Corpus ID: 198147849

Some New Results for Poisson Binomial Models

@article{Rosenman2019SomeNR,
  title={Some New Results for Poisson Binomial Models},
  author={Evan Rosenman},
  journal={ArXiv},
  year={2019},
  volume={abs/1907.09053}
}
  • Evan Rosenman
  • Published 21 July 2019
  • Mathematics, Computer Science
  • ArXiv
We consider a problem of ecological inference, in which individual-level covariates are known, but labeled data is available only at the aggregate level. The intended application is modeling voter preferences in elections. In Rosenman and Viswanathan (2018), we proposed modeling individual voter probabilities via a logistic regression, and posing the problem as a maximum likelihood estimation for the parameter vector beta. The likelihood is a Poisson binomial, the distribution of the sum of… Expand
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References

SHOWING 1-10 OF 31 REFERENCES
Using Poisson Binomial GLMs to Reveal Voter Preferences
We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. WeExpand
Who Supported Obama in 2012?: Ecological Inference through Distribution Regression
TLDR
The novel approach to distribution regression exploits the connection between Gaussian process regression and kernel ridge regression, giving a coherent, Bayesian approach to learning and inference and a convenient way to include prior information in the form of a spatial covariance function. Expand
A Probabilistic Approach for Learning with Label Proportions Applied to the US Presidential Election
TLDR
This work forms EI as machine learning problem as learning with label proportions (LLP), and develops a new, probabilistic, LLP method that is as good as or better than existing state-of-the-art LLP methods. Expand
Ecological inference for 2 × 2 tables
A fundamental problem in many disciplines, including political science, sociology and epidemiology, is the examination of the association between two binary variables across a series of 2 × 2 tables,Expand
STATISTICAL APPLICATIONS OF THE POISSON-BINOMIAL AND CONDITIONAL BERNOULLI DISTRIBUTIONS
The distribution of Z1 +···+ZN is called Poisson-Binomial if the Zi are independent Bernoulli random variables with not-all-equal probabilities of success. It is noted that such a distribution andExpand
Binomial-Beta Hierarchical Models for Ecological Inference
TLDR
The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and King's ecological inference model, which reveals some features of the data that King's approach does not and allows the data analyst to adjust for covariates. Expand
A statistical framework for ecological and aggregate studies
TLDR
This work provides a framework within which ecological and aggregate data studies may be viewed, and some approaches to inference in such studies are reviewed, clarifying the assumptions on which they are based. Expand
Bayesian Approaches to Distribution Regression
TLDR
This work frames their models in a neural network style, allowing for simple MAP inference using backpropagation to learn the parameters, as well as MCMC-based inference which can fully propagate uncertainty. Expand
Improving ecological inference using individual-level data.
TLDR
A hierarchical model framework for estimating individual-level associations using a combination of aggregate and individual data is outlined and a comprehensive simulation study is performed, under a variety of realistic conditions, to determine when aggregate data are sufficient for accurate inference, and when they also require individual- level information. Expand
Understanding the 2016 US Presidential Election using ecological inference and distribution regression with census microdata
We combine fine-grained spatially referenced census data with the vote outcomes from the 2016 US presidential election. Using this dataset, we perform ecological inference using distributionExpand
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