# Some New Results for Poisson Binomial Models

@article{Rosenman2019SomeNR, title={Some New Results for Poisson Binomial Models}, author={Evan T R Rosenman}, journal={ArXiv}, year={2019}, volume={abs/1907.09053} }

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…

## One Citation

The Poisson binomial distribution -- Old & New

- Mathematics
- 2019

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We…

## References

SHOWING 1-10 OF 31 REFERENCES

Using Poisson Binomial GLMs to Reveal Voter Preferences

- Mathematics
- 2018

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. We…

Who Supported Obama in 2012?: Ecological Inference through Distribution Regression

- Computer Science, MathematicsKDD
- 2015

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.

A Probabilistic Approach for Learning with Label Proportions Applied to the US Presidential Election

- Computer Science2017 IEEE International Conference on Data Mining (ICDM)
- 2017

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.

Ecological inference for 2 × 2 tables

- Mathematics
- 2004

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,…

STATISTICAL APPLICATIONS OF THE POISSON-BINOMIAL AND CONDITIONAL BERNOULLI DISTRIBUTIONS

- Mathematics
- 1997

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 and…

Binomial-Beta Hierarchical Models for Ecological Inference

- Computer Science
- 1999

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.

A statistical framework for ecological and aggregate studies

- Computer Science
- 2001

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.

Bayesian Approaches to Distribution Regression

- Mathematics, Computer ScienceAISTATS
- 2018

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.

Improving ecological inference using individual-level data.

- Computer Science, MedicineStatistics in medicine
- 2006

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.

Understanding the 2016 US Presidential Election using ecological inference and distribution regression with census microdata

- Mathematics
- 2016

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 distribution…