mixtools: An R Package for Analyzing Mixture Models

The mixtools package for R provides a set of functions for analyzing a variety of finite mixture models. These functions include both traditional methods, such as EM algorithms for univariate and multivariate normal mixtures, and newer methods that reflect some recent research in finite mixture models. In the latter category, mixtools provides algorithms for estimating parameters in a wide range of different mixture-of-regression contexts, in multinomial mixtures such as those arising from discretizing continuous multivariate data, in nonparametric situations where the multivariate component densities are completely unspecified, and in semiparametric situations such as a univariate location mixture of symmetric but otherwise unspecified densities. Many of the algorithms of the mixtools package are EM algorithms or are based on EM-like ideas, so this article includes an overview of EM algorithms for finite mixture models.

Mathematical methods and models for radiation carcinogenesis studies

Research on radiation carcinogenesis requires a twofold approach. Studies of primary molecular lesions and subsequent cytogenetic changes are essential, but they cannot at present provide numerical estimates of the risk of small doses of ionizing radiations. Such estimates require extrapolations from dose, time, and age dependences of tumor rates observed in animal studies and epidemiological investigations, and they necessitate the use of statistical methods that correct for competing risks. A brief survey is given of the historical roots of such methods, of the basic concepts and quantities which are required, and of the maximum likelihood estimates which can be derived for right censored and double censored data. Non-parametric and parametric models for the analysis of tumor rates and their time and dose dependences are explained

Warranty Data Analysis: A Review

Warranty claims and supplementary data contain useful information about product quality and reliability. Analysing such data can therefore be of benefit to manufacturers in identifying early warnings of abnormalities in their products, providing useful information about failure modes to aid design modification, estimating product reliability for deciding on warranty policy and forecasting future warranty claims needed for preparing fiscal plans. In the last two decades, considerable research has been conducted in warranty data analysis (WDA) from several different perspectives. This article attempts to summarise and review the research and developments in WDA with emphasis on models, methods and applications. It concludes with a brief discussion on current practices and possible future trends in WDA

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks

Bayesian Non-Parametric Inference for Infectious Disease Data

We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a function which only depends on time. Two different types of prior distributions are proposed namely using step-functions and B-splines. The methodology is illustrated using both simulated and real datasets and we show that certain aspects of the epidemic such as seasonality and super-spreading events are picked up without having to explicitly incorporate them into a parametric model