Linzer 2013 - Dynamic Bayesian Forecasting of Presidential Elections - Overview

Summary

Linzer (2013, JASA 108(501): 124-134) unifies structural (fundamentals) election forecasts with state-level trial-heat polls in one dynamic Bayesian model. A historical forecast gives an informative prior for the Election-Day logit vote share in each state; a “reverse” random walk anchored on Election Day carries that prior back through the campaign, so each state’s daily opinion is a compromise between polls and fundamentals, and forecasts move gradually from the latter to the former.

Overview

Problem. Structural models use 10-15 past elections, forecast national shares, and cannot update; polls are noisy, uneven across states and days, and only informative near the election.

Model in one line. $y_k\sim \text{Binomial}({\pi }_{i[k]j[k]},n_k)$, ${\pi }_{ij}={\text{logit}}^{-1}({\beta }_{ij}+{\delta }_j)$, reverse random walks on ${\beta }_{ij}$ and a national ${\delta }_j$, prior ${\beta }_{iJ}\sim N(\text{logit}(h_i),{\tau }_i^{-1})$ and the identifying restriction ${\delta }_J\equiv 0$.

Key results. Applied to 1731 state polls in 2008: state-level mean absolute deviation (MAD) fell from the baseline (Time-for-Change early 3.4%, late 2.6%) to 1.4% on Election Day, 27 states within 1%; only Indiana mispredicted; 95% electoral-vote range 338-387 vs actual 365; the effective advantage appears 1-2 months ahead. Prior precision ${\tau }_i$ should not exceed 20.

Motivating PyMC examples

E40 (“Who will win? Dynamic Bayesian poll aggregation and election forecasting”, 2016 polls, Linzer reverse random walks from a fundamentals prior), E94 (“Ragged information: polls, fundamentals and money in the US midterms”) and E95 (“Election night: updating a frozen forecast as the races are called”). The E40/E94 extensions are in Linzer 2013 - Extensions - House Effects, Correlated Errors and Election-Night Updating (Concept Note).

Source Map

Paper section	Pages	Covered in
1 Introduction	124-125	this note
2 Background: electoral college, characteristics of trial-heat polls, current approaches	125-126	Linzer 2013 - Reverse Random-Walk Model and Priors (poll error sources)
3 Dynamic Bayesian forecasting model (Eqs 1-3), windowing, MCMC	126-128	Linzer 2013 - Reverse Random-Walk Model and Priors
3 Win probabilities and electoral-vote simulation	128	Linzer 2013 - Forecast Computation and Electoral College Simulation
4.1-4.2 Data and structural forecasts (Time-for-Change, normal vote)	128-129	Linzer 2013 - 2008 Application and Results
4.3-4.4 Updating forecasts, MAD, swing states, sensitivity to ${\tau }_i$	129-132	Linzer 2013 - 2008 Application and Results
4.5 Trends in voter preferences; 5 Discussion	132-133	Linzer 2013 - 2008 Application and Results

Connections

The latent daily ${\beta }_{ij}$ is a random-walk state observed through binomial polls; with Gaussian approximation this is a local-level state-space model (Linear-Gaussian State-Space Models, The Kalman Filter, The RTS Smoother). Pooling across states through ${\delta }_j$ is a hierarchical structure (Hierarchical Models).

Relevance to marketing measurement

Combining an informative structural prior with noisy, unevenly sampled trackers is how one would blend an MMM-derived baseline with brand-tracker waves: the prior governs far-ahead forecasts, data take over as they accrue, and a common national shock separates market-wide movements from market-specific ones.

See Also

Bayesian Structural Time-Series Model