miRecSurv package: Prentice-Williams-Peterson models with multiple imputation of unknown number of previous episodes

Left censoring can occur with relative frequency when analysing recurrent events in epi demiological studies, especially observational ones. Concretely, the inclusion of individuals that were already at risk before the effective initiation in a cohort study, may cause the unawareness of prior episodes that have already been experienced, and this will easily lead to biased and inefficient estimates. The miRecSurv package is based on the use of models with specific baseline hazard, with multiple imputation of the number of prior episodes when unknown by means of the COMPoisson distribution, a very flexible count distribution that can handle over-, suband equidispersion, with a stratified model depending on whether the individual had or had not previously been at risk, and the use of a frailty term. The usage of the package is illustrated by means of a real data example based on a occupational cohort study and a simulation study

Finite Mixtures of Mean-Parameterized Conway-Maxwell-Poisson Models

For modeling count data, the Conway-Maxwell-Poisson (CMP) distribution is a popular generalization of the Poisson distribution due to its ability to characterize data over- or under-dispersion. While the classic parameterization of the CMP has been well-studied, its main drawback is that it is does not directly model the mean of the counts. This is mitigated by using a mean-parameterized version of the CMP distribution. In this work, we are concerned with the setting where count data may be comprised of subpopulations, each possibly having varying degrees of data dispersion. Thus, we propose a finite mixture of mean-parameterized CMP distributions. An EM algorithm is constructed to perform maximum likelihood estimation of the model, while bootstrapping is employed to obtain estimated standard errors. A simulation study is used to demonstrate the flexibility of the proposed mixture model relative to mixtures of Poissons and mixtures of negative binomials. An analysis of dog mortality data is presented. As a generalization of the Poisson distribution and a common alternative to other discrete distributions, the Conway-Maxwell-Poisson (CMP) distribution has the flexibility to explicitly characterize data over- or under-dispersion. The mean-parameterized version of the CMP has received increasing attention in the literature due to its ability to directly model the data mean. When the mean further depends on covariates, then the mean-parameterized CMP regression model can be treated in a generalized linear models framework. In this work, we propose a mixture of mean-parameterized CMP regressions model to apply on data which are potentially comprised of subpopulations with different conditional means and varying degrees of dispersions. An EM algorithm is constructed to find maximum likelihood estimates of the model. A simulation study is performed to test the proposed mixture of mean-parameterized CMP regressions model, and to compare it to model fits using mixtures of Poisson regressions and mixtures of negative binomial regressions. An analysis of the spread of a viral infection in potato plants is performed using these different mixtures of count regressions models, where we show the mixture of mean-parameterized CMP regressions to be an effective model

Bayesian and maximum likelihood inference approaches for the discrete generalized Sibuya distribution with censored data

This paper presents inferences under classical (maximum likelihood, ML) and Bayesian approaches for the parameters of the generalized Sibuya (GS) probability distribution considering complete and right censored lifetime data. Under a Bayesian approach, the joint posterior probability distributions of interest are estimated using Markov Chain Monte Carlo (MCMC) simulation methods. A comprehensive simulation study is carried out to assess the performance of the estimation procedure. The usefulness of the GS model is also assessed with applications to two real data sets. Despite its merits, one limitation of the generalized Sibuya distribution is that it does not present great flexibility of fit of the hazard function as compared to other existing lifetime models

Bayesian Inference for Assessing Effects of Email Marketing Campaigns

Email marketing has been an increasingly important tool for today’s businesses. In this paper, we propose a counting-process-based Bayesian method for quantifying the effectiveness of email marketing campaigns in conjunction with customer characteristics. Our model explicitly addresses the seasonality of data, accounts for the impact of customer characteristics on their purchasing behavior, and evaluates effects of email offers as well as their interactions with customer characteristics. Using the proposed method, together with a propensity-scorebased unit-matching technique for alleviating potential confounding, we analyze a large email marketing data set of an online ticket marketplace to evaluate the short- and long-term effectiveness of their email campaigns. It is shown that email offers can increase customer purchase rate both immediately and during a longer term. Customers’ characteristics such as length of shopping history, purchase recency, average ticket price, average ticket count, and number of genres purchased also affect customers’ purchase rate. A strong positive interaction is uncovered between email offer and purchase recency, suggesting that customers who have been inactive recently are more likely to take advantage of promotional offers.Statistic

A Data-Driven Predictive Model of Reliability Estimation Using State-Space Stochastic Degradation Model

The concept of the Industrial Internet of Things (IIoT) provides the foundation to apply data-driven methodologies. The data-driven predictive models of reliability estimation can become a major tool in increasing the life of assets, lowering capital cost, and reducing operating and maintenance costs. Classical models of reliability assessment mainly rely on lifetime data. Failure data may not be easily obtainable for highly reliable assets. Furthermore, the collected historical lifetime data may not be able to accurately describe the behavior of the asset in a unique application or environment. Therefore, it is not an optimal approach anymore to conduct a reliability estimation based on classical models. Fortunately, most of the industrial assets have performance characteristics whose degradation or decay over the operating time can be related to their reliability estimates. The application of the degradation methods has been recently increasing due to their ability to keep track of the dynamic conditions of the system over time. The main purpose of this study is to develop a data-driven predictive model of reliability assessment based on real-time data using a state-space stochastic degradation model to predict the critical time for initiating maintenance actions in order to enhance the value and prolonging the life of assets. The new degradation model developed in this thesis is introducing a new mapping function for the General Path Model based on series of Gamma Processes degradation models in the state-space environment by considering Poisson distributed weights for each of the Gamma processes. The application of the developed algorithm is illustrated for the distributed electrical systems as a generic use case. A data-driven algorithm is developed in order to estimate the parameters of the new degradation model. Once the estimates of the parameters are available, distribution of the failure time, time-dependent distribution of the degradation, and reliability based on the current estimate of the degradation can be obtained

Statistical Analysis of Online Eye and Face-Tracking Applications in Marketing

Eye-tracking and face-tracking technology have been widely adopted to study viewers' attention and emotional response. In the dissertation, we apply these two technologies to investigate effective online contents that are designed to attract and direct attention and engage viewers emotional responses. In the first part of the dissertation, we conduct a series of experiments that use eye-tracking technology to explore how online models' facial cues affect users' attention on static e-commerce websites. The joint effects of two facial cues, gaze direction and facial expression on attention, are estimated by Bayesian ANOVA, allowing various distributional assumptions. We also consider the similarities and differences in the effects of facial cues among American and Chinese consumers. This study offers insights on how to attract and retain customers' attentions for advertisers that use static advertisement on various websites or ad networks. In the second part of the dissertation, we conduct a face-tracking study where we investigate the relation between experiment participants' emotional responseswhile watching comedy movie trailers and their watching intentions to the actual movies. Viewers' facial expressions are collected in real-time and converted to emo- tional responses with algorithms based on facial coding system. To analyze the data, we propose to use a joint modeling method that link viewers' longitudinal emotion measurements and their watching intentions. This research provides recommenda- tions to filmmakers on how to improve the effectiveness of movie trailers, and how to boost audiences' desire to watch the movies