We propose a new general approach for estimating the effect of a binary treatment on a continuous and potentially highly skewed response variable, the generalized quantile treatment effect (GQTE). The GQTE is defined as the difference between a function of the quantiles under the two treatment conditions. As such, it represents a generalization over the standard approaches typically used for estimating a treatment effect (i.e., the average treatment effect and the quantile treatment effect) because it allows the comparison of any arbitrary characteristic of the outcome’s distribution under the two treatments. Following Dominici et al. (2005), we assume that a pre-specified transformation of the two quantiles is modeled as a smooth function of the percentiles. This assumption allows us to link the two quantile functions and thus to borrow information from one distribution to the other. The main theoretical contribution we provide is the analytical derivation of a closed form expression for the likelihood of the model. Exploiting this result we propose a novel Bayesian inferential methodology for the GQTE. We show some finite sample properties of our approach through a simulation study which confirms that in some cases it performs better than other nonparametric methods. As an illustration we finally apply our methodology to the 1987 National Medicare Expenditure Survey data to estimate the difference in the single hospitalization medical cost distributions between cases (i.e., subjects affected by smoking attributable diseases) and controls.

Recent financial disasters emphasised the need to investigate the consequences associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting market participants’ risk capital. Commonly used risk management tools fail to account for potential spillover effects among institutions because they only provide individual risk assessment. We contribute to the analysis of the interdependence effects of extreme events, providing an estimation tool for evaluating the co-movement Value-at-Risk. In particular, our approach relies on a Bayesian quantile regression framework. We propose a Markov chain Monte Carlo algorithm, exploiting the representation of the Asymmetric Laplace distribution as a location-scale mixture of Normals. Moreover, since risk measures are usually evaluated on time series data and returns typically change over time, we extend the model to account for the dynamics of the tail behaviour. We apply our model to a sample of U.S. companies belonging to different sectors of the Standard and Poor’s Composite Index and we provide an evaluation of the marginal contribution to the overall risk of each individual institution.

It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical approach in which we model the distribution of the weights of the nonsampled units in the population and simultaneously include them as predictors in a nonparametric Gaussian process regression. We use simulation studies to evaluate the performance of our procedure and compare it to the classical design-based estimator. We apply our method to the Fragile Family and Child Wellbeing Study. Our studies find the Bayesian nonparametric finite population estimator to be more robust than the classical design-based estimator without loss in efficiency, which works because we induce regularization for small cells and thus this is a way of automatically smoothing the highly variable weights.

We examine necessary and sufficient conditions for posterior consistency under $g$-priors, including extensions to hierarchical and empirical Bayesian models. The key features of this article are that we allow the number of regressors to grow at the same rate as the sample size and define posterior consistency under the sup vector norm instead of the more conventional Euclidean norm. We consider in particular the empirical Bayesian model of George and Foster (2000), the hyper-$g$-prior of Liang et al. (2008), and the prior considered by Zellner and Siow (1980).

The classical parametric and semiparametric Bernstein – von Mises (BvM) results are reconsidered in a non-classical setup allowing finite samples and model misspecification. In the case of a finite dimensional nuisance parameter we obtain an upper bound on the error of Gaussian approximation of the posterior distribution for the target parameter which is explicit in the dimension of the nuisance and target parameters. This helps to identify the so called critical dimension $p_n$ of the full parameter for which the BvM result is applicable. In the important i.i.d. case, we show that the condition “$p_n^3/n$ is small” is sufficient for the BvM result to be valid under general assumptions on the model. We also provide an example of a model with the phase transition effect: the statement of the BvM theorem fails when the dimension $p_n$ approaches $n^{1/3}$ . The results are extended to the case of infinite dimensional parameters with the nuisance parameter from a Sobolev class.

This paper analyses the effect of preferential sampling in Geostatistics when the choice of new sampling locations is the main interest of the researcher. A Bayesian criterion based on maximizing utility functions is used. Simulated studies are presented and highlight the strong influence of preferential sampling in the decisions. The computational complexity is faced by treating the new local sampling locations as a model parameter and the optimal choice is then made by analysing its posterior distribution. Finally, an application is presented using rainfall data collected during spring in Rio de Janeiro. The results showed that the optimal design is substantially changed under preferential sampling effects. Furthermore, it was possible to identify other interesting aspects related to preferential sampling effects in estimation and prediction in Geostatistics.

A utility-function approach to optimal spatial sampling design is a powerful way to quantify what “optimality” means. The emphasis then should be to capture all possible contributions to utility, including scientific impact and the cost of sampling. The resulting sampling plan should contain a component of designed randomness that would allow for a non-parametric design-based analysis if model-based assumptions were in doubt.