394 research outputs found
Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
We propose an infinitesimal dispersion index for Markov counting processes. We show that, under standard moment existence conditions, a process is infinitesimally (over-) equi-dispersed if, and only if, it is simple (compound), i.e. it increases in jumps of one (or more) unit(s), even though infinitesimally equi-dispersed processes might be under-, equi- or over-dispersed using previously studied indices. Compound processes arise, for example, when introducing continuous-time white noise to the rates of simple processes resulting in Lévy-driven SDEs. We construct multivariate infinitesimally over dispersed compartment models and queuing networks, suitable for applications where moment constraints inherent to simple processes do not hold.Continuous time, Counting Markov process, Birth-death process, Environmental stochasticity, Infinitesimal over-dispersion, Simultaneous events
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
Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
We propose an infinitesimal dispersion index for Markov counting processes.
We show that, under standard moment existence conditions, a process is
infinitesimally (over-) equi-dispersed if, and only if, it is simple
(compound), i.e. it increases in jumps of one (or more) unit(s), even though
infinitesimally equi-dispersed processes might be under-, equi- or
over-dispersed using previously studied indices. Compound processes arise, for
example, when introducing continuous-time white noise to the rates of simple
processes resulting in Levy-driven SDEs. We construct multivariate
infinitesimally over-dispersed compartment models and queuing networks,
suitable for applications where moment constraints inherent to simple processes
do not hold.Comment: 26 page
Dynamic Variation in Sexual Contact Rates in a Cohort of HIV-Negative Gay Men
Human immunodeficiency virus (HIV) transmission models that include variability in sexual behavior over time have shown increased incidence, prevalence, and acute-state transmission rates for a given population risk profile. This raises the question of whether dynamic variation in individual sexual behavior is a real phenomenon that can be observed and measured. To study this dynamic variation, we developed a model incorporating heterogeneity in both between-person and within-person sexual contact patterns. Using novel methodology that we call iterated filtering for longitudinal data, we fitted this model by maximum likelihood to longitudinal survey data from the Centers for Disease Control and Prevention's Collaborative HIV Seroincidence Study (1992–1995). We found evidence for individual heterogeneity in sexual behavior over time. We simulated an epidemic process and found that inclusion of empirically measured levels of dynamic variation in individual-level sexual behavior brought the theoretical predictions of HIV incidence into closer alignment with reality given the measured per-act probabilities of transmission. The methods developed here provide a framework for quantifying variation in sexual behaviors that helps in understanding the HIV epidemic among gay men
Values and Beliefs Held About Parenting and Education by School Staff and Parents of Pupils with Special Educational Needs in the Context of Home- School Collaboration
Effective collaboration between school staff and parents of children identified as having special educational needs is considered to be an essential component of the child’s successful education. Differences in beliefs and perspectives adopted by the school staff and parents play an important role in the process of collaboration. However, little is known about the precise relationship between the beliefs and the process of collaboration.
The purpose of this study was to explore the values and beliefs held by the school staff and parents in the areas of parenting and education. The study also explored the link between these beliefs and the process of collaboration within four parent-teacher dyads from mainstream primary schools.
Focus groups and semi-structured interviews based on repertory grid technique were used. The findings highlighted an overall similarity in the participants’ views on collaboration and in their important beliefs about parenting and education. At the same time, differences in perspectives adopted by parents and teachers were also identified.
The author discusses how these differences in perspectives are manifested in the process of collaboration from the point of Cultural Capital Theory. The factors such as power differentials, trust between parents and teachers, and limited resources and constraints of educational system are highlighted. Implication for practice for teachers and educational psychologists are discussed
Systemic Infinitesimal Over-dispersion on General Stochastic Graphical Models
Stochastic models of interacting populations have crucial roles in scientific
fields such as epidemiology and ecology, yet the standard approach to extending
an ordinary differential equation model to a Markov chain does not have
sufficient flexibility in the mean-variance relationship to match data (e.g.
\cite{bjornstad2001noisy}). A previous theory on time-homogeneous dynamics over
a single arrow by \cite{breto2011compound} showed how gamma white noise could
be used to construct certain over-dispersed Markov chains, leading to widely
used models (e.g. \cite{breto2009time,he2010plug}). In this paper, we define
systemic infinitesimal over-dispersion, developing theory and methodology for
general time-inhomogeneous stochastic graphical models. Our approach, based on
Dirichlet noise, leads to a new class of Markov models over general direct
graphs. It is compatible with modern likelihood-based inference methodologies
(e.g. \cite{ionides2006inference,ionides2015inference,king2008inapparent}) and
therefore we can assess how well the new models fit data. We demonstrate our
methodology on a widely analyzed measles dataset, adding Dirichlet noise to a
classical SEIR (Susceptible-Exposed-Infected-Recovered) model. We find that the
proposed methodology has higher log-likelihood than the gamma white noise
approach, and the resulting parameter estimations provide new insights into the
over-dispersion of this biological system.Comment: 47 page
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