1,618 research outputs found
Bayesian nonparametric dependent model for partially replicated data: the influence of fuel spills on species diversity
We introduce a dependent Bayesian nonparametric model for the probabilistic
modeling of membership of subgroups in a community based on partially
replicated data. The focus here is on species-by-site data, i.e. community data
where observations at different sites are classified in distinct species. Our
aim is to study the impact of additional covariates, for instance environmental
variables, on the data structure, and in particular on the community diversity.
To that purpose, we introduce dependence a priori across the covariates, and
show that it improves posterior inference. We use a dependent version of the
Griffiths-Engen-McCloskey distribution defined via the stick-breaking
construction. This distribution is obtained by transforming a Gaussian process
whose covariance function controls the desired dependence. The resulting
posterior distribution is sampled by Markov chain Monte Carlo. We illustrate
the application of our model to a soil microbial dataset acquired across a
hydrocarbon contamination gradient at the site of a fuel spill in Antarctica.
This method allows for inference on a number of quantities of interest in
ecotoxicology, such as diversity or effective concentrations, and is broadly
applicable to the general problem of communities response to environmental
variables.Comment: Main Paper: 22 pages, 6 figures. Supplementary Material: 11 pages, 1
figur
Extreme robustness of scaling in sample space reducing processes explains Zipf's law in diffusion on directed networks
It has been shown recently that a specific class of path-dependent stochastic
processes, which reduce their sample space as they unfold, lead to exact
scaling laws in frequency and rank distributions. Such Sample Space Reducing
processes (SSRP) offer an alternative new mechanism to understand the emergence
of scaling in countless processes. The corresponding power law exponents were
shown to be related to noise levels in the process. Here we show that the
emergence of scaling is not limited to the simplest SSRPs, but holds for a huge
domain of stochastic processes that are characterized by non-uniform prior
distributions. We demonstrate mathematically that in the absence of noise the
scaling exponents converge to (Zipf's law) for almost all prior
distributions. As a consequence it becomes possible to fully understand
targeted diffusion on weighted directed networks and its associated scaling
laws law in node visit distributions. The presence of cycles can be properly
interpreted as playing the same role as noise in SSRPs and, accordingly,
determine the scaling exponents. The result that Zipf's law emerges as a
generic feature of diffusion on networks, regardless of its details, and that
the exponent of visiting times is related to the amount of cycles in a network
could be relevant for a series of applications in traffic-, transport- and
supply chain management.Comment: 11 pages, 5 figure
The Evolutionary Unfolding of Complexity
We analyze the population dynamics of a broad class of fitness functions that
exhibit epochal evolution---a dynamical behavior, commonly observed in both
natural and artificial evolutionary processes, in which long periods of stasis
in an evolving population are punctuated by sudden bursts of change. Our
approach---statistical dynamics---combines methods from both statistical
mechanics and dynamical systems theory in a way that offers an alternative to
current ``landscape'' models of evolutionary optimization. We describe the
population dynamics on the macroscopic level of fitness classes or phenotype
subbasins, while averaging out the genotypic variation that is consistent with
a macroscopic state. Metastability in epochal evolution occurs solely at the
macroscopic level of the fitness distribution. While a balance between
selection and mutation maintains a quasistationary distribution of fitness,
individuals diffuse randomly through selectively neutral subbasins in genotype
space. Sudden innovations occur when, through this diffusion, a genotypic
portal is discovered that connects to a new subbasin of higher fitness
genotypes. In this way, we identify innovations with the unfolding and
stabilization of a new dimension in the macroscopic state space. The
architectural view of subbasins and portals in genotype space clarifies how
frozen accidents and the resulting phenotypic constraints guide the evolution
to higher complexity.Comment: 28 pages, 5 figure
4-D Tomographic Inference: Application to SPECT and MR-driven PET
Emission tomographic imaging is framed in the Bayesian and information theoretic framework. The first part of the thesis is inspired by the new possibilities offered by PET-MR systems, formulating models and algorithms for 4-D tomography and for the integration of information from multiple imaging modalities. The second part of the thesis extends the models described in the first part, focusing on the imaging hardware. Three key aspects for the design of new imaging systems are investigated: criteria and efficient algorithms for the optimisation and real-time adaptation of the parameters of the imaging hardware; learning the characteristics of the imaging hardware; exploiting the rich information provided by depthof- interaction (DOI) and energy resolving devices. The document concludes with the description of the NiftyRec software toolkit, developed to enable 4-D multi-modal tomographic inference
Markovian Dynamics on Complex Reaction Networks
Complex networks, comprised of individual elements that interact with each
other through reaction channels, are ubiquitous across many scientific and
engineering disciplines. Examples include biochemical, pharmacokinetic,
epidemiological, ecological, social, neural, and multi-agent networks. A common
approach to modeling such networks is by a master equation that governs the
dynamic evolution of the joint probability mass function of the underling
population process and naturally leads to Markovian dynamics for such process.
Due however to the nonlinear nature of most reactions, the computation and
analysis of the resulting stochastic population dynamics is a difficult task.
This review article provides a coherent and comprehensive coverage of recently
developed approaches and methods to tackle this problem. After reviewing a
general framework for modeling Markovian reaction networks and giving specific
examples, the authors present numerical and computational techniques capable of
evaluating or approximating the solution of the master equation, discuss a
recently developed approach for studying the stationary behavior of Markovian
reaction networks using a potential energy landscape perspective, and provide
an introduction to the emerging theory of thermodynamic analysis of such
networks. Three representative problems of opinion formation, transcription
regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see
http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm
Maximum Configuration Principle for Driven Systems with Arbitrary Driving
Depending on context, the term entropy is used for a thermodynamic quantity, a measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in equilibrium or processes without memory, the mathematical expression for these different concepts of entropy appears to be the so-called Boltzmann–Gibbs–Shannon entropy, H. For processes with memory, such as driven- or self- reinforcing-processes, this is no longer true: the different entropy concepts lead to distinct functionals that generally differ from H. Here we focus on the maximum configuration entropy (that predicts empirical distribution functions) in the context of driven dissipative systems. We develop the corresponding framework and derive the entropy functional that describes the distribution of observable states as a function of the details of the driving process. We do this for sample space reducing (SSR) processes, which provide an analytically tractable model for driven dissipative systems with controllable driving. The fact that a consistent framework for a maximum configuration entropy exists for arbitrarily driven non-equilibrium systems opens the possibility of deriving a full statistical theory of driven dissipative systems of this kind. This provides us with the technical means needed to derive a thermodynamic theory of driven processes based on a statistical theory. We discuss the Legendre structure for driven systems
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