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© 2019 International Society for Bayesian Analysis. We build on recent work concerning message passing approaches to approximate fitting and inference for arbitrarily large regression models. The focus is on regression models where the response variable is modeled to have an elaborate distribution, which is loosely defined to mean a distribution that is more complicated than common distributions such as those in the Bernoulli, Poisson and Normal families. Examples of elaborate response families considered here are the Negative Binomial and t families. Variational message passing is more challenging due to some of the conjugate exponential families being non-standard and numerical integration being needed. Nevertheless, a factor graph fragment approach means the requisite calculations only need to be done once for a particular elaborate response distribution family. Computer code can be compartmentalized, including that involving numerical integration. A major finding of this work is that the modularity of variational message passing extends to elaborate response regression models.

© 2017 Elsevier B.V. During colon cancer, epigenetic alterations contribute to the dysregulation of major cellular functions and signaling pathways. Modifications in chromatin signatures such as H3K4me3 and H3K9ac, which are associated with transcriptionally active genes, can lead to genomic instability and perturb the expression of gene sets associated with oncogenic processes. In order to further elucidate early pre-tumorigenic epigenetic molecular events driving CRC, we integrated diverse, genome-wide, epigenetic inputs (by high throughput sequencing of RNA, H3K4me3, and H3K9ac) and compared differentially expressed transcripts (DE) and enriched regions (DER) in an in-vivo rat colon cancer progression model. Carcinogen (AOM) effects were detected genome-wide at the RNA (116 DE genes), K9ac (49 DERs including 24 genes) and K4me3 (7678 DERs including 3792 genes) level. RNA-seq differential expression and pathway analysis indicated that interferon-associated innate immune responses were impacted by AOM exposure. Despite extensive associations between K4me3 DERs and colon tumorigenesis (1210 genes were linked to colorectal carcinoma) including FOXO3, GNAI2, H2AFX, MSH2, NR3C1, PDCD4 and VEGFA, these changes were not reflected at the RNA gene expression level during early cancer progression. Collectively, our results indicate that carcinogen-induced changes in gene K4me3 DERs are harbingers of future transcriptional events, which drive malignant transformation of the colon.

We propose a procedure for testing the linearity of a scalar-on-function regression relationship. To do so, we use the functional generalized additive model (FGAM), a recently developed extension of the functional linear model. For a functional covariate X(t), the FGAM models the mean response as the integral with respect to t of F{X(t),t} where F is an unknown bivariate function. The FGAM can be viewed as the natural functional extension of generalized additive models. We show how the functional linear model can be represented as a simple mixed model nested within the FGAM. Using this representation, we then consider restricted likelihood ratio tests for zero variance components in mixed models to test the null hypothesis that the functional linear model holds. The methods are general and can also be applied to testing for interactions in a multivariate additive model or for testing for no effect in the functional linear model. The performance of the proposed tests is assessed on simulated data and in an application to measuring diesel truck emissions, where strong evidence of nonlinearities in the relationship between the functional predictor and the response are found.

We introduce a new method for forecasting emergency call arrival rates that combines integer-valued time series models with a dynamic latent factor structure. Covariate information is captured via simple constraints on the factor loadings. We directly model the count-valued arrivals per hour, rather than using an artificial assumption of normality. This is crucial for the emergency medical service context, in which the volume of calls may be very low. Smoothing splines are used in estimating the factor levels and loadings to improve long-term forecasts. We impose time series structure at the hourly level, rather than at the daily level, capturing the fine-scale dependence in addition to the long-term structure. Our analysis considers all emergency priority calls received by Toronto EMS between January 2007 and December 2008 for which an ambulance was dispatched. Empirical results demonstrate significantly reduced error in forecasting call arrival volume. To quantify the impact of reduced forecast errors, we design a queueing model simulation that approximates the dynamics of an ambulance system. The results show better performance as the forecasting method improves. This notion of quantifying the operational impact of improved statistical procedures may be of independent interest., Published in at http://dx.doi.org/10.1214/10-AOAS442 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)