26,203 research outputs found
Modeling Adoption and Usage of Competing Products
The emergence and wide-spread use of online social networks has led to a
dramatic increase on the availability of social activity data. Importantly,
this data can be exploited to investigate, at a microscopic level, some of the
problems that have captured the attention of economists, marketers and
sociologists for decades, such as, e.g., product adoption, usage and
competition.
In this paper, we propose a continuous-time probabilistic model, based on
temporal point processes, for the adoption and frequency of use of competing
products, where the frequency of use of one product can be modulated by those
of others. This model allows us to efficiently simulate the adoption and
recurrent usages of competing products, and generate traces in which we can
easily recognize the effect of social influence, recency and competition. We
then develop an inference method to efficiently fit the model parameters by
solving a convex program. The problem decouples into a collection of smaller
subproblems, thus scaling easily to networks with hundred of thousands of
nodes. We validate our model over synthetic and real diffusion data gathered
from Twitter, and show that the proposed model does not only provides a good
fit to the data and more accurate predictions than alternatives but also
provides interpretable model parameters, which allow us to gain insights into
some of the factors driving product adoption and frequency of use
Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments
Optical microscopy provides rich spatio-temporal information characterizing
in vivo molecular motion. However, effective forces and other parameters used
to summarize molecular motion change over time in live cells due to latent
state changes, e.g., changes induced by dynamic micro-environments,
photobleaching, and other heterogeneity inherent in biological processes. This
study focuses on techniques for analyzing Single Particle Tracking (SPT) data
experiencing abrupt state changes. We demonstrate the approach on GFP tagged
chromatids experiencing metaphase in yeast cells and probe the effective forces
resulting from dynamic interactions that reflect the sum of a number of
physical phenomena. State changes are induced by factors such as microtubule
dynamics exerting force through the centromere, thermal polymer fluctuations,
etc. Simulations are used to demonstrate the relevance of the approach in more
general SPT data analyses. Refined force estimates are obtained by adopting and
modifying a nonparametric Bayesian modeling technique, the Hierarchical
Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT
applications. The HDP-SLDS method shows promise in systematically identifying
dynamical regime changes induced by unobserved state changes when the number of
underlying states is unknown in advance (a common problem in SPT applications).
We expand on the relevance of the HDP-SLDS approach, review the relevant
background of Hierarchical Dirichlet Processes, show how to map discrete time
HDP-SLDS models to classic SPT models, and discuss limitations of the approach.
In addition, we demonstrate new computational techniques for tuning
hyperparameters and for checking the statistical consistency of model
assumptions directly against individual experimental trajectories; the
techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One
publication available freely as an open-access article at
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763
Behavioral Modernity and the Cultural Transmission of Structured Information: The Semantic Axelrod Model
Cultural transmission models are coming to the fore in explaining increases
in the Paleolithic toolkit richness and diversity. During the later
Paleolithic, technologies increase not only in terms of diversity but also in
their complexity and interdependence. As Mesoudi and O'Brien (2008) have shown,
selection broadly favors social learning of information that is hierarchical
and structured, and multiple studies have demonstrated that teaching within a
social learning environment can increase fitness. We believe that teaching also
provides the scaffolding for transmission of more complex cultural traits.
Here, we introduce an extension of the Axelrod (1997} model of cultural
differentiation in which traits have prerequisite relationships, and where
social learning is dependent upon the ordering of those prerequisites. We
examine the resulting structure of cultural repertoires as learning
environments range from largely unstructured imitation, to structured teaching
of necessary prerequisites, and we find that in combination with individual
learning and innovation, high probabilities of teaching prerequisites leads to
richer cultural repertoires. Our results point to ways in which we can build
more comprehensive explanations of the archaeological record of the Paleolithic
as well as other cases of technological change.Comment: 24 pages, 7 figures. Submitted to "Learning Strategies and Cultural
Evolution during the Paleolithic", edited by Kenichi Aoki and Alex Mesoudi,
and presented at the 79th Annual Meeting of the Society for American
Archaeology, Austin TX. Revised 5/14/1
The Origin and Properties of Intracluster Stars in a Rich Cluster
We use a multi million particle N-body + SPH simulation to follow the
formation of a rich galaxy cluster in a Lambda+CDM cosmology, with the goal of
understanding the origin and properties of intracluster stars. The simulation
includes gas cooling, star formation, the effects of a uniform UVB and feedback
from supernovae. Halos that host galaxies as faint as M_R = -19.0 are resolved
by this simulation, which includes 85% of the total galaxy luminosity in a rich
cluster. We find that the accumulation of intracluster light (ICL) is an
ongoing process, linked to infall and stripping events. The unbound star
fraction increases with time and is 20% at z = 0, consistent with observations
of galaxy clusters. The surface brightness profile of the cD shows an excess
compared to a de Vaucouleur profile near 200 kpc, which is also consistent with
observations. Both massive and small galaxies contribute substantially to the
formation of the ICL, with stars stripped preferentially from the outer parts
of their stellar distributions. Simulated observations of planetary nebulae
(PNe) show significant substructure in velocity space. Despite this, individual
intracluster PNe might be useful mass tracers if more than 5 fields at a range
of radii have measured line-of-sight velocities, where an accurate mass
calculation depends more on the number of fields than the number of PNe
measured per field. However, the orbits of IC stars are more anisotropic than
those of galaxies or dark matter, which leads to a systematic underestimate of
cluster mass relative to that calculated with galaxies, if not accounted for in
dynamical models. Overall, the properties of ICL formed in a hierarchical
scenario are in good agreement with current observations. (Abridged)Comment: Replaced with MNRAS published version. One corrected figure, minor
text changes. MNRAS, 355, 15
Nonparametric Bayes modeling of count processes
Data on count processes arise in a variety of applications, including
longitudinal, spatial and imaging studies measuring count responses. The
literature on statistical models for dependent count data is dominated by
models built from hierarchical Poisson components. The Poisson assumption is
not warranted in many applications, and hierarchical Poisson models make
restrictive assumptions about over-dispersion in marginal distributions. This
article proposes a class of nonparametric Bayes count process models, which are
constructed through rounding real-valued underlying processes. The proposed
class of models accommodates applications in which one observes separate
count-valued functional data for each subject under study. Theoretical results
on large support and posterior consistency are established, and computational
algorithms are developed using Markov chain Monte Carlo. The methods are
evaluated via simulation studies and illustrated through application to
longitudinal tumor counts and asthma inhaler usage
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