epinet: An R Package to Analyze Epidemics Spread across Contact Networks

We present the R package epinet, which provides tools for analyzing the spread of epidemics through populations. We assume that the relationships among individuals in a population are modeled by a contact network described by an exponential-family random graph model and that the disease being studied spreads across the edges of this network from infectious to susceptible individuals. We use a susceptible-exposed-infectiousremoved compartmental model to describe the progress of the disease within each host. We describe the functionality of the package, which consists of routines that perform simulation, plotting, and inference. The main inference routine utilizes a Bayesian approach and a Markov chain Monte Carlo algorithm. We demonstrate the use of the package through two examples, one involving simulated data and one using data from an actual measles outbreak

Using Neural Networks to Price and Hedge Variable Annuity Guarantees

This paper explores the use of neural networks to reduce the computational cost of pricing and hedging variable annuity guarantees. Pricing these guarantees can take a considerable amount of time because of the large number of Monte Carlo simulations that are required for the fair value of these liabilities to converge. This computational requirement worsens when Greeks must be calculated to hedge the liabilities of these guarantees. A feedforward neural network is a universal function approximator that is proposed as a useful machine learning technique to interpolate between previously calculated values and avoid running a full simulation to obtain a value for the liabilities. We propose methodologies utilizing neural networks for both the tasks of pricing as well as hedging four different varieties of variable annuity guarantees. We demonstrated a significant efficiency gain using neural networks in this manner. We also experimented with different error functions in the training of the neural networks and examined the resulting changes in network performance

Bayesian inference for contact networks given epidemic data

In this article, we estimate the parameters of a simple random network and a stochastic epidemic on that network using data consisting of recovery times of infected hosts. The SEIR epidemic model we fit has exponentially distributed transmission times with gamma distributed latent (exposed) and infective periods on a network where every tie exists with the same probability, independent of other ties. We employ a Bayesian framework and MCMC integration to make estimates of the joint posterior distribution of the model parameters. We discuss the accuracy of the estimates of different parameters under various prior assumptions and, in particular, show that it is possible in many scientifically interesting cases to accurately recover the network parameter p. We demonstrate some of the important aspects of our approach by studying a measles outbreak in Hagelloch, Germany in 1861 consisting of 188 affected individuals. We provide an R package to carry out these analyses, which is available publicly on the Comprehensive R Archive Network (CRAN). Keywords: Erdős-Rényi, exponential random graph model (ERGM), stochastic SEIR epidemic, MCMC, measles This work was funded by NIH grant R01-GM083603-01

Modeling county-level spatio-temporal mortality rates using dynamic linear models

The lifestyles and backgrounds of individuals across the United States differ widely. Some of these differences are easily measurable (ethnicity, age, income, etc.) while others are not (stress levels, empathy, diet, exercise, etc.). Though every person is unique, individuals living closer together likely have more similar lifestyles than individuals living hundreds of miles apart. Because lifestyle and environmental factors contribute to mortality, spatial correlation may be an important feature in mortality modeling. However, many of the current mortality models fail to account for spatial relationships. This paper introduces spatio-temporal trends into traditional mortality modeling using Bayesian hierarchical models with conditional auto-regressive (CAR) priors. We show that these priors, commonly used for areal data, are appropriate for modeling county-level spatial trends in mortality data covering the contiguous United States. We find that mortality rates of neighboring counties are highly correlated. Additionally, we find that mortality improvement or deterioration trends between neighboring counties are also highly correlated

Automated Factor Slice Sampling

<div><p>Markov chain Monte Carlo (MCMC) algorithms offer a very general approach for sampling from arbitrary distributions. However, designing and tuning MCMC algorithms for each new distribution can be challenging and time consuming. It is particularly difficult to create an efficient sampler when there is strong dependence among the variables in a multivariate distribution. We describe a two-pronged approach for constructing efficient, automated MCMC algorithms: (1) we propose the “factor slice sampler,” a generalization of the univariate slice sampler where we treat the selection of a coordinate basis (factors) as an additional tuning parameter, and (2) we develop an approach for automatically selecting tuning parameters to construct an efficient factor slice sampler. In addition to automating the factor slice sampler, our tuning approach also applies to the standard univariate slice samplers. We demonstrate the efficiency and general applicability of our automated MCMC algorithm with a number of illustrative examples. This article has online supplementary materials.</p></div