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Register a new userEnsuring Reliable Monte Carlo Estimates of Network Properties
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The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the network, access limitations, or the population of interest is hard to reach. In such cases, the application of random walk-based Markov chain Monte Carlo (MCMC) methods to estimate multiple network features is common. However, the reliability of these estimates has been largely ignored. We consider and further develop multivariate MCMC output analysis methods in the context of network sampling to directly address the reliability of the multivariate estimation. This approach yields principled, computationally efficient, and broadly applicable methods for assessing the Monte Carlo estimation procedure. In particular, with respect to two random-walk algorithms, a simple random walk and a Metropolis-Hastings random walk, we construct and compare network parameter estimates, effective sample sizes, coverage probabilities, and stopping rules, all of which speaks to the estimation reliability.
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This article reviews the application of advanced Monte Carlo techniques in the context of Multilevel Monte Carlo (MLMC). MLMC is a strategy employed to compute expectations which can be biased in some sense, for instance, by using the discretization of a associated probability law. The MLMC approach works with a hierarchy of biased approximations which become progressively more accurate and more expensive. Using a telescoping representation of the most accurate approximation, the method is able to reduce the computational cost for a given level of error versus i.i.d. sampling from this latter approximation. All of these ideas originated for cases where exact sampling from couples in the hierarchy is possible. This article considers the case where such exact sampling is not currently possible. We consider Markov chain Monte Carlo and sequential Monte Carlo methods which have been introduced in the literature and we describe different strategies which facilitate the application of MLMC within these methods.
An important task in machine learning and statistics is the approximation of a probability measure by an empirical measure supported on a discrete point set. Stein Points are a class of algorithms for this task, which proceed by sequentially minimising a Stein discrepancy between the empirical measure and the target and, hence, require the solution of a non-convex optimisation problem to obtain each new point. This paper removes the need to solve this optimisation problem by, instead, selecting each new point based on a Markov chain sample path. This significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement. The new algorithms are illustrated on a set of challenging Bayesian inference problems, and rigorous theoretical guarantees of consistency are established.
Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network renormalization group method which can be used straightforwardly on modern computing architectures. We demonstrate the efficiency of the technique and show that Monte Carlo tensor network renormalization provides an attractive path to improving the accuracy of a wide class of challenging computations while also providing useful estimates of uncertainty and a statistical guarantee of unbiased results.
We present current methods for estimating treatment effects and spillover effects under interference, a term which covers a broad class of situations in which a units outcome depends not only on treatments received by that unit, but also on treatments received by other units. To the extent that units react to each other, interact, or otherwise transmit effects of treatments, valid inference requires that we account for such interference, which is a departure from the traditional assumption that units outcomes are affected only by their own treatment assignment. Interference and associated spillovers may be a nuisance or they may be of substantive interest to the researcher. In this chapter, we focus on interference in the context of randomized experiments. We review methods for when interference happens in a general network setting. We then consider the special case where interference is contained within a hierarchical structure. Finally, we discuss the relationship between interference and contagion. We use the interference R package and simulated data to illustrate key points. We consider efficient designs that allow for estimation of the treatment and spillover effects and discuss recent empirical studies that try to capture such effects.
We use a multivariate formulation of sequential Monte Carlo filter that utilizes mechanistic models for Ebola virus propagation and available incidence data to simultaneously estimate the disease progression states and the model parameters. This method has the advantage of performing the inference online as the new data becomes available and estimates the evolution of basic reproductive ratio $R_0(t)$ of the Ebola outbreak through time. Our analysis identifies a peak in the basic reproductive ratio close to the time when Ebola cases were reported in Europe and the USA.
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