Advances In Stochastic Modeling Research Articles

Foreword to the Special Section on Meta-Level and Adversarial Tracking

The nine papers in this special section focus on meta-level and adversarial tracking. A plethora of well-established tracking algorithms aim to estimate, over time, the latent kinematic state (e.g., position, velocity, higher order kinematics, or any other spatiotemporal characteristic) of a single or multiple targets based on the available sensory observations, including from several sources. Here, we refer to such techniques as sensor-level trackers. Meta-level and adversarial tracking presents a shift away from the traditional viewpoint of a scene where objects move independently of one another in an unpremeditated manner and without regard to possible competition or group structures, toward an integrated viewpoint where intents, anomalies, group interactions, and characteristics of competitors/adversaries can be automatically learned. This also enables more accurate state estimation by capitalizing on inferred meta-level information. The papers included here showcase a diverse set of recent relevant technical developments and applications. It comprises of nine selected articles, drawing on recent advances in stochastic modeling, computational methods, statistical filtering, sensing systems, and others.

A Simulation-Based Approach to Statistical Alignment.

Classic alignment algorithms utilize scoring functions which maximize similarity or minimize edit distances. These scoring functions account for both insertion-deletion (indel) and substitution events. In contrast, alignments based on stochastic models aim to explicitly describe the evolutionary dynamics of sequences by inferring relevant probabilistic parameters from input sequences. Despite advances in stochastic modeling during the last two decades, scoring-based methods are still dominant, partially due to slow running times of probabilistic approaches. Alignment inference using stochastic models involves estimating the probability of events, such as the insertion or deletion of a specific number of characters. In this work, we present SimBa-SAl, a simulation-based approach to statistical alignment inference, which relies on an explicit continuous time Markov model for both indels and substitutions. SimBa-SAl has several advantages. First, using simulations, it decouples the estimation of event probabilities from the inference stage, which allows the introduction of accelerations to the alignment inference procedure. Second, it is general and can accommodate various stochastic models of indel formation. Finally, it allows computing the maximum-likelihood alignment, the probability of a given pair of sequences integrated over all possible alignments, and sampling alternative alignments according to their probability. We first show that SimBa-SAl allows accurate estimation of parameters of the long-indel model previously developed by Miklós et al. (2004). We next show that SimBa-SAl is more accurate than previously developed pairwise alignment algorithms, when analyzing simulated as well as empirical data sets. Finally, we study the goodness-of-fit of the long-indel and TKF91 models. We show that although the long-indel model fits the data sets better than TKF91, there is still room for improvement concerning the realistic modeling of evolutionary sequence dynamics.

Theorizing benefits and constraints in collaborative environmental governance: a transdisciplinary social-ecological network approach for empirical investigations

When environmental processes cut across socioeconomic boundaries, traditional top-down government approaches struggle to effectively manage and conserve ecosystems. In such cases, governance arrangements that foster multiactor collaboration are needed. The effectiveness of such arrangements, however, depends on how well any ecological interdependencies across governed ecosystems are aligned with patterns of collaboration. This inherent interdisciplinary and complex problem has impeded progress in developing a better understanding of how to govern ecosystems for conservation in an increasingly interconnected world. We argue for the development of empirically informed theories, which are not only able to transcend disciplinary boundaries, but are also explicit in taking these complex social-ecological interdependences into account. We show how this emerging research frontier can be significantly improved by incorporating recent advances in stochastic modeling of multilevel social networks. An empirical case study from an agricultural landscape in Madagascar is reanalyzed to demonstrate these improvements.

A seamless approach towards stochastic modeling: Sparse grid collocation and data driven input models

Many physical systems of fundamental and industrial importance are significantly affected by the underlying fluctuations/variations in boundary, initial conditions as well as variabilities in operating and surrounding conditions. There has been increasing interest in analyzing and quantifying the effects of uncertain inputs in the solution of partial differential equations that describe these physical phenomena. Such analysis naturally leads to a rigorous methodology to design/control physical processes in the presence of multiple sources of uncertainty. A general application of these ideas to many significant problems in engineering is mainly limited by two issues. The first is the significant effort required to convert complex deterministic software/legacy codes into their stochastic counterparts. The second bottleneck to the utility of stochastic modeling is the construction of realistic, viable models of the input variability. This work attempts to demystify stochastic modeling by providing easy-to-implement strategies to address these two issues. In the first part of the paper, strategies to construct realistic input models that encode the variabilities in initial and boundary conditions as well as other parameters are provided. In the second part of the paper, we review recent advances in stochastic modeling and provide a road map to trivially convert any deterministic code into its stochastic counterpart. Several illustrative examples showcasing the ease of converting deterministic codes to stochastic codes are provided.

Horizontal Permeability Anisotropy Developed from the Upscaling of Anisotropic Facies Patterns: ABSTRACT

Traditionally, the size and shape of grid blocks owe more to the limitations of numerical simulation procedures than to any consideration of geological heterogeneity. Geological systems, and hence associated permeability and porosity fields, are inherently complex, being characterized by nested levels of heterogeneity. Moreover, for directionally dependent variables, such as permeability, a heterogeneous nature at small scales will lead directly to anisotropy in average (or measured) values at larger scales. The representation of geologically complex volumes as individual horizontal and vertical permeability values has long been recognized as a necessary simplification. Recent advances in stochastic modeling have vastly improved the representation of complex geology in unknown interwell regions. The high level of detail provided by such models often requires several million grid blocks. This degree of detail cannot, however, be used in flow simulations, and hence, scaling up is necessary. The difficulties in scaling up of rock-property data are based on the conflicting requirements of significantly reducing the number of grid blocks, while maintaining a reasonable degree of detail in the representation of heterogeneity. To analyze whether grid blocks adequately represent complex heterogeneities the authors constructed complex, geologically realistic channel-levee complexes, using an object-modeling (Boolean) approach. This approach has themore » advantage over reservoir, or outcrop, derived data in so much as the 3-D architecture is fully known. The disadvantages are that the realizations are too simplistic, not necessarily geologically realistic, and contain only one scale of heterogeneity. In the present context, however, simplification of both geological and scale-related heterogeneities can be seen as advantageous in the interpretation of the results.« less