1,097 research outputs found
Analysis of SIR epidemic models with sociological phenomenon
We propose two SIR models which incorporate sociological behavior of groups
of individuals. It is these differences in behaviors which impose different
infection rates on the individual susceptible populations, rather than
biological differences. We compute the basic reproduction number for each
model, as well as analyze the sensitivity of to changes in sociological
parameter values
Composition-differentiation operators on the Dirichlet space
We investigate composition-differentiation operators acting on the Dirichlet
space of the unit disk. Specifically, we determine characterizations for
bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In
addition, for particular classes of inducing maps, we derive an adjoint
formula, compute the norm, and identify the spectrum
Analysis of SIR Epidemic Models with Sociological Phenomenon
We propose two SIR models which incorporate sociological behavior of groups of individuals. It is these differences in behaviors which impose different infection rates on the individual susceptible populations, rather than biological differences. We compute the basic reproduction number for each model, as well as analyze the sensitivity of R0 to changes in sociological parameter values
An Alternative Prior Process for Nonparametric Bayesian Clustering
Prior distributions play a crucial role in Bayesian approaches to clustering.
Two commonly-used prior distributions are the Dirichlet and Pitman-Yor
processes. In this paper, we investigate the predictive probabilities that
underlie these processes, and the implicit "rich-get-richer" characteristic of
the resulting partitions. We explore an alternative prior for nonparametric
Bayesian clustering -- the uniform process -- for applications where the
"rich-get-richer" property is undesirable. We also explore the cost of this
process: partitions are no longer exchangeable with respect to the ordering of
variables. We present new asymptotic and simulation-based results for the
clustering characteristics of the uniform process and compare these with known
results for the Dirichlet and Pitman-Yor processes. We compare performance on a
real document clustering task, demonstrating the practical advantage of the
uniform process despite its lack of exchangeability over orderings
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