Related papers: Theory: Multidimensional Space of Events
To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
In the present paper we demonstrate the results of a statistical analysis of some characteristics of precipitation events and propose a kind of a theoretical explanation of the proposed models in terms of mixed Poisson and mixed exponential…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…
We consider Bayesian multiple hypothesis problem with independent and identically distributed observations. The classical, Sanov's theorem-based, analysis of the error probability allows one to characterize the best achievable error…
Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…
As physics searches for invariants in observations, this paper looks for invariants of probabilistic observation without assuming physical structure. Structure emerges from the basic assumption of science that new information shall lead to…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…
Projections of future climate change rely heavily on climate models, and combining climate models through a multi-model ensemble is both more accurate than a single climate model and valuable for uncertainty quantification. However,…
Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…
There is a class of models for pol/mil/econ bargaining and conflict that is loosely based on the Median Voter Theorem which has been used with great success for about 30 years. However, there are fundamental mathematical limitations to…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
We introduce a class of backward stochastic differential equations (BSDEs) on the Wasserstein space of probability measures. This formulation extends the classical correspondence between BSDEs, stochastic control, and partial differential…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
This paper introduces the class of multidimensional self-exciting processes with dependencies (MSPD), which is a unifying writing for a large class of processes: counting, loss, intensity, and also shifted processes. The framework takes…
Event management in sensor networks is a multidisciplinary field involving several steps across the processing chain. In this paper, we discuss the major steps that should be performed in real- or near real-time event handling including…
Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such…