Statistical Inference for Partially Observed Markov Processes via the R Package pomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.Comment: In press at the Journal of Statistical Software. A version of this paper is provided at the pomp package website: http://kingaa.github.io/pom

Particle filtering in compartmental projection models

Simulation models are important tools for real-time forecasting of pandemics. Models help health decision makers examine interventions and secure strong guidance when anticipating outbreak evolution. However, models usually diverge from the real observations. Stochastics involved in pandemic systems, such as changes in human contact patterns play a substantial role in disease transmissions and are not usually captured in traditional dynamic models. In addition, models of emerging diseases face the challenge of limited epidemiological knowledge about the natural history of disease. Even when the information about natural history is available -- for example for endemic seasonal diseases -- transmission models are often simplified and are involved with omissions. Availability of data streams can provide a view of early days of a pandemic, but fail to predict how the pandemic will evolve. Recent developments of computational statistics algorithms such as Sequential Monte Carlo and Markov Chain Monte Carlo, provide the possibility of creating models based on historical data as well as re-grounding models based on ongoing data observations. The objective of this thesis is to combine particle filtering -- a Sequential Monte Carlo algorithm -- with system dynamics models of pandemics. We developed particle filtering models that can recurrently be re-grounded as new observations become available. To this end, we also examined the effectiveness of this arrangement which is subject to specifics of the configuration (e.g., frequency of data sampling). While clinically-diagnosed cases are valuable incoming data stream during an outbreak, new generation of geo-spatially specific data sources, such as search volumes can work as a complementary data resource to clinical data. As another contribution, we used particle filtering in a model which can be re-grounded based on both clinical and search volume data. Our results indicate that the particle filtering in combination with compartmental models provides accurate projection systems for the estimation of model states and also model parameters (particularly compared to traditional calibration methodologies and in the context of emerging communicable diseases). The results also suggest that more frequent sampling from clinical data improves predictive accuracy outstandingly. The results also present that assumptions to make regarding the parameters associated with the particle filtering itself and changes in contact rate were robust across adequacy of empirical data since the beginning of the outbreak and inter-observation interval. The results also support the use of data from Google search API along with clinical data

Iterated filtering methods for Markov process epidemic models

Dynamic epidemic models have proven valuable for public health decision makers as they provide useful insights into the understanding and prevention of infectious diseases. However, inference for these types of models can be difficult because the disease spread is typically only partially observed e.g. in form of reported incidences in given time periods. This chapter discusses how to perform likelihood-based inference for partially observed Markov epidemic models when it is relatively easy to generate samples from the Markov transmission model while the likelihood function is intractable. The first part of the chapter reviews the theoretical background of inference for partially observed Markov processes (POMP) via iterated filtering. In the second part of the chapter the performance of the method and associated practical difficulties are illustrated on two examples. In the first example a simulated outbreak data set consisting of the number of newly reported cases aggregated by week is fitted to a POMP where the underlying disease transmission model is assumed to be a simple Markovian SIR model. The second example illustrates possible model extensions such as seasonal forcing and over-dispersion in both, the transmission and observation model, which can be used, e.g., when analysing routinely collected rotavirus surveillance data. Both examples are implemented using the R-package pomp (King et al., 2016) and the code is made available online.Comment: This manuscript is a preprint of a chapter to appear in the Handbook of Infectious Disease Data Analysis, Held, L., Hens, N., O'Neill, P.D. and Wallinga, J. (Eds.). Chapman \& Hall/CRC, 2018. Please use the book for possible citations. Corrected typo in the references and modified second exampl

His+ reversions Caused in Salmonella typhimurium by different types of ionizing radiation

The yield of his+ reversions in the Ames Salmonella tester strain TA2638 has been determined for 60Co γ rays, 140 kV X rays, 5.4 keV characteristic X rays, 2.2 MeV protons, 3.1 MeV α particles, and 18 MeV/U Fe ions. Inactivation studies were performed with the same radiations. For both mutation and inactivation, the maximum effectiveness per unit absorbed dose was obtained for the characteristic X rays, which have a dose averaged linear energy transfer (LET) of roughly 10 keV/μm. The ratio of the effectiveness of this radiation to γ rays was 2 for inactivation and about 1.4 for the his+ reversion. For both end points the effectiveness decreases substantially at high LET, i.e., for the α particles and the Fe ions. The composition of the bottom and the top agar was the one recommended by Maron and Ames [Mutat. Res. 113, 173-215 (1983)] for application in chemical mutagenicity tests. The experiments with the less penetrating radiations differed from the usual protocol by utilization of a technique of plating the bacteria on the surface of the top agar. As in an earlier study [Roos et al., Radiat. Res. 104, 102-108 (1985)] greatly enhanced yields of mutations, relative to the spontaneous reversion rate, were obtained in these experiments by performing the irradiations 6 h after plating, which differs from the conventional procedure to irradiate the bacteria shortly after plating

Inference of Infectious Disease Dynamics from Genetic Data via Sequential Monte Carlo

When an epidemic moves through a population of hosts, the process of transmission may leave a signature in the genetic sequences of the pathogen. Patterns in pathogen sequences may therefore be a rich source of information on disease dynamics. Genetic sequences may replace or supplement other epidemiological observations. Furthermore, sequences may contain information not present in other datatypes, opening the possibility of inferences inaccessible by other means. The field of phylodynamic inference aims to reconstruct disease dynamics from pathogen genetic sequences. Although a wide variety of phylodynamic inference methods have been proposed, most methods for fitting mechanistic models of disease operate in two disjoint steps, first estimating the phylogeny of the pathogen and then fitting models of disease dynamics to properties of the estimated phylogeny. Logical inconsistency in demographic assumptions underlying the two stages of inference may create bias in resulting parameter estimates. Joint inference of disease dynamics and phylogeny ensures consistent assumptions, but few methods for joint inference are currently available. The central work of this thesis is a new method for joint inference of disease dynamics and phylogeny from pathogen genetic sequences. This likelihood-based method, which we call genPomp, allows for fitting mechanistic models of arbitrary complexity to genetic sequences. The organization of this thesis is as follows. In Chapter I, we present background on the field of phylodynamic inference. In Chapter II, we use simulation to study a two-stage inference approach proposed by Rasmussen et al. (2011). We find that errors in phylogenetic reconstruction may drive bias in two-stage phylodynamic inference. This result underscores the need for methodology for joint inference of the transmission model and the pathogen phylogeny. In Chapter III, we propose a flexible method for joint inference and demonstrate the feasibility of this method through simulation and a study on stage-specific infectiousness of HIV in Detroit, MI. This method is comprised of a class of algorithms that use sequential Monte Carlo to estimate and maximize likelihoods. In Appendix A we show theoretical support for our algorithms. In Chapter IV, we demonstrate the flexibility of our approach by developing a model of transmission of Vancomycin-resistant enterococcus in a hospital setting. To allow for fitting this model to patient-level data we developed a targeted proposal, detailed in Appendix B. We present exploratory analysis of a hospital outbreak at NIH that motivates the form of the model, and carry out a study on simulated data. Although some assumptions of the simulated example are unrealistic, these initial results will inform future efforts at fitting real data. In Chapter V, we summarize the progress represented in this thesis and consider possibilities for future work.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/146063/1/alxsmth_1.pd