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"sampling methods"
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Theoretical guarantees for approximate sampling from smooth and log-concave densities
Sampling from various kinds of distribution is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, exact sampling from a given distribution is impossible or computationally expensive and, therefore, one needs to resort to approximate sampling strategies. However, there is no well-developed theory providing meaningful non-asymptotic guarantees for the approximate sampling procedures, especially in high dimensional problems. The paper makes some progress in this direction by considering the problem of sampling from a distribution having a smooth and log-concave density defined on ℝρ, for some integer P>0. We establish non-asymptotic bounds for the error of approximating the target distribution by the distribution obtained by the Langevin Monte Carlo method and its variants. We illustrate the effectiveness of the established guarantees with various experiments. Underlying our analysis are insights from the theory of continuous time diffusion processes, which may be of interest beyond the framework of log-concave densities that are considered in the present work.
Journal Article
Bayesian model comparison for time-varying parameter VARs with stochastic volatility
We develop importance sampling methods for computing two popular Bayesian model comparison criteria, namely, the marginal likelihood and the deviance information criterion (DIC) for time-varying parameter vector autoregressions (TVP-VARs), where both the regression coefficients and volatilities are drifting over time. The proposed estimators are based on the integrated likelihood, which are substantially more reliable than alternatives. Using US data, we find overwhelming support for the TVP-VAR with stochastic volatility compared to a conventional constant coefficients VAR with homoskedastic innovations. Most of the gains, however, appear to have come from allowing for stochastic volatility rather than time variation in the VAR coefficients or contemporaneous relationships. Indeed, according to both criteria, a constant coefficients VAR with stochastic volatility outperforms themore general modelwith time-varying parameters.
Journal Article
Speeding Up MCMC by Efficient Data Subsampling
We propose subsampling Markov chain Monte Carlo (MCMC), an MCMC framework where the likelihood function for n observations is estimated from a random subset of m observations. We introduce a highly efficient unbiased estimator of the log-likelihood based on control variates, such that the computing cost is much smaller than that of the full log-likelihood in standard MCMC. The likelihood estimate is bias-corrected and used in two dependent pseudo-marginal algorithms to sample from a perturbed posterior, for which we derive the asymptotic error with respect to n and m, respectively. We propose a practical estimator of the error and show that the error is negligible even for a very small m in our applications. We demonstrate that subsampling MCMC is substantially more efficient than standard MCMC in terms of sampling efficiency for a given computational budget, and that it outperforms other subsampling methods for MCMC proposed in the literature. Supplementary materials for this article are available online.
Journal Article
SAMPLING-BASED VERSUS DESIGN-BASED UNCERTAINTY IN REGRESSION ANALYSIS
Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design-based. In a design-based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design-based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design-based uncertainty instead of, or in addition to, sampling-based uncertainty. We show that our standard errors in general are smaller than the usual infinite-population sampling-based standard errors and provide conditions under which they coincide.
Journal Article
Measuring and Bounding Experimenter Demand
We propose a technique for assessing robustness to demand effects of findings from experiments and surveys. The core idea is that by deliberately inducing demand in a structured way we can bound its influence. We present a model in which participants respond to their beliefs about the researcher’s objectives. Bounds are obtained by manipulating those beliefs with “demand treatments.” We apply the method to 11 classic tasks, and estimate bounds averaging 0.13 standard deviations, suggesting that typical demand effects are probably modest. We also show how to compute demand-robust treatment effects and how to structurally estimate the model.
Journal Article
Crowdsourcing Consumer Research
Data collection in consumer research has progressively moved away from traditional samples (e.g., university undergraduates) and toward Internet samples. In the last complete volume of the Journal of Consumer Research (June 2015–April 2016), 43% of behavioral studies were conducted on the crowdsourcing website Amazon Mechanical Turk (MTurk). The option to crowdsource empirical investigations has great efficiency benefits for both individual researchers and the field, but it also poses new challenges and questions for how research should be designed, conducted, analyzed, and evaluated. We assess the evidence on the reliability of crowdsourced populations and the conditions under which crowdsourcing is a valid strategy for data collection. Based on this evidence, we propose specific guidelines for researchers to conduct high-quality research via crowdsourcing. We hope this tutorial will strengthen the community’s scrutiny on data collection practices and move the field toward better and more valid crowdsourcing of consumer research.
Journal Article
MTurk Character Misrepresentation
This tutorial provides evidence that character misrepresentation in survey screeners by Amazon Mechanical Turk Workers (“Turkers”) can substantially and significantly distort research findings. Using five studies, we demonstrate that a large proportion of respondents in paid MTurk studies claim a false identity, ownership, or activity in order to qualify for a study. The extent of misrepresentation can be unacceptably high, and the responses to subsequent questions can have little correspondence to responses from appropriately identified participants. We recommend a number of remedies to deal with the problem, largely involving strategies to take away the economic motive to misrepresent and to make it difficult for Turkers to recognize that a particular response will gain them access to a study. The major short-run solution involves a two-survey process that first asks respondents to identify their characteristics when there is no motive to deceive, and then limits the second survey to those who have passed this screen. The long-run recommendation involves building an ongoing MTurk participant pool (“panel”) that (1) continuously collects information that could be used to classify respondents, and (2) eliminates from the panel those who misrepresent themselves.
Journal Article