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List of Figures

1.1	Model Verification: Voter Turnout among African Americans in Louisiana Precincts	23
1.2	Non-Minority Turnout in New Jersey Cities and Towns	25
3.1	How a Correlation between the Parameters and Induces Bias	41
4.1	Scatter Plot of Precincts in Marion County, Indiana: Voter Turnout for the U.S. Senate by Fraction Black, 1990	60
4.2	Evaluating Population-Based Weights	64
4.3	Typically Massive Heteroskedasticity in Voting Data	66
5.1	A Data Summary Convenient for Statistical Modeling	81
5.2	Image Plots of Upper and Lower Bounds on	86
5.3	Image Plots of Upper and Lower Bounds on	87
5.4	Image Plots of Width of Bounds	88
5.5	A Scattercross Graph of Voter Turnout by Fraction Hispanic	89
6.1	Features of the Data Generated by Each Parameter	100
6.2	Truncated Bivariate Normal Distributions	105
6.3	A Tomography Plot	114
6.4	Truncated Bivariate Normal Surface Plot	116
7.1	Verifying Individual-Level Distributional Assumptions with Aggregate Data	126
7.2	Observable Implications for Sample Parameter Values	127
7.3	Likelihood Contour Plots	137
8.1	Posterior Distributions of Precinct Parameters	148
8.2	Support of the Joint Distribution of and with Bounds Specified for Drawing	155
9.1	The Worst of Aggregation Bias: Same Truth, Different Observable Implications	160
9.2	The Worst of Distributional Violations: Different True Parameters, Same Observable Implications	163
9.3	Conclusive Evidence of Aggregation Bias from Aggregate Data	176
9.4	Profile Likelihood	178
9.5	Controlling for Aggregation Bias	179
9.6	Extended Model Tradeoffs	180
9.7	A Tomography Plot with Evidence of Multiple Modes	187
9.8	Building a Nonparametric Density Estimate	194
9.9	Nonparametric Density Estimate for a Difficult Case	195
10.1	A Scattercross Graph for Southern Counties, 1968	201
10.2	Tomography Plot of Southern Race Data with Maximum Likelihood Contours	204
10.3	Scatter Plot with Maximum Likelihood Results Superimposed	206
10.4	Posterior Distribution of the Aggregate Quantities of Interest	208
10.5	Comparing Estimates to the Truth at the County Level	210
10.6	27,500 Simulations of	212
10.7	Verifying Uncertainty Estimates	213
10.8	275 Lines Fit to 275 Points	214
11.1	South Carolina Tomography Plot	221
11.2	Posterior Distributions of the State-Wide Fraction in Poverty by Sex in South Carolina	222
11.3	Fractions in Poverty for 3,187 South Carolina Block Groups	223
11.4	Percentiles at Which True Values Fall	224
12.1	A Scattercross Graph of Fraction Black by Fraction Registered	227
12.2	Tomography Plot with Parametric Contours and a Nonparametric Surface Plot	229
12.3	Posterior Distributions of the State-Wide Fraction of Blacks and Whites Registered	231
12.4	Fractions Registered at the County Level	232
12.5	80% Posterior Confidence Intervals by True Values	233
13.1	Fulton County Voter Transitions	236
13.2	Aggregation Bias in Fulton County Data	238
13.3	Fulton County Tomography Plot	239
13.4	Comparing Voter Transition Rate Estimates with the Truth in Fulton County	241
13.5	Alternative Fits to Literacy by Race Data	242
13.6	Black Literacy Tomography Plot and True Points	243
13.7	Comparing Estimates to the County-Level Truth in Literacy by Race Data	244

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