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We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…
We present an extension of the functional data analysis framework for univariate functions to the analysis of surfaces: functions of two variables. The spatial spline regression (SSR) approach developed can be used to model surfaces that…
We introduce and solve a model that mimics the herding effect in financial markets when groups of agents share information. The number of agents in the model is growing and at each time step either (i) with probability $p$ an incoming agent…
Experiments on fracture surface morphologies offer increasing amounts of data that can be analyzed using methods of statistical physics. One finds scaling exponents associated with correlation and structure functions, indicating a rich…
In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed…
Global species richness is a key biodiversity metric. Despite recent efforts to estimate global species richness, the resulting estimates have been highly uncertain and often logically inconsistent. Estimates lower down either the taxonomic…
Capture-recapture studies are widely used to obtain information about abundance (population size or density) of animal populations. A common design is that in which multiple distinct populations are sampled, and the research objective is…
We consider a nonlocal Fisher-KPP equation that models a population structured in space and in phenotype. The population lives in a heterogeneous periodic environment: the diffusion coefficient, the mutation coefficient and the fitness of…
The growth of complex populations, such as microbial communities, forests, and cities, occurs over vastly different spatial and temporal scales. Although research in different fields has developed detailed, system-specific models to…
Many scientific applications involve mixed spatially indexed outcomes of heterogeneous types that are driven by shared latent mechanisms. Modeling such data is challenging due to complex, nonlinear, and potentially nonstationary spatial…
In this paper, we present a new fractional mathematical model to describe the dynamics and the interaction between plants and water in arid and semi-arid environments with and without slope. By the Caputo fractional operator, the model…
Rough volatility is a well-established statistical stylised fact of financial assets. This property has lead to the design and analysis of various new rough stochastic volatility models. However, most of these developments have been carried…
The coexistence of multiple phytoplankton species despite their reliance on similar resources is often explained with mean-field models assuming mixed populations. In reality, observations of phytoplankton indicate spatial aggregation at…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
This paper reviews some of the phenomenological models which have been introduced to incorporate the scaling properties of financial data. It also illustrates a microscopic model, based on heterogeneous interacting agents, which provides a…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on…
We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree $D$, we find a one parameter model, with parameter $\alpha \in [0,1]$ which has a so--called…
Consider an inhomogeneous multi-species TASEP with drift to the left, and define a height function which equals the maximum species number to the left of a lattice site. For each fixed time, the multi-point distributions of these height…
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…