Dynamic Stochastic Model Research Articles

140 - Models of Behavioral Health Integration from Rochester NY

The Azores bullfinch (Pyrrhula murina) is an endemic bird of São Miguel island (Azores Archipelago, Portugal), currently threatened by two of the major causes of biodiversity loss worldwide: invasion of native habitats by exotic plants and habitat destruction by land use changes. The aim of this research was to develop and test a novel spatially explicit modelling framework that predicts the Azores bullfinch responses to alternative realistic scenarios of native forest management. This was done by integrating Multi-Model Inference statistical analysis, Stochastic-Dynamic Modelling and Geographic Information Systems under a common framework relating bird population trends to changes in the surrounding habitats. Overall, in the next 25 years, the Azores bullfinch breeding population was predicted to increase around 19% as a consequence of habitat management actions already implemented (“LIFE Priolo” project) or around 27% in the context of realistic future habitat restoration scenarios. These results represent, respectively, a supplementary increase of more 6% or more 13% in the Azores bullfinch abundance when compared with the trends simulated for the scenario without management. Nevertheless, those actions seemed to be relatively ineffective in promoting the expansion of the species from the actual restricted favourable area, essentially due to local forestry dynamics and on-going plant invasion processes. This novel integrative approach provides a promising baseline to support ecological models with increased realism and predictive power, making the outputs more useful and intuitive to decision-makers and environmental managers.

Identification of stochastic nonlinear models using optimal estimating functions

The first part of the paper examines the asymptotic properties of linear prediction error method estimators, which were recently suggested for the identification of nonlinear stochastic dynamical models. It is shown that their accuracy depends not only on how the model is parameterized, but also on the shape of the unknown distribution of the data. Therefore, it is not obvious in general which linear prediction error method should be preferred. In the second part, the estimating functions approach is introduced and used to construct estimators that are asymptotically optimal with respect to a specific class of estimators. These estimators rely on partial probabilistic parametric models, and therefore neither require the computations of the likelihood function nor any marginalization integrals. The convergence and consistency of the proposed estimators are established under standard regularity and identifiability assumptions akin to those of prediction error methods. The paper is concluded by several numerical simulation examples.

Option Pricing with Polynomial Chaos Expansion Stochastic Bridge Interpolators and Signed Path Dependence

Recent empirical studies in Equity markets show evidence that, while asset log-returns are largely uncorrelated, it is possible to predict with some accuracy their future sign. Such prediction is made over a given forecast horizon based solely on the observed sign of the cumulative log-return over a lookback horizon. This manuscript proposes a methodology to study the impact of such findings on option pricing by embedding into the risk premium the effects of signed path dependence. This is achieved by devising a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansions coupled with stochastic bridge interpolators that includes information from the entire set of observable European call option prices under all available strikes and maturities for a given underlying asset. Under the real-world measure we propose a price dynamics model that is compatible with an asset price process that is largely uncorrelated but still exhibits signed path dependence. The risk premium behaviour is subsequently inferred non-parametrically via a stochastic bridge interpolation that couples the risk neutral Polynomial Chaos Expansion result with the signed path dependence mixture binomial tree dynamic model to obtain a dynamic stochastic model for the implied risk premium process.

Analysis of opinion dynamics under binary exogenous and endogenous signals

We propose and analyze a stochastic model for opinion dynamics over social networks. In the scenario considered, each agent has an opinion level which belongs to a discrete set. At any given time, the agent takes an action 0 or 1 depending on the opinion, and this action can be seen as a binary signal that can influence the other agents in the network. The opinion updates based on the signal from a random neighbor or from an external entity who attempts to manipulate or control the network. In the absence of the external signal or a constant signal, this model is shown to asymptotically produce consensus with a finite number of connected agents. Additionally, the consensus is determined by the signal. On the other hand, when the number of agents is large, the time to achieve consensus can become exponentially large and the dynamics exhibit population equilibrium points that are ”metastable”. These equilibria can be observed with a finite (but large) number of agents through numerical simulations and are shown to persist for a long duration.

Modeling dynamic responses of a cross-river road shield tunnel under stochastic vehicle loads

Vehicle-induced dynamic loads are far more complex than those induced by trains because of their stochastic nature. In this study, we developed the stochastic dynamic vehicle load model and addressed a series of loading scenarios for a large road shield tunnel across the Yangtze River of China. The range analysis results show that, given the three factors influencing the dynamic responses of the tunnel, the pavement roughness plays a more important role than the vehicle type and running speed. The finite element model analysis shows that stress concentration occurs around the corbels fixed to the tunnel haunches; the stress amplitude of the soil responses, ranked in the descending order, is at the tunnel sides, under the tunnel bottom and above the tunnel, respectively. Under the stochastic vehicle loads, the amplitudes of the displacement of the road shield tunnel and the maximal settlement of the surrounding soils are basically one-tenth of those of the subway tunnel; the surrounding soil stress amplitude of the road shield tunnel is about one-third of that of the subway shield tunnel; while the structural stress amplitude of the road shield tunnel, focused around the corbels, are about 4 times of that of the subway shield tunnel. Those insights can be referred by the practitioners, especially those of the cross-river combined road-and-subway shield tunnels.

Estimating a novel stochastic model for within-field disease dynamics of banana bunchy top virus via approximate Bayesian computation.

The Banana Bunchy Top Virus (BBTV) is one of the most economically important vector-borne banana diseases throughout the Asia-Pacific Basin and presents a significant challenge to the agricultural sector. Current models of BBTV are largely deterministic, limited by an incomplete understanding of interactions in complex natural systems, and the appropriate identification of parameters. A stochastic network-based Susceptible-Infected-Susceptible model has been created which simulates the spread of BBTV across the subsections of a banana plantation, parameterising nodal recovery, neighbouring and distant infectivity across summer and winter. Findings from posterior results achieved through Markov Chain Monte Carlo approach to approximate Bayesian computation suggest seasonality in all parameters, which are influenced by correlated changes in inspection accuracy, temperatures and aphid activity. This paper demonstrates how the model may be used for monitoring and forecasting of various disease management strategies to support policy-level decision making.

An Economic Order Quantity Stochastic Dynamic Optimization Model in a Logistic 4.0 Environment

This paper proposes a stock dynamic sizing optimization under the Logistic 4.0 environment. The safety stock is conceived to fill up the demand variability, providing continuous stock availability. Logistic 4.0 and the smart factory topics are considered. It focuses on vertical integration to implement flexible and reconfigurable smart production systems using the information system integration in order to optimize material flow in a 4.0 full-service approach. The proposed methodology aims to reduce the occurring stock-out events through a link among the wear-out items rate and the downstream logistic demand. The failure rate items trend is obtained through life-cycle state detection by a curve fitting technique. Therefore, the optimal safety stock size is calculated and then validated by an auto-tuning iterative modified algorithm. In this study, the reorder time has been optimized. The case study refers to the material management of a very high-speed train.

Core-periphery dynamics in a plant-pollinator network.

Mutualistic networks are highly dynamic, characterized by high temporal turnover of species and interactions. Yet, we have a limited understanding of how the internal structure of these networks and the roles species play in them vary through time. We used 6years of observation data and a novel statistical method (dynamic stochastic block models) to assess how network structure and species' structural position within the network change throughout subseasons of the flowering season and across years in a quantitative plant-pollinator network from a dryland ecosystem in Argentina. Our analyses revealed a core-periphery structure persistent through subseasons and years. Yet, species structural position as core or peripheral was highly dynamic: virtually all species that were at the core in some subseasons were also peripheral in other subseasons, while many other species always remained peripheral. Our results illuminate our understanding of the dynamics of mutualistic networks and have important implications for ecosystem management and conservation.

Evolutionary analysis of adaptive dynamics model under variation of noise environment

This paper proposes a stochastic model for the evolutionary adaptive dynamics of species subject to trait-dependent intrinsic growth rates and the influence of environmental noise. The aim of this paper is twofold: (a) mathematically we make an attempt to investigate the evolutionary adaptive dynamics for models with noises; (b) biologically we investigate how the noises in environment affect the evolutionary stability. We first investigate the extinction and permanence of the population in the presence of environmental noises. Combining evolutionary adaptive dynamics with stochastic dynamics, we then establish a fitness function with stochastic disturbance and obtain the evolutionary conditions for continuously stable strategy and evolutionary branching. Our study finds that under intense competition among species, increasing stochastic disturbance can lead to rapidly stable evolution towards smaller trait values, but there is an opposite effect under weak competition among species. This yields an interesting evolutionary threshold, beyond which any increasing stochastic disturbance can go against evolutionary branching and promote evolutionary stability. We then carry out the evolutionary analysis and numerical simulations to illustrate our theoretical results. Finally, for demonstrating the emergence of high-level polymorphism we perform long-term simulation of evolutionary dynamics.

Behavioral Equilibrium and Evolutionary Dynamics in Asset Markets

This paper analyzes a dynamic stochastic equilibrium model of an asset market based on behavioral and evolutionary principles. The core of the model is a non-traditional game-theoretic framework combining elements of stochastic dynamic games and evolutionary game theory. Its key characteristic feature is that it relies only on objectively observable market data and does not use hidden individual agents' characteristics (such as their utilities and beliefs). A central goal of the study is to identify an investment strategy that allows an investor to survive in the market selection process, i.e., to keep with probability one a strictly positive, bounded away from zero share of market wealth over an infinite time horizon, irrespective of the strategies used by the other players. The main results show that under very general assumptions, such a strategy exists, is asymptotically unique and easily computable.

Estimating the combined costs of clinical and subclinical ketosis in dairy cows.

Clinical ketosis (CK) and subclinical ketosis (SCK) are associated with lower milk production, lower reproductive performance, an increased culling of cows and an increased probability of other disorders. Quantifying the costs related to ketosis will enable veterinarians and farmers to make more informed decisions regarding the prevention and treatment of the disease. The overall aim of this study was to estimate the combined costs of CK and SCK using assumptions and input variables from a typical Dutch context. A herd level dynamic stochastic simulation model was developed, simulating 385 herds with 130 cows each. In the default scenario there was a CK probability of almost 1% and a SCK probability of 11%. The herds under the no risk scenario had no CK and SCK, while the herds under the high-risk scenario had a doubled probability of CK and SCK compared to the default scenario. The results from the simulation model were used to estimate the annual cash flows of the herds, including the costs related to milk production losses, treatment, displaced abomasum, mastitis, calf management, culling and feed, as well as the returns from sales of milk and calves. The difference between the annual net cash flows of farms in the no risk scenario and the default scenario provides the estimate of the herd level costs of ketosis. Average herd level costs of ketosis (CK and SCK combined) were €3,613 per year for a default farm and €7,371 per year for a high-risk farm. The costs for a single CK case were on average €709 (with 5 and 95 percentiles of €64 and €1,196, respectively), while the costs for a single SCK case were on average €150 (with 5 and 95 percentiles of €18 and €422, respectively) for the default farms. The differences in costs between cases occurred due to differences between cases (e.g., cow culled vs cow not culled, getting another disease vs not getting another disease).

Integrated Inspection Planning and Preventive Maintenance for a Markov Deteriorating System Under Scenario-based Demand Uncertainty

In this paper, a single-product, single-machine system under Markovian deterioration of machine condition and demand uncertainty is studied. The objective is to find the optimal intervals for inspection and preventive maintenance activities in a condition-based maintenance planning with discrete monitoring framework. At first, a stochastic dynamic programming model whose state variable is the machine status is presented. In the first model, the demand is assumed to be deterministic and the objective is to minimize the sum of inspection, preventive maintenance, and lost sale costs. Then, in order to take the demand uncertainty into account, the extended model is formulated as a scenario-based two-stage stochastic programming one. In the second model, selecting the best inspection plan and finding the appropriate intervals for preventive maintenance are considered as the first and second stage decisions, respectively. Analyzing an illustrative example to study the effect of demand uncertainty in the problem shows thatthe total average cost is a non-decreasing function of machine state and demand. Moreover, if the machine state is worsened or the demand is increased, the number of inspections increase and the preventive maintenance should be executed at the same time or earlier. Finally, when the unit lost sale cost is greater than a certain amount, ignoring the demand uncertainty is not costly.

Emergency medical service resource allocation in a mass casualty incident by integrating patient prioritization and hospital selection problems

Mass casualty incidents often cause a shortage of resources for emergency medical services such as ambulances and emergency departments. These resources must be effectively managed to save as many lives as possible. Critical decisions in operating emergency medical service systems include the prioritization of patients for ambulance transport and the selection of destination hospitals. We develop a stochastic dynamic model that integrates patient transport prioritization and hospital selection problems. Policy solutions from the model are compared with other plausible heuristics, and our experimental results show that our policy solution outperforms other alternatives. More importantly, we show that there are considerable benefits from optimally selecting hospitals, which suggests that this decision is just as important as the patient prioritization decision. Motivated by the finding, we propose a heuristic policy that considers both patient prioritization and hospital selection. Experimental results demonstrate strong performance of our heuristic policy compared with existing heuristics. In addition, the proposed approach offers practical advantages. Whereas the existing heuristic policies use patient information, our heuristic policy requires information on the hospital state, which is more readily available and reliable.

Optical Manipulation of Biological Cells With a Robot-Tweezers System: A Stochastic Control Approach

Cell manipulation is a key technique involved in many cell surgery applications. Various automatic frameworks have been developed for optical manipulation of biological cells without consideration of stochastic perturbations, such as Brownian motion. In this brief, a stochastic control scheme for optical manipulation of biological cells is developed. On the basis of the stochastic dynamic model of an optically trapped biological cell, a vectorial backstepping control strategy and its adaptive case is formulated for cell trajectory tracking. The global noise-to-state stability of a closed-loop system in the presence of stochastic perturbations is analyzed. Simulation results demonstrate the performance of the proposed approach.

Fluctuations-induced regime shifts in the Endogenous Credit system with time delay

Abstract The model of endogenous credit that exhibits multiple steady states and generates phase transitions with catastrophic abruptness has been investigated. This resembles aspects of financial meltdowns witnessed in global capital markets in 2007. In this paper, time delay and fluctuations (noises) are introduced into the endogenous credit model, and a stochastic asset price dynamics model with time delay is established. The effects of time delay, fluctuations and cross-correlation between two noises on the probability distribution and the mean first passage time (MFPT) are analyzed, and the theoretical results are in agreement with the numerical results. It is shown from time series and probability distribution that the noises and time delay can induce regime shifts between two stable states. For the positive cross-correlation between two noises (λ > 0.0), the MFPT exhibits a maximum for some characteristic values of the noise intensity, which identifies the signature of the noise-enhanced stability (NES) phenomenon for asset price. The cross-correlation between two noises enhances the NES phenomenon for asset price, while time delay weakens it. However for the zero and negative intensity of noise correlation (λ ≤ 0.0), the MFPT decreases as the noise intensity increases, namely, the NES phenomenon disappears for λ ≤ 0.0.

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

SummaryBackgroundAn outbreak of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to 95 333 confirmed cases as of March 5, 2020. Understanding the early transmission dynamics of the infection and evaluating the effectiveness of control measures is crucial for assessing the potential for sustained transmission to occur in new areas. Combining a mathematical model of severe SARS-CoV-2 transmission with four datasets from within and outside Wuhan, we estimated how transmission in Wuhan varied between December, 2019, and February, 2020. We used these estimates to assess the potential for sustained human-to-human transmission to occur in locations outside Wuhan if cases were introduced.MethodsWe combined a stochastic transmission model with data on cases of coronavirus disease 2019 (COVID-19) in Wuhan and international cases that originated in Wuhan to estimate how transmission had varied over time during January, 2020, and February, 2020. Based on these estimates, we then calculated the probability that newly introduced cases might generate outbreaks in other areas. To estimate the early dynamics of transmission in Wuhan, we fitted a stochastic transmission dynamic model to multiple publicly available datasets on cases in Wuhan and internationally exported cases from Wuhan. The four datasets we fitted to were: daily number of new internationally exported cases (or lack thereof), by date of onset, as of Jan 26, 2020; daily number of new cases in Wuhan with no market exposure, by date of onset, between Dec 1, 2019, and Jan 1, 2020; daily number of new cases in China, by date of onset, between Dec 29, 2019, and Jan 23, 2020; and proportion of infected passengers on evacuation flights between Jan 29, 2020, and Feb 4, 2020. We used an additional two datasets for comparison with model outputs: daily number of new exported cases from Wuhan (or lack thereof) in countries with high connectivity to Wuhan (ie, top 20 most at-risk countries), by date of confirmation, as of Feb 10, 2020; and data on new confirmed cases reported in Wuhan between Jan 16, 2020, and Feb 11, 2020.FindingsWe estimated that the median daily reproduction number (Rt) in Wuhan declined from 2·35 (95% CI 1·15–4·77) 1 week before travel restrictions were introduced on Jan 23, 2020, to 1·05 (0·41–2·39) 1 week after. Based on our estimates of Rt, assuming SARS-like variation, we calculated that in locations with similar transmission potential to Wuhan in early January, once there are at least four independently introduced cases, there is a more than 50% chance the infection will establish within that population.InterpretationOur results show that COVID-19 transmission probably declined in Wuhan during late January, 2020, coinciding with the introduction of travel control measures. As more cases arrive in international locations with similar transmission potential to Wuhan before these control measures, it is likely many chains of transmission will fail to establish initially, but might lead to new outbreaks eventually.FundingWellcome Trust, Health Data Research UK, Bill & Melinda Gates Foundation, and National Institute for Health Research.

Analysis of COVID-19 epidemic traced data and stochastic discrete transmission dynamic model

The epidemic of novel coronavirus pneumonia has spread throughout the country. The early epidemic cases in many provinces, including Shaanxi, are mainly imported cases. The latest epidemic situation has been decreasing under restrict prevention and control strategies. Accessing the efficacy of control measures, analyzing the impact of population flow on the epidemic situation are of great significance for the study of the epidemic situation in Shaanxi (or other areas with imported cases as the main cases) and the future response to emergent infectious diseases. According to the detailed data published by Shaanxi, we can obtain the transmission chains (infection tree), and the median durations from the illness onset to the first medical visit, to the admission, and then to the final confirmation. We can obtain the daily number of latent, infectious and hospitalized individuals and the spatial distribution of their state evolution. The control reproduction number of COVID-19 epidemic was determined (1.48–1.69). We develop the statistical inference method to calculate the effective regeneration number under the strict control measures in Shaanxi province. Furthermore, a novel stochastic discrete transmission model for COVID-19 was proposed, which integrates possible interventions and import cases. The parameterization of the formulated model was realized through multiple source data. Our main conclusion shows that intermittent population flow, close attention and effective isolation of the floating populationcan effectively reduce the risk of secondary outbreak, which consequently provides decision support for the orderly organization of returning to work/school.

A hardware approach to value function iteration

This paper proposes a novel approach for the computation of dynamic stochastic equilibrium models. We design an FPGA specialized in the computation of a Bellman equation via value function iteration (VFI). Our hardware approach exhibits significant speed gains vis-à-vis GPU-based data-parallelization techniques. The speed gains arise from two layers of parallelism, accessible to hardware developers: instruction-level and pipeline parallelism at the logical resources level. By and large, the paper documents significant computational speed gains from hardware specialization, so far unexplored by the macroeconomic literature.

A Machine Learning Assisted Development of a Model for the Populations of Convective and Stratiform Clouds

AbstractTraditional parameterizations of the interaction between convection and the environment have relied on an assumption that the slowly varying large‐scale environment is in statistical equilibrium with a large number of small and short‐lived convective clouds. They fail to capture nonequilibrium transitions such as the diurnal cycle and the formation of mesoscale convective systems as well as observed precipitation statistics and extremes. Informed by analysis of radar observations, cloud‐permitting model simulation, theory, and machine learning, this work presents a new stochastic cloud population dynamics model for characterizing the interactions between convective and stratiform clouds, with the goal of informing the representation of these interactions in global climate models. Fifteen wet seasons of precipitating cloud observations by a C‐band radar at Darwin, Australia are fed into a machine learning algorithm to obtain transition functions that close a set of coupled equations relating large‐scale forcing, mass flux, the convective cell size distribution, and the stratiform area. Under realistic large‐scale forcing, the derived transition functions show that, on the one hand, interactions with stratiform clouds act to dampen the variability in the size and number of convective cells and therefore in the convective mass flux. On the other, for a given convective area fraction, a larger number of smaller cells is more favorable for the growth of stratiform area than a smaller number of larger cells. The combination of these two factors gives rise to solutions with a few convective cells embedded in a large stratiform area, reminiscent of mesoscale convective systems.

Optimal Storage, Investment and Management under Uncertainty: It is Costly to Avoid Outages!

We show how electricity storage is operated optimally when the load net of renewable output is uncertain. We estimate a diurnal Markov-process representation of how Germany’s residual load changed from hour to hour and design a simple dynamic stochastic electricity system model with non-intermittent generation technologies and storage. We derive the optimal storage, generator output and capacity levels. If storage capacity replaces some generation capacity, the optimal storage strategy must balance arbitrage (between periods of high and low marginal cost) against precautionary storage to ensure energy is available throughout a long peak in net demand. Solving the model numerically under uncertainty (only the transition probabilities to future loads are known), we compare the results to perfect foresight findings. The latter over-estimate the cost-saving potential of energy storage by 27%, as storage can take up arbitrage opportunities that would not be chosen if there was a need for precautionary storage.