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Life course epidemiology is hampered by the absence of large studies with exposures and outcomes measured at different life stages in the same individuals. We describe when the effect of an exposure (A) on an outcome (Y) in a target population is identifiable in a combined ("synthetic") cohort created by pooling an early-life cohort including measures of A with a late-life cohort including measures of Y. We enumerate causal assumptions needed for unbiased effect estimation in the synthetic cohort and illustrate by simulating target populations under four causal models. From each target population, we randomly sampled early- and late-life cohorts and created a synthetic cohort by matching individuals from the two cohorts based on mediators and confounders. We estimated the effect of A on Y in the synthetic cohort, varying matching variables, the match ratio, and the strength of association between matching variables and A. Finally, we compared bias in the synthetic cohort estimates when matching variables did not d-separate A and Y to the bias expected in the original cohort. When the set of matching variables includes all variables d-connecting exposure and outcome (i.e., variables blocking all backdoor and front-door pathways), the synthetic cohort yields unbiased effect estimates. Even when matching variables did not fully account for confounders, the synthetic cohort estimate was sometimes less biased than comparable estimates in the original cohort. Methods based on merging cohorts may hasten the evaluation of early- and mid-life determinants of late-life health but rely on available measures of both confounders and mediators. [ABSTRACT FROM AUTHOR]

We address the problems of causal structure inference from conditional independence facts when latent confounders are admitted. The conditions that allow one to identify latent confounders and fully or partially recognize causal links are described. The updated implicative rules for orienting edges under confounding are suggested. We propose several new rules that are able to reveal bows and confounded causal edges. The rules rely on facts of absence of certain authentic edges (edge absence may be implied by Verma constraint or given in input as a priori requirement). [ABSTRACT FROM AUTHOR]

We address the problems of causal structure reconstruction given conditional independence facts when latent confounders are allowed. We examine the conditions that allow one to partially or fully identify authentic causal links and latent confounders. The updated implicative rules for orienting edges under confounding are suggested. As demonstrated, it is possible to construct the new rules, which can reveal confounded causal edges and bows. The rules rely on facts of the absence of certain authentic edges (such facts may be justified by non-independence constraints, like Verma constraint, or subject-based requirements). [ABSTRACT FROM AUTHOR]

Abstract Background Causal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model. Methods It remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability – the causal false-positive risk – is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied. Results Results show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias. Conclusion While the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

Allostatic self-efficacy (ASE) represents a computational theory of fatigue and depression. In brief, it postulates that (i) fatigue is a feeling state triggered by a metacognitive diagnosis of loss of control over bodily states (persistently elevated interoceptive surprise); and that (ii) generalization of low self-efficacy beliefs beyond bodily control induces depression. Here, we converted ASE theory into a structural causal model (SCM). This allowed identification of empirically testable hypotheses regarding causal relationships between the variables of interest. Applying conditional independence tests to questionnaire data from healthy volunteers, we sought to identify contradictions to the proposed SCM. Moreover, we estimated two causal effects proposed by ASE theory using three different methods. Our analyses identified specific aspects of the proposed SCM that were inconsistent with the available data. This enabled formulation of an updated SCM that can be tested against future data. Second, we confirmed the predicted negative average causal effect from metacognition of allostatic control to fatigue across all three different methods of estimation. Our study represents an initial attempt to refine and formalize ASE theory using methods from causal inference. Our results confirm key predictions from ASE theory but also suggest revisions which require empirical verification in future studies.

OpenMarkov is an open-source software tool for probabilistic graphical models. It has been developed especially for medicine, but has also been used to build applications in other fields and for tuition, in more than 30 countries. In this paper we explain how to use it as a pedagogical tool to teach the main concepts of Bayesian networks and influence diagrams, such as conditional dependence and independence, d-separation, Markov blankets, explaining away, optimal policies, expected utilities, etc., and some inference algorithms: logic sampling, likelihood weighting, and arc reversal. The facilities for learning Bayesian networks interactively can be used to illustrate step by step the performance of the two basic algorithms: search-and-score and PC. [ABSTRACT FROM AUTHOR]

This article proposes the usage of the d-separation criterion in Markov Boundary Discovery algorithms, instead of or alongside the statistical tests of conditional independence these algorithms usually rely on. This is a methodological improvement applicable when designing, studying or improving such algorithms, but it is not applicable for productive use, because computing the d-separation criterion requires complete knowledge of a Bayesian network. Yet Bayesian networks can be made available to the algorithms when studied in controlled conditions. This approach has the effect of removing sources of suboptimal behavior, allowing the algorithms to perform at their theoretical best and providing insights about their properties. The article also discusses an extension of this approach, namely to use d-separation as a complement to the usual statistical tests performed on synthetic datasets in order to ascertain the overall accuracy of the tests chosen by the algorithms, for further insights into their behavior. To exemplify these two approaches, two Markov Boundary Discovery algorithms were used, namely the Incremental Association Markov Blanket algorithm and the Iterative Parent–Child-Based Search of Markov Blanket algorithm. Firstly, these algorithms were configured to use d-separation alone as their conditional independence test, computed on known Bayesian networks. Subsequently, the algorithms were configured to use the statistical G-test complemented by d-separation to evaluate their behavior on synthetic data. [ABSTRACT FROM AUTHOR]

The problems of causal inference of models from empirical data (by independence-based methods) and some error mechanisms are examined. We demonstrate that the known rules for orienting edges of model can produce misleading results under presence of latent confounders. We propose corrections to the orientation rules aiming to successfully extend them for inference of models beyond the ancestral model class. The necessary assumptions justifying the inference of adequate causal relationships from data are suggested. [ABSTRACT FROM AUTHOR]

Background: Causal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model.Methods: It remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability - the causal false-positive risk - is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied.Results: Results show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias.Conclusion: While the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel algorithm for optimizing decision variables with respect to an outcome variable of interest in complex problems, such as those arising from big data. The proposed algorithm builds on the notion of Markov blankets in Bayesian networks to alleviate the computational challenges associated with optimization tasks in complex datasets. Through a case study, we apply the algorithm to optimize medication prescriptions for diabetic patients, who have different characteristics, suffer from multiple comorbidities, and take multiple medications concurrently. In particular, we demonstrate how the optimal combination of diabetic medications can be found by examining the comparative effectiveness of the medications among similar patients. The case study is based on 5 years of data for 19,223 diabetic patients. Our results indicate that certain patient characteristics (e.g., clinical and demographic features) influence optimal treatment decisions. Among patients examined, monotherapy with metformin was the most common optimal medication decision. The results are consistent with the relevant clinical guidelines and reports in the medical literature. The proposed algorithm obviates the need for knowledge of the whole Bayesian network model, which can be very complex in big data problems. The procedure can be applied to any complex Bayesian network with numerous features, multiple decision variables, and a target variable.

OpenMarkov is an open-source software tool for probabilistic graphical models. It has been developed especially for medicine, but has also been used to build applications in other fields and for tuition, in more than 30 countries. In this paper we explain how to use it as a pedagogical tool to teach the main concepts of Bayesian networks and influence diagrams, such as conditional dependence and independence, d-separation, Markov blankets, explaining away, optimal policies, expected utilities, etc., and some inference algorithms: logic sampling, likelihood weighting, and arc reversal. The facilities for learning Bayesian networks interactively can be used to illustrate step by step the performance of the two basic algorithms: search-and-score and PC.

Abstract Path analysis allows one to test the consistency of data to hypothesized causal relationships between variables. Often, interest lies in how the hypothesized dependencies differ between groups. Multigroup comparisons can be made by imposing various constraints: constraints on the topology, the path coefficients, the residual variances, and more. To date, only classical path analysis and structural equation modeling can account for differences between groups. These techniques have assumptions that are often not appropriate for ecological studies. The d‐sep test and the recently developed generalized chi‐squared test relax many of these assumptions for path models that can be represented as directed acyclic graphs (DAGs), but are currently lacking a multigroup test. In this paper, we develop a multigroup extension to the d‐sep test. Furthermore, we show how a recently developed generalized chi‐squared test and AIC for DAGs can be used for multigroup testing. The approaches are illustrated by a worked example and implemented in the commonly used statistical package, R. Practical recommendations for multigroup modeling are made, and advantages and disadvantages of the multigroup d‐sep and the chi‐squared test are discussed.

Path models, expressed as Directed Acyclic Graphs (DAGs), and the testing of such DAGs via a d-sep test, have become popular because they can incorporate complicated data structures that are difficult or impossible to accommodate in classical structural equation modeling. However, d-sep tests cannot accommodate DAGs that include unmeasured (latent) variables. We describe (i) how to convert a DAG with latent variables into an observationally equivalent graph without latents (a Mixed Acyclic Graph, MAG), (ii) how this MAG identifies which latents can/cannot be ignored without changing the causal meaning of the original DAG, and (iii) how to perform the MAG equivalent of a d-sep test. [ABSTRACT FROM AUTHOR]

Path analysis allows one to test the consistency of data to hypothesized causal relationships between variables. Often, interest lies in how the hypothesized dependencies differ between groups. Multigroup comparisons can be made by imposing various constraints: constraints on the topology, the path coefficients, the residual variances, and more. To date, only classical path analysis and structural equation modeling can account for differences between groups. These techniques have assumptions that are often not appropriate for ecological studies. The d‐sep test and the recently developed generalized chi‐squared test relax many of these assumptions for path models that can be represented as directed acyclic graphs (DAGs), but are currently lacking a multigroup test. In this paper, we develop a multigroup extension to the d‐sep test. Furthermore, we show how a recently developed generalized chi‐squared test and AIC for DAGs can be used for multigroup testing. The approaches are illustrated by a worked example and implemented in the commonly used statistical package, R. Practical recommendations for multigroup modeling are made, and advantages and disadvantages of the multigroup d‐sep and the chi‐squared test are discussed. [ABSTRACT FROM AUTHOR]

This article proposes the usage of the d-separation criterion in Markov Boundary Discovery algorithms, instead of or alongside the statistical tests of conditional independence these algorithms usually rely on. This is a methodological improvement applicable when designing, studying or improving such algorithms, but it is not applicable for productive use, because computing the d-separation criterion requires complete knowledge of a Bayesian network. Yet Bayesian networks can be made available to the algorithms when studied in controlled conditions. This approach has the effect of removing sources of suboptimal behavior, allowing the algorithms to perform at their theoretical best and providing insights about their properties. The article also discusses an extension of this approach, namely to use d-separation as a complement to the usual statistical tests performed on synthetic datasets in order to ascertain the overall accuracy of the tests chosen by the algorithms, for further insights into their behavior. To exemplify these two approaches, two Markov Boundary Discovery algorithms were used, namely the Incremental Association Markov Blanket algorithm and the Iterative Parent–Child-Based Search of Markov Blanket algorithm. Firstly, these algorithms were configured to use d-separation alone as their conditional independence test, computed on known Bayesian networks. Subsequently, the algorithms were configured to use the statistical G-test complemented by d-separation to evaluate their behavior on synthetic data.

This paper proposes a novel algorithm for optimizing decision variables with respect to an outcome variable of interest in complex problems, such as those arising from big data. The proposed algorithm builds on the notion of Markov blankets in Bayesian networks to alleviate the computational challenges associated with optimization tasks in complex datasets. Through a case study, we apply the algorithm to optimize medication prescriptions for diabetic patients, who have different characteristics, suffer from multiple comorbidities, and take multiple medications concurrently. In particular, we demonstrate how the optimal combination of diabetic medications can be found by examining the comparative effectiveness of the medications among similar patients. The case study is based on 5 years of data for 19,223 diabetic patients. Our results indicate that certain patient characteristics (e.g., clinical and demographic features) influence optimal treatment decisions. Among patients examined, monotherapy with metformin was the most common optimal medication decision. The results are consistent with the relevant clinical guidelines and reports in the medical literature. The proposed algorithm obviates the need for knowledge of the whole Bayesian network model, which can be very complex in big data problems. The procedure can be applied to any complex Bayesian network with numerous features, multiple decision variables, and a target variable. [ABSTRACT FROM AUTHOR]

We explain how to obtain a generalized maximum‐likelihood chi‐square statistic,XML2, and a full‐model Akaike Information Criterion (AIC) statistic for piecewise structural equation modeling (SEM); that is, structural equations without latent variables whose causal topology can be represented as a directed acyclic graph (DAG). The full piecewise SEM is decomposed into submodels as a Markov network, each of which can have different distributional assumptions or functional links and that can be modeled by any method that produces maximum‐likelihood parameter estimates. The generalized XML2 is a function of the difference in the maximum likelihoods of the model and its saturated equivalent and the full‐model AIC is calculated by summing the AIC statistics of each of the submodels. [ABSTRACT FROM AUTHOR]

Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl (2006b) constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated application of the rules of do-calculus and known properties of probabilities, and it ultimately either derives an expression for the causal distribution, or fails to identify the effect, in which case the effect is non-identifiable. In this paper, the R package causaleffect is presented, which provides an implementation of this algorithm. Functionality of causaleffect is also demonstrated through examples.

Abstract Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used estimation approach. We present an algorithmic framework for efficiently testing, constructing, and enumerating m -separators in ancestral graphs (AGs), a class of graphical causal models that can represent uncertainty about the presence of latent confounders. Furthermore, we prove a reduction from causal effect identification by covariate adjustment to m -separation in a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs). Jointly, these results yield constructive criteria that characterize all adjustment sets as well as all minimal and minimum adjustment sets for identification of a desired causal effect with multiple exposures and outcomes in the presence of latent confounding. Our results extend several existing solutions for special cases of these problems. Our efficient algorithms allowed us to empirically quantify the identifiability gap between covariate adjustment and the do-calculus in random DAGs and MAGs, covering a wide range of scenarios. Implementations of our algorithms are provided in the R package dagitty. [ABSTRACT FROM AUTHOR]

Abstract: Testing independencies is a fundamental task in reasoning with Bayesian networks (BNs). In practice, d‐separation is often used for this task, since it has linear‐time complexity. However, many have had difficulties understanding d‐separation in BNs. An equivalent method that is easier to understand, called m‐separation, transforms the problem from directed separation in BNs into classical separation in undirected graphs. Two main steps of this transformation are pruning the BN and adding undirected edges. In this paper, we propose u‐separation as an even simpler method for testing independencies in a BN. Our approach also converts the problem into classical separation in an undirected graph. However, our method is based upon the novel concepts of inaugural variables and rationalization. Thereby, the primary advantage of u‐separation over m‐separation is that m‐separation can prune unnecessarily and add superfluous edges. Our experiment results show that u‐separation performs 73% fewer modifications on average than m‐separation. [ABSTRACT FROM AUTHOR]

Globally, the proportion of elderly individuals in the population has increased substantially in the last few decades. However, the risk factors that should be managed in advance to ensure a natural process of mental decline due to aging remain unknown. In this study, a dataset consisting of a Brazilian elderly sample was modelled using a Bayesian Network (BN) approach to uncover connections between cognitive performance measures and potential influence factors. Regarding its structure (a Directed Acyclic Graph), it was investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome (MetS) and the indicator of mental decline referred to as Cognitive Impairment (CI). In this investigation, the concept known in the context of a BN as D-separation has been employed. Results of the conducted study revealed that the dependence between MetS and Cognitive Variables (CI and its direct determinants) in fact exists and depends on both Body Mass Index (BMI) and age. [ABSTRACT FROM AUTHOR]

We suggest Darwinian Networks (DNs) as a simplification of working with Bayesian networks (BNs). DNs adapt a handful of well-known concepts in biology into a single framework that is surprisingly simple yet remarkably robust. With respect to modeling, on one hand, DNs not only represent BNs but also faithfully represent the testing of independencies in a more straightforward fashion. On the other hand, with respect to three exact inference algorithms in BNs, DNs simplify each of them while unifying all of them. DNs can determine good elimination orderings using the same platform as used for modeling and inference. Finally, we demonstrate how DNs can represent two additional frameworks. Practical benefits of DNs include faster algorithms for inference and modeling. [ABSTRACT FROM AUTHOR]

Directed acyclic graphs (DAGs) are useful tools for visualizing the hypothesized causal structures in an intuitive way and selecting relevant confounders in causal inference. However, in spite of their increasing use in clinical and surgical research, the causal graphs might also be misused by a lack of understanding of the central principles. In this article, we aim to introduce the basic terminology and fundamental rules of DAGs, and DAGitty, a user-friendly program that easily displays DAGs. Specifically, we describe how to determine variables that should or should not be adjusted based on the backdoor criterion with examples. In addition, the occurrence of the various types of biases is discussed with caveats, including the problem caused by the traditional approach using p -values for confounder selection. Moreover, a detailed guide to DAGitty is provided with practical examples regarding minimally invasive surgery. Essentially, the primary benefit of DAGs is to aid researchers in clarifying the research questions and the corresponding designs based on the domain knowledge. With these strengths, we propose that the use of DAGs may contribute to rigorous research designs, and lead to transparency and reproducibility in research on minimally invasive surgery.

The aim of the paper is to relate Bell's notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of Bell's local causality and Markovity. [ABSTRACT FROM AUTHOR]

Questions How do land-use legacies and distance to forest patches influence tree colonization at a post-agricultural heathland? Are colonizing species with different life-history traits affected differently by these factors? Is the effect of increased nutrient availability from land-use legacies mediated by the understorey vegetation? Location Nørholm hede, a 350-ha heathland in southwest Denmark developing naturally after abandonment of traditional agricultural practices in 1895. Methods Using 140 plots (0.03 ha), we quantified the vegetation structure, soil properties and natural recruitment of tree/shrubs in the heathland. Further, we used high-resolution Li DAR data to classify the vegetation and identify forest patches. In the analysis, we first used a logistic mixed model to test whether colonization of tree and shrub species differed between areas with different land-use history and whether it was influenced by the distance to forest patches and life-history traits (seed mass) of colonizing species. Then, to determine how different factors influence colonization, we explored the direct and indirect relationships among nutrient availability, density of adult trees, canopy cover, cover of Deschampsia flexuosa and the probability of seedling colonization in each plot using a confirmatory multilevel path analysis. Results The probability of seedling colonization for small- and large-seeded species decreased with distance to forest patches. This response was more pronounced at the previously cultivated area. Multilevel path analysis showed that colonizing species with different life-history traits were affected by different factors. Small-seeded species were negatively affected by increased nutrient availability mediated by an increase in the cover of D. flexuosa. This effect was not found for large-seeded species. Moreover, the density of trees/shrubs (>2 m) increased the probability of colonization of small-seeded species, whereas higher canopy cover had a positive effect on large-seeded species. Conclusions Our analyses demonstrate that the interactions between abiotic factors, biotic interactions and life-history traits of colonizing species can lead to distinct patterns of tree colonization. Land-use legacies can have long-lasting, indirect effects on tree colonization by altering the composition of the understorey vegetation, which in turn can delay tree encroachment and slow down the succession from heathland to forest. [ABSTRACT FROM AUTHOR]

This paper presents and extends Latent Growth Modeling (LGM) as a complementary method for analyzing longitudinal data, modeling the process of change over time, testing time-centric hypotheses, and building longitudinal theories. We first describe the basic tenets of LGM and offer guidelines for applying LGM to Information Systems (IS) research, specifically how to pose research questions that focus on change over time and how to implement LGM models to test time-centric hypotheses. Second and more important, we theoretically extend LGM by proposing a model validation criterion, namely "d-separation," to evaluate why and when LGM works and test its fundamental properties and assumptions. Our d-separation criterion does not rely on any distributional assumptions of the data; it is grounded in the fundamental assumption of the theory of conditional independence. Third, we conduct extensive simulations to examine a multitude of factors that affect LGM performance. Finally, as a practical application, we apply LGM to model the relationship between word-of-mouth communication (online product reviews) and book sales over time with longitudinal 26-week data from Amazon. The paper concludes by discussing the implications of LGM for helping IS researchers develop and test longitudinal theories. [ABSTRACT FROM AUTHOR]

Directed Gaussian graphical models are statistical models that use a directed acyclic graph (DAG) to represent the conditional independence structures between a set of jointly normal random variables. The DAG specifies the model through recursive factorization of the parametrization, via restricted conditional distributions. In this paper, we make an attempt to characterize the DAGs whose vanishing ideals are toric ideals. In particular, we give some combinatorial criteria to construct such DAGs from smaller DAGs which have toric vanishing ideals. An associated monomial map called the shortest trek map plays an important role in our description of toric Gaussian DAG models. For DAGs whose vanishing ideal is toric, we prove results about the generating sets of those toric ideals. [ABSTRACT FROM AUTHOR]

The need to model and test hypotheses about complex ecological systems has led to a steady increase in use of path analytical techniques, which allow the modeling of multiple multivariate dependencies reflecting hypothesized causation and mechanisms. The aim is to achieve the estimation of direct, indirect, and total effects of one variable on another and to assess the adequacy of whole models. Path analytical techniques based on maximum likelihood currently used in ecology are rarely adequate for ecological data, which are often sparse, multi-level, and may contain nonlinear relationships as well as nonnormal response data such as counts or proportion data. Here I introduce a more flexible approach in the form of the joint application of hierarchical Bayes, Markov chain Monte Carlo algorithms, Shipley's d-sep test, and the potential outcomes framework to fit path models as well as to decompose and estimate effects. An example based on the direct and indirect interactions between ants, two insect herbivores, and a plant species demonstrates the implementation of these techniques, using freely available software. [ABSTRACT FROM AUTHOR]

This paper considers the problem of estimating the bounds on the average controlled direct effects (ACDEs) of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable. When the response variable is observed, Cai, et al.(2008) derived the formulas for the sharp bounds on the ACDEs. When the response variable is unobserved, the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs, which is an extension of the result of Kuroki(2005) to ACDEs. The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved, but also to provide their formulas when the answer is affirmative. [ABSTRACT FROM AUTHOR]

Consider a family $${(X_i)_{i \in I}}$$ of random variables endowed with the structure of a Bayesian network, and a subset S of I. This paper examines the problem of computing the probability distribution of the subfamily $${(X_{a})_{a \in S}}$$ (respectively the probability distribution of $${ (X_{b})_{b \in {\bar{S}}}}$$ , where $${{\bar{S}} = I - S}$$ , conditional on $${(X_{a})_{a \in S}}$$). This paper presents some theoretical results that makes it possible to compute joint and conditional probabilities over a subset of variables by computing over separate components. In other words, it is demonstrated that it is possible to decompose this task into several parallel computations, each related to a subset of S (respectively of $${{\bar{S}}}$$); these partial results are then put together as a final product. In computing the probability distribution over $${(X_a)_{a \in S}}$$ , this procedure results in the production of a structure of level two Bayesian network structure for S. [ABSTRACT FROM AUTHOR]

This paper describes how to test, and potentially falsify, a multivariate causal hypothesis involving only observed variables (i.e., a path analysis) when the data have a hierarchical or multilevel structure, when different variables are potentially defined at different levels of such a hierarchy, and when different variables have different sampling distributions. The test is a generalization of Shipley's d-sep test and can be conducted using standard statistical programs capable of fitting generalized mixed models. [ABSTRACT FROM AUTHOR]

The new trends in manufacturing toward modularity and flexibility result in a larger number of inter- dependent operations in a process, leading to complex multistage manufacturing processes. Identifying the variation flow and implementing quality control in such processes is very challenging because of the complex interactions among different stages. This article presents a systematic model building methodology to identify the underlying interactions among stages through the integration of advanced statistical techniques in graphical models and engineering insights to manufacturing processes. A statistical testing procedure is developed to efficiently construct the chain graph of the key product characteristics in a process, making use of identified relationships at previous stages. A case study validating the effectiveness of the proposed procedure is also presented. [ABSTRACT FROM AUTHOR]

Abstract: We assessed the effects of both biotic processes and abiotic factors on the community composition of vascular plant species and invertebrates at a site in northern Norway. Plant species were assigned to functional (woody versus herbaceous) and biogeographic (boreal versus alpine) groups. Invertebrate species were classified as either herbivore or predator. When species interactions and effects of the abiotic environment were partitioned, boreal species appeared to influence the distribution of alpine species and woody species the distribution of herbaceous species. Analysis of partial correlations indicated that facilitation was the dominant mode of interaction between the two pairs of plant groups. Among abiotic factors, the thermal environment probably influenced all components of the plant and invertebrate communities, except for predatory invertebrates, and wind appeared important in determining the composition of woody and alpine components of the plant community but not the herbaceous component. The composition of the boreal component of the plant community apparently influenced the composition of all invertebrate communities, except for predatory invertebrates. The composition of the woody component of the plant community influenced the composition of both herbivore and predator communities. The alpine plant-community composition influenced predatory invertebrate community composition. Woody plant community composition influenced the composition of both herbivore and predator communities. Our analytic approach, based on two kinds of structural equation models (d-separation and path analysis), provides a useful method for identifying the biotic as well as abiotic factors that influence community structure. [Copyright &y& Elsevier]

Active networks are network architectures with processors that are capable of executing code carried by the packets passing through them. A critical network management concern is the optimization of such networks and tight bounds on their performance serve as useful design benchmarks. A new bound on communication rates is developed that applies to network coding, which is a promising active network application that has processors transmit packets that are general functions, for example a bit-wise XOR, of selected received packets. The bound generalizes an edge-cut bound on routing rates by progressively removing edges from the network graph and checking whether certain strengthened d-separation conditions are satisfied. The bound improves on the cut-set bound and its efficacy is demonstrated by showing that routing is rate-optimal for some commonly cited examples in the networking literature. [ABSTRACT FROM AUTHOR]

Consider a case where cause-effect relationships between variables can be described as a causal diagram and the corresponding Gaussian linear structural equation model. In order to identify total effects in studies with an unobserved response variable, this paper proposes graphical criteria for selecting both covariates and variables caused by the response variable. The results enable us not only to judge from the graph structure whether a total effect can be expressed through the observed covariances, but also to provide its closed-form expression in case where its answer is affirmative. The graphical criteria of this paper are helpful to infer total effects when it is difficult to observe a response variable. [ABSTRACT FROM AUTHOR]