate nonremitters were identified, while maintaining a false positive rate < or = 20%. The goals of providing maximal opportunity to achieve remission, while minimizing exposure to ineffective treatment can be satisfied by use of duration adaptive designs (DAD). While use of conditional probabilities has been the traditional method for early detection of nonremitters, this approach is inferior to use of signal detection methods. The findings also contradicted the widely held view that patients with late-life depression require longer treatment duration.

Quality Meets Quantity: Case Studies, Conditional Probability, and Counterfactuals

In contrast to statistical methods, a number of case study methods—collectively referred to as Mill's methods, used by generations of social science researchers—only consider deterministic relationships. They do so to their detriment because heeding the basic lessons of statistical inference can prevent serious inferential errors. Of particular importance is the use of conditional probabilities to compare relevant counterfactuals. A prominent example of work using Mill's methods is Theda Skocpol's States and Social Revolutions. Barbara Geddes's widely assigned critique of Skocpol's claim of a causal relationship between foreign threat and social revolution is valid if this relationship is considered to be deterministic. If, however, we interpret Skocpol's hypothesized causal relationship to be probabilistic, Geddes's data support Skocpol's hypothesis. But Skocpol, unlike Geddes, failed to provide the data necessary to compare conditional probabilities. Also problematic for Skocpol is the fact that when one makes causal inferences, conditional probabilities are of interest only insofar as they provide information about relevant counterfactuals.Jasjeet S. Sekhon thanks Walter R. Mebane Jr., Henry Brady, Bear Braumoeller, Shigeo Hirano, Gary King, John Londregan, Bruce Rusk, Theda Skocpol, Suzanne M. Smith, Jonathan N. Wand, the editors of Perspectives on Politics, and three anonymous reviewers for valuable comments and advice.

The conditional probabilities of survival in patients with anaplastic astrocytoma or glioblastoma multiforme

Background By the use of conditional probabilities of survival, we studied the yearly survival rates for individual tumor survivors. Methods Conditional survival rate was estimated in 114 consecutive patients with anaplastic astrocytoma or glioblastoma multiforme. Conditional probabilities of surviving some years given survival to a specific period of time after craniotomy and 95% confidence intervals were calculated in the individual tumor survivors. Results The estimated median survival was 30 months for 45 patients with anaplastic astrocytoma and 12 months for 69 patients with glioblastma multiforme. The conditional probabilities of surviving next one year given survival to 1 year, 2 years, 3 years, 4 years, or 5 years after craniotomy for anaplastic astrocytoma were 86.2%, 75.0%, 85.9%, 77.8%, or 85.7%, respectively; for glioblastoma multiforme 64.8%, 58.7%, 85.7%, 80.0%, or 75.0%, respectively. The conditional probability of surviving to 5 years given survival to 2 years after craniotomy for anaplastic astrocytoma, i.e., surviving an additional 3 years, was 50.1%, which was better than observed 5-year survival rate (28.6%); for glioblastoma multiforme it was 40.2%, which also was better than observed 5-year survival rate (12.4%). Conclusions The conditional probability of survival was a good method to clinically predict yearly survival rate for indi-vidual tumor survivors. In addition, the method can estimate the probabilities of surviving next some years given survival to a specific period of time after craniotomy. It also showed a more encouraging result than observed survival rate in patients with supratentorial malignant astrocytomas.

A probabilistic approach to the site percolation problems using fractal tree

A simple method based on the use of conditional probabilities, for deriving the particle cluster distribution is discussed for the site-percolation problem. The method is applied to a fractal tree (Inhomogeneous Bethe lattice) in the case of finite clusters. The extrema of the corresponding distribution are analytically analyzed and the known results for the homogeneous case are obtained.

The dependence of voter shares under a two-vote system

In an electoral system where each voter is allowed to select up to two candidates in a double-seat constituency, the combination of votes forms a special kind of contingency table. The usual hypothesis of complete independence of the voter shares for the candidates is of interest, but it is shown to be almost unattainable. The correlation coefficient of the voter shares is constructed. It is shown to be equivalent to Pearson's phi coefficient. The limitations of the coefficient are discussed. It is found that the use of conditional probabilities gives a better understanding of the dependence of the voter shares under the system considered.

The incidence and utility of the ACID, ACIDS, and SCAD profiles in a referred population

THE ACID, ACIDS, and SCAD profiles are examples of subtest patterns from the WISC-III that have been proposed as potentially helpful in differential diagnosis of exceptionalities. This study investigated the prevalence and utility of these profiles in a large referred population. Although the incidence rates of the ACID and ACIDS profiles in some groups were greater than rates reported for the standardization sample, incidence levels were found to be low in all clinical groups studied. The SCAD profile evidenced generally higher incidence rates but none greater than the rates reported for the standardization sample. The findings support the use of conditional probabilities and incremental gains based on the actual incidence from a referred population to assist in differential diagnosis; however, none of the profiles are recommended as a criterion for determining exceptionality.

Use of conditional probabilities for determining relationships between amino acid sequence and protein secondary structure.

The conditional probability, P(sigma/x), is a statement of the probability that the value of sigma will be found given the prior information that a value of x has been observed. Here sigma represents any one of the secondary structure types, alpha, beta, tau, and rho for helix, sheet, turn, and random, respectively, and x represents a sequence attribute, including, but not limited to: (1) hydropathy; (2) hydrophobic moments assuming helix and sheet; (3) Richardson and Richardson helical N-cap and C-cap values; (4) Chou-Fasman conformational parameters for helix, P alpha, for sheet, P beta, and for turn, P tau; and (5) Garnier, Osguthorpe, and Robson (GOR) information values for helix, I alpha, for sheet, I beta, for turn, I tau, and for random structure, I rho. Plots of P(sigma/x) vs. x are demonstrated to provide information about the correlation between structure and attribute, sigma and x. The separations between different P(sigma/x) vs. x curves indicate the capacity of a given attribute to discriminate between different secondary structural types and permit comparison of different attributes. P(alpha/x), P(beta/x), P(tau/x) and P(rho/x) vs. x plots show that the most useful attributes for discriminating helix are, in order: hydrophobic moment assuming helix greater than P alpha much greater than N-cap greater than C-cap approximately I alpha approximately I tau. The information value for turns, I tau, was found to discriminate helix better than turns. Discrimination for sheet was found to be in the following order: I beta much greater than P beta approximately hydropathy greater than I rho approximately hydrophobic moment assuming sheet. Three attributes, at their low values, were found to give significant discrimination for the absence of helix: I alpha approximately P alpha approximately hydrophobic moment assuming helix. Also, three other attributes were found to indicate the absence of sheet: P beta much greater than I rho approximately hydropathy. Indications of the absence of sigma could be as useful for some applications as the indication of the presence of sigma.