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A suite of generally applicable statistical methods based on empirical bootstrapping is presented for calculating uncertainty and testing the significance of quantitative differences in temperature and/or ice active site densities between ice nucleation temperature spectra derived from droplet freezing experiments. Such experiments are widely used to determine the heterogeneous ice nucleation properties and ice nucleation particle concentration spectra of different particle samples, as well as in studies of homogeneous freezing. Our methods avoid most of the assumptions and approximations inherent to existing approaches, and when sufficiently large sample sizes are used (approximately >150 droplets and >=1000 bootstrap samples in our system), can capture the full range of random variability and error in ice nucleation spectra. Applications include calculation of accurate confidence intervals and confidence bands, quantitative statistical testing of differences between observed freezing spectra, accurate subtraction of the background filtered water freezing signal, and calculation of a range of statistical parameters using data from a single droplet array freezing experiment if necessary. By providing additional statistical tools to the community, this work will improve the quality and accuracy of statistical tests and representations of uncertainty in future ice nucleation research, and will allow quantitative comparisons of the ice nucleation ability of different particles and surfaces.

Social influence cannot be identified from purely observational data on social networks, because such influence is generically confounded with latent homophily, i.e., with a node's network partners being informative about the node's attributes and therefore its behavior. If the network grows according to either a latent community (stochastic block) model, or a continuous latent space model, then latent homophilous attributes can be consistently estimated from the global pattern of social ties. We show that, for common versions of those two network models, these estimates are so informative that controlling for estimated attributes allows for asymptotically unbiased and consistent estimation of social-influence effects in linear models. In particular, the bias shrinks at a rate which directly reflects how much information the network provides about the latent attributes. These are the first results on the consistent non-experimental estimation of social-influence effects in the presence of latent homophily, and we discuss the prospects for generalizing them., Comment: 35 pages, 4 figures

To identify pathways between stress indicators and adverse pregnancy outcomes, we applied a nonparametric graph-learning algorithm, PC-KCI, to data from an observational prospective cohort study. The Measurement of Maternal Stress study (MOMS) followed 744 women with a singleton intrauterine pregnancy recruited between June 2013 and May 2015. Infant adverse pregnancy outcomes were prematurity (

The main point of our paper was to dispute the commonly held view that Bayesian statistics is or should be an algorithmic, inductive process culminating in the calculation of the posterior probabilities of competing models. Instead, we argued that effective data analysis – Bayesian or otherwise – proceeds more messily through a jagged process of formulating research hypotheses, exploring their implications in light of data, and rejecting aspects of our models in light of systematic misfits compared to available data or other sources of information. We associate this last bit with Popper’s falsification or (weakly) with Kuhn’s scientific revolutions, but these connections with classical philosophy of science are not crucial. Our real point is that Bayesian data analysis, in the form that we understand and practise, requires the active involvement of the researcher in constructing and criticizingmodels, and that from this perspective the entire process of Bayesian prior-to-posterior inference can be seen as an elaborate way of understanding the implications of a model so that it can be effectively tested. Just as a chicken is said to be nothing but an egg’s way of making another egg, so posterior inference is a way that a model can evaluate itself. But this inference and evaluation process, in our view, has essentially nothing to do with calculations of the posterior probability of competingmodels. Aswe discuss in our paper, for technical, philosophical, and historical reasons we tend not to trust such marginal posterior probabilities. (See Figure 1 of our paper for the sort of reasoning that we do not like.) Given all this, the discussion of our paper is remarkably uncontentious: none of the five discussants express support for the standard (according to Wikipedia) view of an overarching inductive Bayesian inference, and all agree with us that the messiness of

In Left Turn: How Liberal Bias Distorts The American Mind, Tim Groseclose argues that media effects play a crucial role in American politics. His case rests on three arguments: (1) that journalists tend overwhelmingly to be liberal rather than conservative; (2) that their innate political bias slants their views in empirically measurable ways; and (3) that this bias fundamentally shapes American politics, by bringing US citizens further to the left than they would naturally be. According to Groseclose, in a world where media bias did not exist, American citizens would on average hold views close to those of Ben Stein or Bill O'Reilly. In such a world, John McCain would have defeated Barack Obama by a popular vote margin of 56%—42% in the 2008 presidential election.In making these claims, Groseclose draws on his own research, and on recent media scholarship by both political scientists and economists, making the broader claim that peer-reviewed social science—which seeks to deal with problems such as endogeneity and selection bias—should be the starting point for public arguments about the role of the media. His book, then, is clearly an effort to bring social scientific arguments into mainstream debates. Groseclose makes no secret of his conservative political leanings—but recent books from left-leaning political scientists such as Jacob Hacker and Paul Pierson are equally unapologetic. It is at least plausible that political scientists' typical unwillingness to engage directly in political arguments has weakened the discipline's capacity for public engagement.In this symposium a diverse group of contributors have been invited to engage with Groseclose's arguments in ways that bring together specific empirical and/or theoretical points and arguments aimed at the broader “political science public sphere” that Perspectives on Politics seeks to nurture. Contributors were asked to consider these five questions: (1): How do we best measure media effects? (2): If media bias exists, what are its plausible sources? (3): Can one use work on media effects to determine what people's views would be in the absence of such bias? (4): Do you agree that American politics is insufficiently representative, and if so what do you consider the primary sources of this problem? (5): What kinds of political and/or media institutions or practices might enhance democratic discourse?—Henry Farrell, Associate Editor

A substantial school in the philosophy of science identies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian

We informally call a stochastic process learnable if it admits a generalization error approaching zero in probability for any concept class with finite VC-dimension (IID processes are the simplest example). A mixture of learnable processes need not be learnable itself, and certainly its generalization error need not decay at the same rate. In this paper, we argue that it is natural in predictive PAC to condition not on the past observations but on the mixture component of the sample path. This definition not only matches what a realistic learner might demand, but also allows us to sidestep several otherwise grave problems in learning from dependent data. In particular, we give a novel PAC generalization bound for mixtures of learnable processes with a generalization error that is not worse than that of each mixture component. We also provide a characterization of mixtures of absolutely regular (β-mixing) processes, of independent probability-theoretic interest.

The literature on statistical learning for time series assumes the asymptotic independence or “mixing” of the data-generating process. These mixing assumptions are never tested, and there are no methods for estimating mixing rates from data. We give an estimator for the beta-mixing rate based on a single stationary sample path and show it is L1-risk consistent.

We introduce mixed LICORS, an algorithm for learning nonlinear, high-dimensional dynamics from spatio-temporal data, suitable for both prediction and simulation. Mixed LICORS extends the recent LICORS algorithm (Goerg and Shalizi, 2012) from hard clustering of predictive distributions to a non-parametric, EM-like soft clustering. This retains the asymptotic predictive optimality of LICORS, but, as we show in simulations, greatly improves out-of-sample forecasts with limited data. The new method is implemented in the publicly-available R package LICORS.

Conventional maps of election results can give a misleading picture of the popular support that candidates have because population is highly non-uniform and equal areas on a map may not correspond to equal numbers of voters. Taking the example of the 2004 United States presidential election, we show how this problem can be corrected using a cartogram — a map in which the sizes of regions such as states are rescaled according to population or some other variable of interest.

The literature on statistical learning for time series often assumes asymptotic independence or "mixing" of the data-generating process. These mixing assumptions are never tested, nor are there methods for estimating mixing coefficients from data. Additionally, for many common classes of processes (Markov processes, ARMA processes, etc.) general functional forms for various mixing rates are known, but not specific coefficients. We present the first estimator for beta-mixing coefficients based on a single stationary sample path and show that it is risk consistent. Since mixing rates depend on infinite-dimensional dependence, we use a Markov approximation based on only a finite memory length $d$. We present convergence rates for the Markov approximation and show that as $d\rightarrow\infty$, the Markov approximation converges to the true mixing coefficient. Our estimator is constructed using $d$-dimensional histogram density estimates. Allowing asymptotics in the bandwidth as well as the dimension, we prove $L^1$ concentration for the histogram as an intermediate step. Simulations wherein the mixing rates are calculable and a real-data example demonstrate our methodology., 30 pages, 8 figures. Longer version of arXiv:1103.0941 [stat.ML]

The importance of applying game theory to the evolution of information in the presence of noise has recently become widely recognized. This Special Issue addresses the theme of spontaneously emergent order in both classical and quantum systems subject to external noise, and includes papers directly related to game theory or the development of supporting techniques. In the following editorial overview we examine the broader context of the subject, including the tension between the destructive and creative aspects of noise, and foreshadow the significance of some of the subsequent papers in the volume.

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight., Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestions

Computational mechanics, an approach to structural complexity, defines a process's causal states and gives a procedure for finding them. We show that the causal-state representation—an ∈-machine—is the minimal one consistent with accurate prediction. We establish several results on ∈-machine optimality and uniqueness and on how ∈-machines compare to alternative representations. Further results relate measures of randomness and structural complexity obtained from ∈-machines to those from ergodic and information theories.