A simple algorithm for checking compatibility among discrete conditional distributions

Kuo, Kun-Lin; Wang, Yuchung J.

doi:10.1016/j.csda.2011.02.017

Cited by 11 publications

(6 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The advantage of chained equations imputation is that we do not need to specify the joint distribution of the variables. In cases where it is not known that there is a joint distribution, several methods for checking compatibility have been proposed (e.g., [ 16 , 31 - 35 ]). In practice, these methods are either limited to discrete distributions or are difficult to apply for multivariate distributions of more than 2 or 3 dimensions.…”

Section: Discussionmentioning

confidence: 99%

Joint modelling rationale for chained equations

Hughes

White

Seaman

et al. 2014

BMC Med Res Methodol

115

View full text Add to dashboard Cite

BackgroundChained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples.MethodsTaking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied.ResultsWe provide an additional “non-informative margins” condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak.ConclusionsSince chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible.

show abstract

Section: Discussionmentioning

confidence: 99%

Joint modelling rationale for chained equations

Hughes

White

Seaman

et al. 2014

BMC Med Res Methodol

115

View full text Add to dashboard Cite

show abstract

“…and p(X ∪ Y ) are substantially equivalent, since the latter (under suitable conditions) may be recovered from the former through lightening-and-promotion, as shown by Lemma 2(v) (Kuo and Wang, 2011, pp. 2460-2461.…”

Section: Compatibility Of Probability Kernels and Sure Compatibility mentioning

confidence: 92%

“…, m. Another limitation is its expensiveness, as the acceptance of the compatibility hypothesis requires a test (with positive result) on each cycle within the graph (T • , E, R). Algorithms may be devised to simplify this testing process by exploiting redundancies implicit in the graph (Wang and Kuo, 2010;Kuo and Wang, 2011;Yao, Chen and Wang, 2014). Lastly we remark that, of the cases covered by Theorem 3, special notice should be given to the case in which the conditioned variables Y 1 , .…”

Section: Compatibility Beyond Structural Assurance: the Multiple Kernmentioning

confidence: 99%

Compatibility of distributions in probabilistic models: an algebraic frame and some characterizations

Burigana

Vicovaro

2020

Alg. Stat.

View full text Add to dashboard Cite

“…The problem of characterizing a joint distribution by a collection of compatible CSDs has been extensively studied in the past two decades (see Refs . For more recent development, see Refs ).…”

Section: Conditionally Specified Distributionsmentioning

confidence: 99%

Gibbs ensembles for incompatible dependency networks

Chen

Wang

2013

WIREs Computational Stats

Self Cite

View full text Add to dashboard Cite

In most statistical applications, the Gibbs sampler is the method of choice for inference regarding conditionally specified distributions that are compatible. Compatibility ensures that a unique Gibbs distribution exists. For machine learning of complex models such as dependency networks, the conditional models are sometimes incompatible. In this paper, we review an ensemble approach using the Gibbs sampler as the base procedure. A Gibbs ensemble consists of many joint distributions resulting from different scan orders of the same conditional model, and the solution is a weighted sum of the ensemble. The algorithm is scalable and can handle large data sets of high dimensionality. The proposed approach provides joint distributions that conform with the conditional specifications better than the solutions obtained by linear programming and by a fixed-scan Gibbs sampler alone. Owing to incompatibility, the invariant distribution of a Gibbs sampler is scan-order dependent. A Gibbs ensemble is the collection of joint distributions estimated from the Gibbs samples of different scan orders.

show abstract

A simple algorithm for checking compatibility among discrete conditional distributions

Cited by 11 publications

References 26 publications

Joint modelling rationale for chained equations

Joint modelling rationale for chained equations

Compatibility of distributions in probabilistic models: an algebraic frame and some characterizations

Gibbs ensembles for incompatible dependency networks

Contact Info

Product

Resources

About