Three essays on crime policy and the Bayesian bootstrap

This dissertation consists of three chapters. In the first chapter, I analyze credible intervals for quantiles constructed using Bayesian bootstrap techniques and show that credible intervals constructed using the "continuity-corrected" Bayesian bootstrap (Banks, 1988) have frequentist coverage probability error of only O(n [superscript -1]). In addition, I show that these "continuity-corrected" Bayesian bootstrap credible intervals achieve the same frequentist coverage probability as the frequentist confidence intervals of Goldman and Kaplan (2017), up to some error term of magnitude O(n [superscript -1]). Furthermore, I demonstrate that credible intervals constructed using the "continuity-corrected" Bayesian bootstrap have less frequentist coverage probability error than those constructed using the Bayesian bootstrap (Rubin, 1981). In the second chapter, I investigate three strikes laws, which mandate sharply increased sentences for criminals who commit a specific number of felonies. Specifically, I analyze the effect of these laws on violent crime rates using municipal-level data from the FBI. I compare violent crime rates of border municipalities in states with differing treatment statuses using a difference-in-differences specification with a sample matched on pre-treatment outcomes. I find no statistical evidence that three strikes laws reduce violent crime rates. I rule out reductions in violent crime rates greater than 1.3 [percent] and reject the hypothesis that three strikes laws reduce violent crime rates at the 5 [percent] significance level. Additional analyses and robustness checks support my main findings. In the third chapter, I examine medical marijuana laws (MMLs), which legalize the use, possession, and cultivation of marijuana by individuals with qualifying medical conditions. Namely, I employ municipal-level data from the FBI to analyze the effect of MMLs on violent crime rates. I compare municipalities in border regions with different treatments statuses using a difference-in-differences specification with a sample matched on pre-treatment outcomes. I find a lack of evidence for MMLs increasing violent crime rates, but I cannot eliminate the possibility of small-to-medium positive effects. However, I rule out increases in violent crime rates greater than 9.9 [percent] and reject the hypothesis that MMLs increase violent crime at the 10 [percent] significance level.

Painless Posterior Sampling: Bayesian Bootstrapped Correlation Coefficients

We propose the Bayesian bootstrap (BB) as a generic, simple, and accessible method for sampling from the posterior distribution of various correlation coefficients that are commonly used in the social-behavioral sciences. In a series of examples, we demonstrate how the BB can be used to estimate Pearson's, Spearman's, Gaussian rank, Kendall's tau, and polychoric correlations. We also describe an approach based on a region of practical equivalence to evaluate differences and null associations among the estimated correlations. Key advantages of the proposed methods are illustrated using two psychological datasets. In addition, we have implemented the methodology in the R package BBcor.

Election polling is not dead: A Bayesian bootstrap method yields accurate forecasts

We present a new Bayesian bootstrap method for election forecasts that combines traditional polling questions about people’s own intentions with their expectations about how others will vote. It treats each participant’s election winner expectation as an optimal Bayesian forecast given private and public evidence available to that individual. It then infers the independent evidence and aggregates it across participants. The bootstrap forecast outperforms aggregate national polls in the 2020 U.S. election, as well as the forecasts based on traditional polling questions posed on large national probabilistic samples before the 2018 and 2020 U.S. elections. The bootstrap forecast puts most weight on people’s expectations about how their social contacts will vote, which might incorporate information about voters who are difficult to reach or who hide their true intentions. Beyond election polling, the new method is expected to improve the validity of other social science surveys.

A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

Bootstrap resampling techniques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional ϕ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended, introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e., bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

A Bayesian Nonparametric Learning Approach to Ensemble Models Using the Proper Bayesian Bootstrap

Bootstrap resampling techinques, introduced by Efron and Rubin, can be presented in a general Bayesian framework, approximating the statistical distribution of a statistical functional φ(F), where F is a random distribution function. Efron’s and Rubin’s bootstrap procedures can be extended introducing an informative prior through the Proper Bayesian bootstrap. In this paper different bootstrap techniques are used and compared in predictive classification and regression models based on ensemble approaches, i.e. bagging models involving decision trees. Proper Bayesian bootstrap, proposed by Muliere and Secchi, is used to sample the posterior distribution over trees, introducing prior distributions on the covariates and the target variable. The results obtained are compared with respect to other competitive procedures employing different bootstrap techniques. The empirical analysis reports the results obtained on simulated and real data.

Bayesian bootstrap quantile regression for probabilistic photovoltaic power forecasting

Photovoltaic (PV) systems are widely spread across MV and LV distribution systems and the penetration of PV generation is solidly growing. Because of the uncertain nature of the solar energy resource, PV power forecasting models are crucial in any energy management system for smart distribution networks. Although point forecasts can suit many scopes, probabilistic forecasts add further flexibility to an energy management system and are recommended to enable a wider range of decision making and optimization strategies. This paper proposes methodology towards probabilistic PV power forecasting based on a Bayesian bootstrap quantile regression model, in which a Bayesian bootstrap is applied to estimate the parameters of a quantile regression model. A novel procedure is presented to optimize the extraction of the predictive quantiles from the bootstrapped estimation of the related coefficients, raising the predictive ability of the final forecasts. Numerical experiments based on actual data quantify an enhancement of the performance of up to 2.2% when compared to relevant benchmarks.