arXiv subjects

Andrew Gelman

Publications and source records attributed to Andrew Gelman.

At least 91 records · Page 5Linked to original sources

arXiv2015

Age-aggregation bias in mortality trends

In a recent article in PNAS, Case and Deaton show a figure illustrating "a marked increase in the all-cause mortality of middle-aged white non-Hispanic men and women in the United States between 1999 and 2013." The authors state that their numbers "are not age-adjusted within the 10-y 45-54 age group." They calculated the mortality rate each year by dividing the total number of deaths for the age group by the population of the age group. We suspected an aggregation bias. After adjusting for changes in age composition, we find there is no longer a steady increase in mortality rates for this age group. Instead there is an increasing trend from 1999-2005 and a constant trend thereafter. Moreover, stratifying age-adjusted mortality rates by sex shows a marked increase only for women and not men, contrary to the article's headline. We stress that this does not change a key finding of the Case and Deaton paper: the comparison of non-Hispanic U.S. middle-aged whites to other countries and other ethnic groups. These comparisons hold up after our age adjustment. While we do not believe that age-adjustment invalidates comparisons between countries, it does affect claims concerning the absolute increase in mortality among U.S. middle-aged white non-Hispanics. Breaking down the trends in this group by region of the country shows other interesting patterns: since 1999 there has been an increase in death rates among women in the south. In contrast, death rates for both sexes have been declining in the northeast, the region where mortality rates were lowest to begin with. These graphs demonstrate the value of this sort of data exploration, and we are grateful to Case and Deaton for focusing attention on these mortality trends.

stat.AP↗

arXiv2015

A Model-Based Approach to Climate Reconstruction Using Tree-Ring Data

Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for non-climatic and climatic variability. In this approach we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and compare the modeling approach to current methodology using an example case of Scots pine from Tornetrask, Sweden to reconstruct growing season temperature. We describe how current approaches translate into particular model assumptions. We explore how changes to various components in the model-based approach affect the resulting reconstruction. We show that minor changes in model specification can have little effect on model fit but lead to large changes in the predictions. In particular, the periods of relatively warmer and cooler temperatures are robust between models, but the magnitude of the resulting temperatures are highly model dependent. Such sensitivity may not be apparent with traditional approaches because the underlying statistical model is often hidden or poorly described.

stat.AP↗

arXiv2015

Bayesian Nonparametric Weighted Sampling Inference

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.

stat.ME↗

arXiv2015

Beyond subjective and objective in statistics

We argue that the words "objectivity" and "subjectivity" in statistics discourse are used in a mostly unhelpful way, and we propose to replace each of them with broader collections of attributes, with objectivity replaced by transparency, consensus, impartiality, and correspondence to observable reality, and subjectivity replaced by awareness of multiple perspectives and context dependence. The advantage of these reformulations is that the replacement terms do not oppose each other. Instead of debating over whether a given statistical method is subjective or objective (or normatively debating the relative merits of subjectivity and objectivity in statistical practice), we can recognize desirable attributes such as transparency and acknowledgment of multiple perspectives as complementary goals. We demonstrate the implications of our proposal with recent applied examples from pharmacology, election polling, and socioeconomic stratification.

stat.OT↗

arXiv2015

Design of the Millennium Villages Project Sampling Plan: a simulation study for a multi-module survey

The Millennium Villages Project (MVP) is a ten-year integrated rural development project implemented in ten sub-Saharan African sites. At its conclusion we will conduct an evaluation of its causal effect on a variety of development outcomes, measured via household surveys in treatment and comparison areas. Outcomes are measured by six survey modules, with sample sizes for each demographic group determined by budget, logistics, and the group's vulnerability. We design a sampling plan that aims to reduce effort for survey enumerators and maximize precision for all outcomes. We propose two-stage sampling designs, sampling households at the first stage, followed by a second stage sample that differs across demographic groups. Two-stage designs are usually constructed by simple random sampling (SRS) of households and proportional within-household sampling, or probability proportional to size sampling (PPS) of households with fixed sampling within each. No measure of household size is proportional for all demographic groups, putting PPS schemes at a disadvantage. The SRS schemes have the disadvantage that multiple individuals sampled per household decreases efficiency due to intra-household correlation. We conduct a simulation study (using both design- and model-based survey inference) to understand these tradeoffs and recommend a sampling plan for the Millennium Villages Project. Similar design issues arise in other studies with surveys that target different demographic groups.

stat.AP↗

arXiv2015

Automatic Variational Inference in Stan

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult to automate. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI). The user only provides a Bayesian model and a dataset; nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We implement ADVI in Stan (code available now), a probabilistic programming framework. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

stat.ML↗

arXiv2014

The Mythical Swing Voter

The only acceptable form of polling in the multi-billion dollar survey research field utilizes representative samples. We argue that with proper statistical adjustment, non-representative polling can provide accurate predictions, and often in a much more timely and cost-effective fashion. We demonstrate this by applying multilevel regression and post-stratification (MRP) to a 2012 election survey on the Xbox gaming platform. Not only do the transformed top-line projections from this data closely trend standard indicators, but we use the unique nature of the data's size and panel to answer a meaningful political puzzle. We find that reported swings in public opinion polls are generally not due to actual shifts in vote intention, but rather are the result of temporary periods of relatively low response rates among supporters of the reportedly slumping candidate. This work shows great promise for using non-representative polling to measure public opinion and the first product of this new polling technique raises the possibility that decades of large, reported swings in public opinion-including the perennial "convention bounce"-are mostly artifacts of sampling bias.

cs.SI↗

arXiv2014

How Bayesian Analysis Cracked the Red-State, Blue-State Problem

In the United States as in other countries, political and economic divisions cut along geographic and demographic lines. Richer people are more likely to vote for Republican candidates while poorer voters lean Democratic; this is consistent with the positions of the two parties on economic issues. At the same time, richer states on the coasts are bastions of the Democrats, while most of the generally lower-income areas in the middle of the country strongly support Republicans. During a research project lasting several years, we reconciled these patterns by fitting a series of multilevel models to perform inference on geographic and demographic subsets of the population. We were using national survey data with relatively small samples in some states, ethnic groups and income categories; this motivated the use of Bayesian inference to partially pool between fitted models and local data. Previous, non-Bayesian analyses of income and voting had failed to connect individual and state-level patterns. Now that our analysis has been done, we believe it could be replicated using non-Bayesian methods, but Bayesian inference helped us crack the problem by directly handling the uncertainty that is inherent in working with sparse data.

stat.ME↗

arXiv2013

Should the democrats move to the left on economic policy?

Could John Kerry have gained votes in the 2004 Presidential election by more clearly distinguishing himself from George Bush on economic policy? At first thought, the logic of political preferences would suggest not: the Republicans are to the right of most Americans on economic policy, and so in a one-dimensional space with party positions measured with no error, the optimal strategy for the Democrats would be to stand infinitesimally to the left of the Republicans. The median voter theorem suggests that each party should keep its policy positions just barely distinguishable from the opposition. In a multidimensional setting, however, or when voters vary in their perceptions of the parties' positions, a party can benefit from putting some daylight between itself and the other party on an issue where it has a public-opinion advantage (such as economic policy for the Democrats). We set up a plausible theoretical model in which the Democrats could achieve a net gain in votes by moving to the left on economic policy, given the parties' positions on a range of issue dimensions. We then evaluate this model based on survey data on voters' perceptions of their own positions and those of the candidates in 2004. Under our model, it turns out to be optimal for the Democrats to move slightly to the right but staying clearly to the left of the Republicans' current position on economic issues.

stat.AP↗

arXiv2013

Understanding predictive information criteria for Bayesian models

We review the Akaike, deviance, and Watanabe-Akaike information criteria from a Bayesian perspective, where the goal is to estimate expected out-of-sample-prediction error using a biascorrected adjustment of within-sample error. We focus on the choices involved in setting up these measures, and we compare them in three simple examples, one theoretical and two applied. The contribution of this review is to put all these information criteria into a Bayesian predictive context and to better understand, through small examples, how these methods can apply in practice.

stat.ME↗

arXiv2013

Convincing Evidence

Textbooks on statistics emphasize care and precision, via concepts such as reliability and validity in measurement, random sampling and treatment assignment in data collection, and causal identification and bias in estimation. But how do researchers decide what to believe and what to trust when choosing which statistical methods to use? How do they decide the credibility of methods? Statisticians and statistical practitioners seem to rely on a sense of anecdotal evidence based on personal experience and on the attitudes of trusted colleagues. Authorship, reputation, and past experience are thus central to decisions about statistical procedures.

stat.ME↗

arXiv2013

Simulation-efficient shortest probability intervals

Bayesian highest posterior density (HPD) intervals can be estimated directly from simulations via empirical shortest intervals. Unfortunately, these can be noisy (that is, have a high Monte Carlo error). We derive an optimal weighting strategy using bootstrap and quadratic programming to obtain a more compu- tationally stable HPD, or in general, shortest probability interval (Spin). We prove the consistency of our method. Simulation studies on a range of theoret- ical and real-data examples, some with symmetric and some with asymmetric posterior densities, show that intervals constructed using Spin have better cov- erage (relative to the posterior distribution) and lower Monte Carlo error than empirical shortest intervals. We implement the new method in an R package (SPIn) so it can be routinely used in post-processing of Bayesian simulations.

stat.CO↗

arXiv2012

The anti-Bayesian moment and its passing

The present article is the reply to the discussion of our earlier "Not only defended but also applied" (arXiv:1006.5366, to appear in The American Statistician) that arose from our memory of a particularly intemperate anti-Bayesian statement in Feller's beautiful and classic book on probability theory. We felt that it was worth exploring the very extremeness of Feller's words, along with similar anti-Bayesian remarks by others, in order to better understand the background underlying controversies that still exist regarding the foundations of statistics. We thank the four discussants of our article for their contributions to our understanding of these controversies as they have existed in the past and persist today.

stat.OT↗

arXiv2012

"Not only defended but also applied": The perceived absurdity of Bayesian inference

The missionary zeal of many Bayesians of old has been matched, in the other direction, by a view among some theoreticians that Bayesian methods are absurd-not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian nature of the so-called doomsday argument. We analyze in this note the intellectual background behind various misconceptions about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal.

math.ST↗

arXiv2012

In praise of the referee

There has been a lively debate in many fields, including statistics and related applied fields such as psychology and biomedical research, on possible reforms of the scholarly publishing system. Currently, referees contribute so much to improve scientific papers, both directly through constructive criticism and indirectly through the threat of rejection. We discuss ways in which new approaches to journal publication could continue to make use of the valuable efforts of peer reviewers.

stat.OT↗

arXiv2012

On the Stationary Distribution of Iterative Imputations

Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling problem with relatively simple univariate regressions. In this paper, we begin to characterize the stationary distributions of iterative imputations and their statistical properties. More precisely, when the conditional models are compatible (defined in the text), we give a set of sufficient conditions under which the imputation distribution converges in total variation to the posterior distribution of a Bayesian model. When the conditional models are incompatible but are valid, we show that the combined imputation estimator is consistent.

math.ST↗

arXiv2011

The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that avoids the random walk behavior and sensitivity to correlated parameters that plague many MCMC methods by taking a series of steps informed by first-order gradient information. These features allow it to converge to high-dimensional target distributions much more quickly than simpler methods such as random walk Metropolis or Gibbs sampling. However, HMC's performance is highly sensitive to two user-specified parameters: a step size ε and a desired number of steps L. In particular, if L is too small then the algorithm exhibits undesirable random walk behavior, while if L is too large the algorithm wastes computation. We introduce the No-U-Turn Sampler (NUTS), an extension to HMC that eliminates the need to set a number of steps L. NUTS uses a recursive algorithm to build a set of likely candidate points that spans a wide swath of the target distribution, stopping automatically when it starts to double back and retrace its steps. Empirically, NUTS perform at least as efficiently as and sometimes more efficiently than a well tuned standard HMC method, without requiring user intervention or costly tuning runs. We also derive a method for adapting the step size parameter ε on the fly based on primal-dual averaging. NUTS can thus be used with no hand-tuning at all. NUTS is also suitable for applications such as BUGS-style automatic inference engines that require efficient "turnkey" sampling algorithms.

stat.CO↗

arXiv2011

Inherent Difficulties of Non-Bayesian Likelihood-based Inference, as Revealed by an Examination of a Recent Book by Aitkin

For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example is Murray Aitkin's recent book, {\em Statistical Inference}, which presents an approach to statistical hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and illustrates his method using some simple examples of inference from iid data and two-way tests of independence. We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.

stat.ME↗