Conscripting Private Resources to Meet Urban Needs: The Statutory and Constitutional Validity of Affordable Housing Impact Fees in New York

In the closing decade of the 20th century, American cities face difficult financial predicaments. Urban tax bases have atrophied, and the confidence rating of municipal bonds has been downgraded. At the same time, city expenditures have increased as century-old infrastructure begins to crumble and urban demographics demand an ever increasing array of public services. To meet these challenges, New York City would do well to adopt impact fee and linkage arrangements, which would require developers to contribute to State coffers in proportion to the expected environmental, social, and economic impact of their development projects. To pass constitutional muster, however, any impact fee arrangement would have to be carefully worded to require impact fee payments towards the development of affordable housing for only those projects that can be demonstrably shown to have an adverse expected impact on the availability of affordable housing in the city

Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains.Comment: Published in at http://dx.doi.org/10.1214/10-AOS792 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The magnetar model for Type I superluminous supernovae I: Bayesian analysis of the full multicolour light curve sample with MOSFiT

We use the new Modular Open Source Fitter for Transients (MOSFiT) to model 38 hydrogen-poor superluminous supernovae (SLSNe). We fit their multicolour light curves with a magnetar spin-down model and present the posterior distributions of magnetar and ejecta parameters. The colour evolution can be well matched with a simple absorbed blackbody. We find the following medians (1$\sigma$ ranges): spin period 2.4 ms (1.2-4 ms); magnetic field $0.8\times 10^{14}$ G (0.2-1.8 $\times 10^{14}$ G); ejecta mass 4.8 Msun (2.2-12.9 Msun); kinetic energy $3.9\times 10^{51}$ erg (1.9-9.8 $\times 10^{51}$ erg). This significantly narrows the parameter space compared to our priors, showing that although the model is flexible, the parameter space relevant to SLSNe is well constrained by existing data. The requirement that the instantaneous engine power is $\sim 10^{44}$ erg at the light curve peak necessitates either a large rotational energy (P<2 ms), or more commonly that the spin-down and diffusion timescales be well-matched. We find no evidence for separate populations of fast- and slow-declining SLSNe, which instead form a continuum both in light curve widths and inferred parameters. Variations in the spectra are well explained through differences in spin-down power and photospheric radii at maximum-light. We find no correlations between any model parameters and the properties of SLSN host galaxies. Comparing our posteriors to stellar evolution models, we show that SLSNe require rapidly rotating (fastest 10%) massive stars (> 20 Msun), and that this is consistent with the observed SLSN rate. High mass, low metallicity, and likely binary interaction all serve to maintain rapid rotation essential for magnetar formation. By reproducing the full set of SLSN light curves, our posteriors can be used to inform photometric searches for SLSNe in future survey data

Training samples in objective Bayesian model selection

Central to several objective approaches to Bayesian model selection is the use of training samples (subsets of the data), so as to allow utilization of improper objective priors. The most common prescription for choosing training samples is to choose them to be as small as possible, subject to yielding proper posteriors; these are called minimal training samples. When data can vary widely in terms of either information content or impact on the improper priors, use of minimal training samples can be inadequate. Important examples include certain cases of discrete data, the presence of censored observations, and certain situations involving linear models and explanatory variables. Such situations require more sophisticated methods of choosing training samples. A variety of such methods are developed in this paper, and successfully applied in challenging situations

Optimal predictive model selection

Often the goal of model selection is to choose a model for future prediction, and it is natural to measure the accuracy of a future prediction by squared error loss. Under the Bayesian approach, it is commonly perceived that the optimal predictive model is the model with highest posterior probability, but this is not necessarily the case. In this paper we show that, for selection among normal linear models, the optimal predictive model is often the median probability model, which is defined as the model consisting of those variables which have overall posterior probability greater than or equal to 1/2 of being in a model. The median probability model often differs from the highest probability model

Posterior propriety and admissibility of hyperpriors in normal hierarchical models

Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior performance. As an extreme, but not uncommon, example use of the wrong hyperparameter priors can even lead to impropriety of the posterior. For exchangeable hierarchical multivariate normal models, we first determine when a standard class of hierarchical priors results in proper or improper posteriors. We next determine which elements of this class lead to admissible estimators of the mean under quadratic loss; such considerations provide one useful guideline for choice among hierarchical priors. Finally, computational issues with the resulting posterior distributions are addressed.Comment: Published at http://dx.doi.org/10.1214/009053605000000075 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org