A New Family of Non-Local Priors for Chain Event Graph Model Selection

Collazo, Rodrigo A.; Smith, Jim Q.

doi:10.1214/15-ba981

Cited by 21 publications

(20 citation statements)

References 29 publications

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“…See also Consonni et al . () for strategies to set moment prior parameters when comparing binomial probabilities and Collazo and Smith () for their use in chain event graphs.…”

Section: Prior Formulation and Parsimony Propertiesmentioning

confidence: 99%

“…In equation (2.6) g determines the prior separation in the binomial success probabilities across components and the prior informativeness. As discussed in Section 2.3 large g leads to informative priors with little separation across components, and there is a range of g-values that can be interpreted as being minimally informative in a fairly robust manner across k. See also Consonni et al (2013) for strategies to set moment prior parameters when comparing binomial probabilities and Collazo and Smith (2016) for their use in chain event graphs. An issue in expressions (2.4) and (2.6) is the computation of the normalizing constant C k : a non-trivial expectation of a product of quadratic forms.…”

Section: Choice Of Penalty Functionmentioning

confidence: 99%

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On Choosing Mixture Components via Non-Local Priors

Fuquene

Steel

Rossell

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Choosing the number of mixture components remains an elusive challenge. Model selection criteria can be either overly liberal or conservative and return poorly separated components of limited practical use. We formalize non‐local priors (NLPs) for mixtures and show how they lead to well‐separated components with non‐negligible weight, interpretable as distinct subpopulations. We also propose an estimator for posterior model probabilities under local priors and NLPs, showing that Bayes factors are ratios of posterior‐to‐prior empty cluster probabilities. The estimator is widely applicable and helps to set thresholds to drop unoccupied components in overfitted mixtures. We suggest default prior parameters based on multimodality for normal–T‐mixtures and minimal informativeness for categorical outcomes. We characterize theoretically the NLP‐induced sparsity, derive tractable expressions and algorithms. We fully develop normal, binomial and product binomial mixtures but the theory, computation and principles hold more generally. We observed a serious lack of sensitivity of the Bayesian information criterion, insufficient parsimony of the Akaike information criterion and a local prior, and a mixed behaviour of the singular Bayesian information criterion. We also considered overfitted mixtures; their performance was competitive but depended on tuning parameters. Under our default prior elicitation NLPs offered a good compromise between sparsity and power to detect meaningfully separated components.

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“…See also Consonni et al . () for strategies to set moment prior parameters when comparing binomial probabilities and Collazo and Smith () for their use in chain event graphs.…”

Section: Prior Formulation and Parsimony Propertiesmentioning

confidence: 99%

Section: Choice Of Penalty Functionmentioning

confidence: 99%

On Choosing Mixture Components via Non-Local Priors

Fuquene

Steel

Rossell

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Another possible research stream is to explore causal and explanatory analyses using graphical models such as Bayesian Networks (Pearl, 2009; Schenekenberg et al, 2011) and Chain Event Graphs (Smith & Anderson, 2008;Collazo & Smith, 2015). Finally, in a future study it will also be very interesting to examine the impact of different layers of hidden neurons defined for the ANN algorithm on the results.…”

Section: Resultsmentioning

confidence: 99%

A Comparative Study Between Artificial Neural Network and Support Vector Machine for Acute Coronary Syndrome Prognosis

Collazo¹,

Pessôa²,

Bahiense

et al. 2016

Pesqui. Oper.

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ABSTRACT. Despite medical advances, mortality due to acute coronary syndrome remains high. For this reason, it is important to identify the most critical factors for predicting the risk of death in patients hospitalized with this disease. To improve medical decisions, it is also helpful to construct models that enable us to represent how the main driving factors relate to patient outcomes. In this study, we compare the capability of Artificial Neural Network (ANN) and Support Vector Machine (SVM) models to distinguish between patients hospitalized with acute coronary syndrome who have low or high risk of death. Input variables are selected using the wrapper approach associated with a mutual information filter and two new proposed filters based on Euclidean distance. Because of missing data, the use of a filter is an important step in increasing the size of the usable data set and maximizing the performance of the classification models. The computational results indicate that the SVM model performs better. The most relevant input variables are age, any previous revascularization, and creatinine, regardless of the classification algorithms and filters used. However, the Euclidean filters also identify a second important group of input variables: age, creatinine and systemic arterial hypertension.

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“…The first component on the right hand side of the equation can be evaluated by applying the results in Equation ( 19), and the second component can be simplified to Equation (32). By doing this, we have the expression in Equation (31).…”

Section: Composite Singular and Stochastic Manipulations Under Routine Interventionmentioning

confidence: 99%

“…Now, we run the algorithm for α = 0.001, α = 0.01, α = 0.1, α = 1, α = 3, α = 5, where α is the prior parameter representing the number of phantom units entering the root node. We assess the resulted models in terms of situational errors [31] and MAP scores. The situational error (The total situational error of a tree is evaluated as γ(T ) = ∑ v∈V T ||θ * v − θv || 2 ) for a situation v measures the Euclidean distance between the true conditional probabilities θ * v and the mean posterior probabilities θv estimated on the best scoring model.…”

Section: A Comparison Studymentioning

confidence: 99%

Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure

Smith

2021

Entropy

Self Cite

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Graph-based causal inference has recently been successfully applied to explore system reliability and to predict failures in order to improve systems. One popular causal analysis following Pearl and Spirtes et al. to study causal relationships embedded in a system is to use a Bayesian network (BN). However, certain causal constructions that are particularly pertinent to the study of reliability are difficult to express fully through a BN. Our recent work demonstrated the flexibility of using a Chain Event Graph (CEG) instead to capture causal reasoning embedded within engineers’ reports. We demonstrated that an event tree rather than a BN could provide an alternative framework that could capture most of the causal concepts needed within this domain. In particular, a causal calculus for a specific type of intervention, called a remedial intervention, was devised on this tree-like graph. In this paper, we extend the use of this framework to show that not only remedial maintenance interventions but also interventions associated with routine maintenance can be well-defined using this alternative class of graphical model. We also show that the complexity in making inference about the potential relationships between causes and failures in a missing data situation in the domain of system reliability can be elegantly addressed using this new methodology. Causal modelling using a CEG is illustrated through examples drawn from the study of reliability of an energy distribution network.

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A New Family of Non-Local Priors for Chain Event Graph Model Selection

Cited by 21 publications

References 29 publications

On Choosing Mixture Components via Non-Local Priors

On Choosing Mixture Components via Non-Local Priors

A Comparative Study Between Artificial Neural Network and Support Vector Machine for Acute Coronary Syndrome Prognosis

Causal Algebras on Chain Event Graphs with Informed Missingness for System Failure

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