A revisit of the distribution of linear combinations of Dirichlet components

Kuo, Kun-Lin; Jiang, T.

doi:10.1080/03610926.2017.1307402

Cited by 3 publications

(2 citation statements)

References 13 publications

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“…Combining the results using Slutsky's lemma establishes (13). Using Corollary 3.4 of Kuo and Jiang (2018), the posterior variance of µ 1 is…”

Section: Discussionmentioning

confidence: 99%

Causal predictive inference and target trial emulation

Yiu¹,

Fong²,

Walker³

et al. 2022

Preprint

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Causal inference from observational data can be viewed as a missing data problem arising from a hypothetical population-scale randomized trial matched to the observational study. This links a target trial protocol with a corresponding generative predictive model for inference, providing a complete framework for transparent communication of causal assumptions and statistical uncertainty on treatment effects, without the need for counterfactuals. The intuitive foundation for the work is that a whole population randomized trial would provide answers to any observable causal question with certainty. Thus, our fundamental problem of causal inference is the missingness of the hypothetical target trial data, which we solve through repeated imputation from a generative predictive model conditioned on the observational data. Causal assumptions map to intuitive conditions on the transportability of predictive models across populations and conditions. We demonstrate our approach on a real data application to studying the effects of maternal smoking on birthweights using extensions of Bayesian additive regression trees and inverse probability weighting.

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“…Combining the results using Slutsky's lemma establishes (13). Using Corollary 3.4 of Kuo and Jiang (2018), the posterior variance of µ 1 is…”

Section: Discussionmentioning

confidence: 99%

Causal predictive inference and target trial emulation

Yiu¹,

Fong²,

Walker³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…The PDF (4.16) is a piecewise polynomial of degree n − 2 in x. Such a simple structure is to be contrasted with the PDF of the random quadratic form xBx † , where x is a real random vector sampled uniformly at random from the sphere in R n [31,28], which is a far more complicated function of x.…”

Section: 16)mentioning

confidence: 99%

Co-rank 1 projections and the randomised Horn problem

Forrester,

Zhang

2019

Preprint

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Let x be a normalised standard complex Gaussian vector, and project an Hermitian matrix A onto the hyperplane orthogonal to x. In a recent paper Faraut [Tunisian J. Math. 1 (2019), 585-606] has observed that the corresponding eigenvalue PDF has an almost identical structure to the eigenvalue PDF for the rank 1 perturbation A + bxx † , and asks for an explanation. We provide one by way of a common derivation involving the secular equations and associated Jacobians. This applies too in related setting, for example when x is a real Gaussian and A Hermitian, and also in a multiplicative setting AU BU † where A, B are fixed unitary matrices with B a multiplicative rank 1 deviation from unity, and U is a Haar distributed unitary matrix. Specifically, in each case there is a dual eigenvalue problem giving rise to a PDF of almost identical structure.

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Corank-1 projections and the randomised Horn problem

Forrester

Zhang

2021

Tunisian J. Math.

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A revisit of the distribution of linear combinations of Dirichlet components

Cited by 3 publications

References 13 publications

Causal predictive inference and target trial emulation

Causal predictive inference and target trial emulation

Co-rank 1 projections and the randomised Horn problem

Corank-1 projections and the randomised Horn problem

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