Exact Solutions to Time-dependent Mdps

NASA Technical Reports Server (NTRS)

Boyan, Justin A.; Littman, Michael L.

2000-01-01

We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.

Composition of web services using Markov decision processes and dynamic programming.

PubMed

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity.

Decision-Theoretic Control of Planetary Rovers

NASA Technical Reports Server (NTRS)

Zilberstein, Shlomo; Washington, Richard; Bernstein, Daniel S.; Mouaddib, Abdel-Illah; Morris, Robert (Technical Monitor)

2003-01-01

Planetary rovers are small unmanned vehicles equipped with cameras and a variety of sensors used for scientific experiments. They must operate under tight constraints over such resources as operation time, power, storage capacity, and communication bandwidth. Moreover, the limited computational resources of the rover limit the complexity of on-line planning and scheduling. We describe two decision-theoretic approaches to maximize the productivity of planetary rovers: one based on adaptive planning and the other on hierarchical reinforcement learning. Both approaches map the problem into a Markov decision problem and attempt to solve a large part of the problem off-line, exploiting the structure of the plan and independence between plan components. We examine the advantages and limitations of these techniques and their scalability.

A decision aid for intensity-modulated radiation-therapy plan selection in prostate cancer based on a prognostic Bayesian network and a Markov model.

PubMed

Smith, Wade P; Doctor, Jason; Meyer, Jürgen; Kalet, Ira J; Phillips, Mark H

2009-06-01

The prognosis of cancer patients treated with intensity-modulated radiation-therapy (IMRT) is inherently uncertain, depends on many decision variables, and requires that a physician balance competing objectives: maximum tumor control with minimal treatment complications. In order to better deal with the complex and multiple objective nature of the problem we have combined a prognostic probabilistic model with multi-attribute decision theory which incorporates patient preferences for outcomes. The response to IMRT for prostate cancer was modeled. A Bayesian network was used for prognosis for each treatment plan. Prognoses included predicting local tumor control, regional spread, distant metastases, and normal tissue complications resulting from treatment. A Markov model was constructed and used to calculate a quality-adjusted life-expectancy which aids in the multi-attribute decision process. Our method makes explicit the tradeoffs patients face between quality and quantity of life. This approach has advantages over current approaches because with our approach risks of health outcomes and patient preferences determine treatment decisions.

Accelerated decomposition techniques for large discounted Markov decision processes

NASA Astrophysics Data System (ADS)

Larach, Abdelhadi; Chafik, S.; Daoui, C.

2017-12-01

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorithm, which is a variant of Tarjan's algorithm that simultaneously finds the SCCs and their belonging levels. Second, a new definition of the restricted MDPs is presented to ameliorate some hierarchical solutions in discounted MDPs using value iteration (VI) algorithm based on a list of state-action successors. Finally, a robotic motion-planning example and the experiment results are presented to illustrate the benefit of the proposed decomposition algorithms.

Discrete event simulation: the preferred technique for health economic evaluations?

PubMed

Caro, Jaime J; Möller, Jörgen; Getsios, Denis

2010-12-01

To argue that discrete event simulation should be preferred to cohort Markov models for economic evaluations in health care. The basis for the modeling techniques is reviewed. For many health-care decisions, existing data are insufficient to fully inform them, necessitating the use of modeling to estimate the consequences that are relevant to decision-makers. These models must reflect what is known about the problem at a level of detail sufficient to inform the questions. Oversimplification will result in estimates that are not only inaccurate, but potentially misleading. Markov cohort models, though currently popular, have so many limitations and inherent assumptions that they are inadequate to inform most health-care decisions. An event-based individual simulation offers an alternative much better suited to the problem. A properly designed discrete event simulation provides more accurate, relevant estimates without being computationally prohibitive. It does require more data and may be a challenge to convey transparently, but these are necessary trade-offs to provide meaningful and valid results. In our opinion, discrete event simulation should be the preferred technique for health economic evaluations today. © 2010, International Society for Pharmacoeconomics and Outcomes Research (ISPOR).

The application of Markov decision process in restaurant delivery robot

NASA Astrophysics Data System (ADS)

Wang, Yong; Hu, Zhen; Wang, Ying

2017-05-01

As the restaurant delivery robot is often in a dynamic and complex environment, including the chairs inadvertently moved to the channel and customers coming and going. The traditional path planning algorithm is not very ideal. To solve this problem, this paper proposes the Markov dynamic state immediate reward (MDR) path planning algorithm according to the traditional Markov decision process. First of all, it uses MDR to plan a global path, then navigates along this path. When the sensor detects there is no obstructions in front state, increase its immediate state reward value; when the sensor detects there is an obstacle in front, plan a global path that can avoid obstacle with the current position as the new starting point and reduce its state immediate reward value. This continues until the target is reached. When the robot learns for a period of time, it can avoid those places where obstacles are often present when planning the path. By analyzing the simulation experiment, the algorithm has achieved good results in the global path planning under the dynamic environment.

Composition of Web Services Using Markov Decision Processes and Dynamic Programming

PubMed Central

Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael

2015-01-01

We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity. PMID:25874247

Integrating Decision Tree and Hidden Markov Model (HMM) for Subtype Prediction of Human Influenza A Virus

NASA Astrophysics Data System (ADS)

Attaluri, Pavan K.; Chen, Zhengxin; Weerakoon, Aruna M.; Lu, Guoqing

Multiple criteria decision making (MCDM) has significant impact in bioinformatics. In the research reported here, we explore the integration of decision tree (DT) and Hidden Markov Model (HMM) for subtype prediction of human influenza A virus. Infection with influenza viruses continues to be an important public health problem. Viral strains of subtype H3N2 and H1N1 circulates in humans at least twice annually. The subtype detection depends mainly on the antigenic assay, which is time-consuming and not fully accurate. We have developed a Web system for accurate subtype detection of human influenza virus sequences. The preliminary experiment showed that this system is easy-to-use and powerful in identifying human influenza subtypes. Our next step is to examine the informative positions at the protein level and extend its current functionality to detect more subtypes. The web functions can be accessed at http://glee.ist.unomaha.edu/.

Optimal dynamic control of resources in a distributed system

NASA Technical Reports Server (NTRS)

Shin, Kang G.; Krishna, C. M.; Lee, Yann-Hang

1989-01-01

The authors quantitatively formulate the problem of controlling resources in a distributed system so as to optimize a reward function and derive optimal control strategies using Markov decision theory. The control variables treated are quite general; they could be control decisions related to system configuration, repair, diagnostics, files, or data. Two algorithms for resource control in distributed systems are derived for time-invariant and periodic environments, respectively. A detailed example to demonstrate the power and usefulness of the approach is provided.

A MAP-based image interpolation method via Viterbi decoding of Markov chains of interpolation functions.

PubMed

Vedadi, Farhang; Shirani, Shahram

2014-01-01

A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.

Effects of stochastic interest rates in decision making under risk: A Markov decision process model for forest management

Treesearch

Mo Zhou; Joseph Buongiorno

2011-01-01

Most economic studies of forest decision making under risk assume a fixed interest rate. This paper investigated some implications of this stochastic nature of interest rates. Markov decision process (MDP) models, used previously to integrate stochastic stand growth and prices, can be extended to include variable interest rates as well. This method was applied to...

Multi-Agent Patrolling under Uncertainty and Threats.

PubMed

Chen, Shaofei; Wu, Feng; Shen, Lincheng; Chen, Jing; Ramchurn, Sarvapali D

2015-01-01

We investigate a multi-agent patrolling problem where information is distributed alongside threats in environments with uncertainties. Specifically, the information and threat at each location are independently modelled as multi-state Markov chains, whose states are not observed until the location is visited by an agent. While agents will obtain information at a location, they may also suffer damage from the threat at that location. Therefore, the goal of the agents is to gather as much information as possible while mitigating the damage incurred. To address this challenge, we formulate the single-agent patrolling problem as a Partially Observable Markov Decision Process (POMDP) and propose a computationally efficient algorithm to solve this model. Building upon this, to compute patrols for multiple agents, the single-agent algorithm is extended for each agent with the aim of maximising its marginal contribution to the team. We empirically evaluate our algorithm on problems of multi-agent patrolling and show that it outperforms a baseline algorithm up to 44% for 10 agents and by 21% for 15 agents in large domains.

A Novel Methodology for Charging Station Deployment

NASA Astrophysics Data System (ADS)

Sun, Zhonghao; Zhao, Yunwei; He, Yueying; Li, Mingzhe

2018-02-01

Lack of charging stations has been a main obstacle to the promotion of electric vehicles. This paper studies deploying charging stations in traffic networks considering grid constraints to balance the charging demand and grid stability. First, we propose a statistical model for charging demand. Then we combine the charging demand model with power grid constraints and give the formulation of the charging station deployment problem. Finally, we propose a theoretical solution for the problem by transforming it to a Markov Decision Process.

Self-Directed Cooperative Planetary Rovers

NASA Technical Reports Server (NTRS)

Zilberstein, Shlomo; Morris, Robert (Technical Monitor)

2003-01-01

The project is concerned with the development of decision-theoretic techniques to optimize the scientific return of planetary rovers. Planetary rovers are small unmanned vehicles equipped with cameras and a variety of sensors used for scientific experiments. They must operate under tight constraints over such resources as operation time, power, storage capacity, and communication bandwidth. Moreover, the limited computational resources of the rover limit the complexity of on-line planning and scheduling. We have developed a comprehensive solution to this problem that involves high-level tools to describe a mission; a compiler that maps a mission description and additional probabilistic models of the components of the rover into a Markov decision problem; and algorithms for solving the rover control problem that are sensitive to the limited computational resources and high-level of uncertainty in this domain.

Local Approximation and Hierarchical Methods for Stochastic Optimization

NASA Astrophysics Data System (ADS)

Cheng, Bolong

In this thesis, we present local and hierarchical approximation methods for two classes of stochastic optimization problems: optimal learning and Markov decision processes. For the optimal learning problem class, we introduce a locally linear model with radial basis function for estimating the posterior mean of the unknown objective function. The method uses a compact representation of the function which avoids storing the entire history, as is typically required by nonparametric methods. We derive a knowledge gradient policy with the locally parametric model, which maximizes the expected value of information. We show the policy is asymptotically optimal in theory, and experimental works suggests that the method can reliably find the optimal solution on a range of test functions. For the Markov decision processes problem class, we are motivated by an application where we want to co-optimize a battery for multiple revenue, in particular energy arbitrage and frequency regulation. The nature of this problem requires the battery to make charging and discharging decisions at different time scales while accounting for the stochastic information such as load demand, electricity prices, and regulation signals. Computing the exact optimal policy becomes intractable due to the large state space and the number of time steps. We propose two methods to circumvent the computation bottleneck. First, we propose a nested MDP model that structure the co-optimization problem into smaller sub-problems with reduced state space. This new model allows us to understand how the battery behaves down to the two-second dynamics (that of the frequency regulation market). Second, we introduce a low-rank value function approximation for backward dynamic programming. This new method only requires computing the exact value function for a small subset of the state space and approximate the entire value function via low-rank matrix completion. We test these methods on historical price data from the PJM Interconnect and show that it outperforms the baseline approach used in the industry.

Risk aversion and risk seeking in multicriteria forest management: a Markov decision process approach

Treesearch

Joseph Buongiorno; Mo Zhou; Craig Johnston

2017-01-01

Markov decision process models were extended to reflect some consequences of the risk attitude of forestry decision makers. One approach consisted of maximizing the expected value of a criterion subject to an upper bound on the variance or, symmetrically, minimizing the variance subject to a lower bound on the expected value.  The other method used the certainty...

Cost-effectiveness Analysis with Influence Diagrams.

PubMed

Arias, M; Díez, F J

2015-01-01

Cost-effectiveness analysis (CEA) is used increasingly in medicine to determine whether the health benefit of an intervention is worth the economic cost. Decision trees, the standard decision modeling technique for non-temporal domains, can only perform CEA for very small problems. To develop a method for CEA in problems involving several dozen variables. We explain how to build influence diagrams (IDs) that explicitly represent cost and effectiveness. We propose an algorithm for evaluating cost-effectiveness IDs directly, i.e., without expanding an equivalent decision tree. The evaluation of an ID returns a set of intervals for the willingness to pay - separated by cost-effectiveness thresholds - and, for each interval, the cost, the effectiveness, and the optimal intervention. The algorithm that evaluates the ID directly is in general much more efficient than the brute-force method, which is in turn more efficient than the expansion of an equivalent decision tree. Using OpenMarkov, an open-source software tool that implements this algorithm, we have been able to perform CEAs on several IDs whose equivalent decision trees contain millions of branches. IDs can perform CEA on large problems that cannot be analyzed with decision trees.

Predicting explorative motor learning using decision-making and motor noise.

PubMed

Chen, Xiuli; Mohr, Kieran; Galea, Joseph M

2017-04-01

A fundamental problem faced by humans is learning to select motor actions based on noisy sensory information and incomplete knowledge of the world. Recently, a number of authors have asked whether this type of motor learning problem might be very similar to a range of higher-level decision-making problems. If so, participant behaviour on a high-level decision-making task could be predictive of their performance during a motor learning task. To investigate this question, we studied performance during an explorative motor learning task and a decision-making task which had a similar underlying structure with the exception that it was not subject to motor (execution) noise. We also collected an independent measurement of each participant's level of motor noise. Our analysis showed that explorative motor learning and decision-making could be modelled as the (approximately) optimal solution to a Partially Observable Markov Decision Process bounded by noisy neural information processing. The model was able to predict participant performance in motor learning by using parameters estimated from the decision-making task and the separate motor noise measurement. This suggests that explorative motor learning can be formalised as a sequential decision-making process that is adjusted for motor noise, and raises interesting questions regarding the neural origin of explorative motor learning.

Predicting explorative motor learning using decision-making and motor noise

PubMed Central

Galea, Joseph M.

2017-01-01

A fundamental problem faced by humans is learning to select motor actions based on noisy sensory information and incomplete knowledge of the world. Recently, a number of authors have asked whether this type of motor learning problem might be very similar to a range of higher-level decision-making problems. If so, participant behaviour on a high-level decision-making task could be predictive of their performance during a motor learning task. To investigate this question, we studied performance during an explorative motor learning task and a decision-making task which had a similar underlying structure with the exception that it was not subject to motor (execution) noise. We also collected an independent measurement of each participant’s level of motor noise. Our analysis showed that explorative motor learning and decision-making could be modelled as the (approximately) optimal solution to a Partially Observable Markov Decision Process bounded by noisy neural information processing. The model was able to predict participant performance in motor learning by using parameters estimated from the decision-making task and the separate motor noise measurement. This suggests that explorative motor learning can be formalised as a sequential decision-making process that is adjusted for motor noise, and raises interesting questions regarding the neural origin of explorative motor learning. PMID:28437451

Symbolic Heuristic Search for Factored Markov Decision Processes

NASA Technical Reports Server (NTRS)

Morris, Robert (Technical Monitor); Feng, Zheng-Zhu; Hansen, Eric A.

2003-01-01

We describe a planning algorithm that integrates two approaches to solving Markov decision processes with large state spaces. State abstraction is used to avoid evaluating states individually. Forward search from a start state, guided by an admissible heuristic, is used to avoid evaluating all states. We combine these two approaches in a novel way that exploits symbolic model-checking techniques and demonstrates their usefulness for decision-theoretic planning.

Use of Inverse Reinforcement Learning for Identity Prediction

NASA Technical Reports Server (NTRS)

Hayes, Roy; Bao, Jonathan; Beling, Peter; Horowitz, Barry

2011-01-01

We adopt Markov Decision Processes (MDP) to model sequential decision problems, which have the characteristic that the current decision made by a human decision maker has an uncertain impact on future opportunity. We hypothesize that the individuality of decision makers can be modeled as differences in the reward function under a common MDP model. A machine learning technique, Inverse Reinforcement Learning (IRL), was used to learn an individual's reward function based on limited observation of his or her decision choices. This work serves as an initial investigation for using IRL to analyze decision making, conducted through a human experiment in a cyber shopping environment. Specifically, the ability to determine the demographic identity of users is conducted through prediction analysis and supervised learning. The results show that IRL can be used to correctly identify participants, at a rate of 68% for gender and 66% for one of three college major categories.

Optimizing Negotiation Conflict in the Cloud Service Negotiation Framework Using Probabilistic Decision Making Model

PubMed Central

Rajavel, Rajkumar; Thangarathinam, Mala

2015-01-01

Optimization of negotiation conflict in the cloud service negotiation framework is identified as one of the major challenging issues. This negotiation conflict occurs during the bilateral negotiation process between the participants due to the misperception, aggressive behavior, and uncertain preferences and goals about their opponents. Existing research work focuses on the prerequest context of negotiation conflict optimization by grouping similar negotiation pairs using distance, binary, context-dependent, and fuzzy similarity approaches. For some extent, these approaches can maximize the success rate and minimize the communication overhead among the participants. To further optimize the success rate and communication overhead, the proposed research work introduces a novel probabilistic decision making model for optimizing the negotiation conflict in the long-term negotiation context. This decision model formulates the problem of managing different types of negotiation conflict that occurs during negotiation process as a multistage Markov decision problem. At each stage of negotiation process, the proposed decision model generates the heuristic decision based on the past negotiation state information without causing any break-off among the participants. In addition, this heuristic decision using the stochastic decision tree scenario can maximize the revenue among the participants available in the cloud service negotiation framework. PMID:26543899

Optimizing Negotiation Conflict in the Cloud Service Negotiation Framework Using Probabilistic Decision Making Model.

PubMed

Rajavel, Rajkumar; Thangarathinam, Mala

2015-01-01

Optimization of negotiation conflict in the cloud service negotiation framework is identified as one of the major challenging issues. This negotiation conflict occurs during the bilateral negotiation process between the participants due to the misperception, aggressive behavior, and uncertain preferences and goals about their opponents. Existing research work focuses on the prerequest context of negotiation conflict optimization by grouping similar negotiation pairs using distance, binary, context-dependent, and fuzzy similarity approaches. For some extent, these approaches can maximize the success rate and minimize the communication overhead among the participants. To further optimize the success rate and communication overhead, the proposed research work introduces a novel probabilistic decision making model for optimizing the negotiation conflict in the long-term negotiation context. This decision model formulates the problem of managing different types of negotiation conflict that occurs during negotiation process as a multistage Markov decision problem. At each stage of negotiation process, the proposed decision model generates the heuristic decision based on the past negotiation state information without causing any break-off among the participants. In addition, this heuristic decision using the stochastic decision tree scenario can maximize the revenue among the participants available in the cloud service negotiation framework.

Generalization of Faustmann's Formula for Stochastic Forest Growth and Prices with Markov Decision Process Models

Treesearch

Joseph Buongiorno

2001-01-01

Faustmann's formula gives the land value, or the forest value of land with trees, under deterministic assumptions regarding future stand growth and prices, over an infinite horizon. Markov decision process (MDP) models generalize Faustmann's approach by recognizing that future stand states and prices are known only as probabilistic distributions. The...

Control Improvement for Jump-Diffusion Processes with Applications to Finance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baeuerle, Nicole, E-mail: nicole.baeuerle@kit.edu; Rieder, Ulrich, E-mail: ulrich.rieder@uni-ulm.de

2012-02-15

We consider stochastic control problems with jump-diffusion processes and formulate an algorithm which produces, starting from a given admissible control {pi}, a new control with a better value. If no improvement is possible, then {pi} is optimal. Such an algorithm is well-known for discrete-time Markov Decision Problems under the name Howard's policy improvement algorithm. The idea can be traced back to Bellman. Here we show with the help of martingale techniques that such an algorithm can also be formulated for stochastic control problems with jump-diffusion processes. As an application we derive some interesting results in financial portfolio optimization.

Reinforcement Learning for Weakly-Coupled MDPs and an Application to Planetary Rover Control

NASA Technical Reports Server (NTRS)

Bernstein, Daniel S.; Zilberstein, Shlomo

2003-01-01

Weakly-coupled Markov decision processes can be decomposed into subprocesses that interact only through a small set of bottleneck states. We study a hierarchical reinforcement learning algorithm designed to take advantage of this particular type of decomposability. To test our algorithm, we use a decision-making problem faced by autonomous planetary rovers. In this problem, a Mars rover must decide which activities to perform and when to traverse between science sites in order to make the best use of its limited resources. In our experiments, the hierarchical algorithm performs better than Q-learning in the early stages of learning, but unlike Q-learning it converges to a suboptimal policy. This suggests that it may be advantageous to use the hierarchical algorithm when training time is limited.

A dynamic fault tree model of a propulsion system

NASA Technical Reports Server (NTRS)

Xu, Hong; Dugan, Joanne Bechta; Meshkat, Leila

2006-01-01

We present a dynamic fault tree model of the benchmark propulsion system, and solve it using Galileo. Dynamic fault trees (DFT) extend traditional static fault trees with special gates to model spares and other sequence dependencies. Galileo solves DFT models using a judicious combination of automatically generated Markov and Binary Decision Diagram models. Galileo easily handles the complexities exhibited by the benchmark problem. In particular, Galileo is designed to model phased mission systems.

Constructing Abstraction Hierarchies Using a Skill-Symbol Loop

PubMed Central

Konidaris, George

2017-01-01

We describe a framework for building abstraction hierarchies whereby an agent alternates skill- and representation-construction phases to construct a sequence of increasingly abstract Markov decision processes. Our formulation builds on recent results showing that the appropriate abstract representation of a problem is specified by the agent’s skills. We describe how such a hierarchy can be used for fast planning, and illustrate the construction of an appropriate hierarchy for the Taxi domain. PMID:28579718

Markov decision processes in natural resources management: observability and uncertainty

USGS Publications Warehouse

Williams, Byron K.

2015-01-01

The breadth and complexity of stochastic decision processes in natural resources presents a challenge to analysts who need to understand and use these approaches. The objective of this paper is to describe a class of decision processes that are germane to natural resources conservation and management, namely Markov decision processes, and to discuss applications and computing algorithms under different conditions of observability and uncertainty. A number of important similarities are developed in the framing and evaluation of different decision processes, which can be useful in their applications in natural resources management. The challenges attendant to partial observability are highlighted, and possible approaches for dealing with it are discussed.

Perseveration effects in detection tasks with correlated decision intervals. [applied to pilot collision avoidance

NASA Technical Reports Server (NTRS)

Gai, E. G.; Curry, R. E.

1978-01-01

An investigation of the behavior of the human decisionmaker is described for a task related to the problem of a pilot using a traffic situation display to avoid collisions. This sequential signal detection task is characterized by highly correlated signals with time varying strength. Experimental results are presented and the behavior of the observers is analyzed using the theory of Markov processes and classical signal detection theory. Mathematical models are developed which describe the main result of the experiment: that correlation in sequential signals induced perseveration in the observer response and a strong tendency to repeat their previous decision, even when they were wrong.

Falling Person Detection Using Multi-Sensor Signal Processing

NASA Astrophysics Data System (ADS)

Toreyin, B. Ugur; Soyer, A. Birey; Onaran, Ibrahim; Cetin, E. Enis

2007-12-01

Falls are one of the most important problems for frail and elderly people living independently. Early detection of falls is vital to provide a safe and active lifestyle for elderly. Sound, passive infrared (PIR) and vibration sensors can be placed in a supportive home environment to provide information about daily activities of an elderly person. In this paper, signals produced by sound, PIR and vibration sensors are simultaneously analyzed to detect falls. Hidden Markov Models are trained for regular and unusual activities of an elderly person and a pet for each sensor signal. Decisions of HMMs are fused together to reach a final decision.

A Markov Decision Process Model for the Optimal Dispatch of Military Medical Evacuation Assets

DTIC Science & Technology

2014-03-27

further background on MEDEVAC and provides a review of pertinent literature . Section 3 provides a de- scription of the problem for which we develop our...best medical evacuation system possible, for those who follow in your footsteps . Special thanks goes to my wife and two children for their...order to generate the computational results necessary to make this paper a success. Lastly, I would like to thank the US Army Medical Evacuation

From Data to Improved Decisions: Operations Research in Healthcare Delivery.

PubMed

Capan, Muge; Khojandi, Anahita; Denton, Brian T; Williams, Kimberly D; Ayer, Turgay; Chhatwal, Jagpreet; Kurt, Murat; Lobo, Jennifer Mason; Roberts, Mark S; Zaric, Greg; Zhang, Shengfan; Schwartz, J Sanford

2017-11-01

The Operations Research Interest Group (ORIG) within the Society of Medical Decision Making (SMDM) is a multidisciplinary interest group of professionals that specializes in taking an analytical approach to medical decision making and healthcare delivery. ORIG is interested in leveraging mathematical methods associated with the field of Operations Research (OR) to obtain data-driven solutions to complex healthcare problems and encourage collaborations across disciplines. This paper introduces OR for the non-expert and draws attention to opportunities where OR can be utilized to facilitate solutions to healthcare problems. Decision making is the process of choosing between possible solutions to a problem with respect to certain metrics. OR concepts can help systematically improve decision making through efficient modeling techniques while accounting for relevant constraints. Depending on the problem, methods that are part of OR (e.g., linear programming, Markov Decision Processes) or methods that are derived from related fields (e.g., regression from statistics) can be incorporated into the solution approach. This paper highlights the characteristics of different OR methods that have been applied to healthcare decision making and provides examples of emerging research opportunities. We illustrate OR applications in healthcare using previous studies, including diagnosis and treatment of diseases, organ transplants, and patient flow decisions. Further, we provide a selection of emerging areas for utilizing OR. There is a timely need to inform practitioners and policy makers of the benefits of using OR techniques in solving healthcare problems. OR methods can support the development of sustainable long-term solutions across disease management, service delivery, and health policies by optimizing the performance of system elements and analyzing their interaction while considering relevant constraints.

Using Markov Decision Processes with Heterogeneous Queueing Systems to Examine Military MEDEVAC Dispatching Policies

DTIC Science & Technology

2017-03-23

Air Force Institute of Technology AFIT Scholar Theses and Dissertations 3-23-2017 Using Markov Decision Processes with Heterogeneous Queueing Systems... TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in...POLICIES THESIS Presented to the Faculty Department of Operational Sciences Graduate School of Engineering and Management Air Force Institute of Technology

Multi-agent cooperation pursuit based on an extension of AALAADIN organisational model

NASA Astrophysics Data System (ADS)

Souidi, Mohammed El Habib; Songhao, Piao; Guo, Li; Lin, Chang

2016-11-01

An approach of cooperative pursuit for multiple mobile targets based on multi-agents system is discussed. In this kind of problem the pursuit process is divided into two kinds of tasks. The first one (coalition problem) is designed to solve the problem of the pursuit team formation. To achieve this mission, we used an innovative method based on a dynamic organisation and reorganisation of the pursuers' groups. We introduce our coalition strategy extended from the organisational agent, group, role model by assigning an access mechanism to the groups inspired by fuzzy logic principles. The second task (motion problem) is the treatment of the pursuers' motion strategy. To manage this problem we applied the principles of the Markov decision process. Simulation results show the feasibility and validity of the given proposal.

A Fresh Perspective on a Familiar Problem: Examining Disparities in Knee Osteoarthritis Using a Markov Model.

PubMed

Karmarkar, Taruja D; Maurer, Anne; Parks, Michael L; Mason, Thomas; Bejinez-Eastman, Ana; Harrington, Melvyn; Morgan, Randall; O'Connor, Mary I; Wood, James E; Gaskin, Darrell J

2017-12-01

Disparities in the presentation of knee osteoarthritis (OA) and in the utilization of treatment across sex, racial, and ethnic groups in the United States are well documented. We used a Markov model to calculate lifetime costs of knee OA treatment. We then used the model results to compute costs of disparities in treatment by race, ethnicity, sex, and socioeconomic status. We used the literature to construct a Markov Model of knee OA and publicly available data to create the model parameters and patient populations of interest. An expert panel of physicians, who treated a large number of patients with knee OA, constructed treatment pathways. Direct costs were based on the literature and indirect costs were derived from the Medical Expenditure Panel Survey. We found that failing to obtain effective treatment increased costs and limited benefits for all groups. Delaying treatment imposed a greater cost across all groups and decreased benefits. Lost income because of lower labor market productivity comprised a substantial proportion of the lifetime costs of knee OA. Population simulations demonstrated that as the diversity of the US population increases, the societal costs of racial and ethnic disparities in treatment utilization for knee OA will increase. Our results show that disparities in treatment of knee OA are costly. All stakeholders involved in treatment decisions for knee OA patients should consider costs associated with delaying and forgoing treatment, especially for disadvantaged populations. Such decisions may lead to higher costs and worse health outcomes.

Multistage Fuzzy Decision Making in Bilateral Negotiation with Finite Termination Times

NASA Astrophysics Data System (ADS)

Richter, Jan; Kowalczyk, Ryszard; Klusch, Matthias

In this paper we model the negotiation process as a multistage fuzzy decision problem where the agents preferences are represented by a fuzzy goal and fuzzy constraints. The opponent is represented by a fuzzy Markov decision process in the form of offer-response patterns which enables utilization of limited and uncertain information, e.g. the characteristics of the concession behaviour. We show that we can obtain adaptive negotiation strategies by only using the negotiation threads of two past cases to create and update the fuzzy transition matrix. The experimental evaluation demonstrates that our approach is adaptive towards different negotiation behaviours and that the fuzzy representation of the preferences and the transition matrix allows for application in many scenarios where the available information, preferences and constraints are soft or imprecise.

Optimizing patient treatment decisions in an era of rapid technological advances: the case of hepatitis C treatment.

PubMed

Liu, Shan; Brandeau, Margaret L; Goldhaber-Fiebert, Jeremy D

2017-03-01

How long should a patient with a treatable chronic disease wait for more effective treatments before accepting the best available treatment? We develop a framework to guide optimal treatment decisions for a deteriorating chronic disease when treatment technologies are improving over time. We formulate an optimal stopping problem using a discrete-time, finite-horizon Markov decision process. The goal is to maximize a patient's quality-adjusted life expectancy. We derive structural properties of the model and analytically solve a three-period treatment decision problem. We illustrate the model with the example of treatment for chronic hepatitis C virus (HCV). Chronic HCV affects 3-4 million Americans and has been historically difficult to treat, but increasingly effective treatments have been commercialized in the past few years. We show that the optimal treatment decision is more likely to be to accept currently available treatment-despite expectations for future treatment improvement-for patients who have high-risk history, who are older, or who have more comorbidities. Insights from this study can guide HCV treatment decisions for individual patients. More broadly, our model can guide treatment decisions for curable chronic diseases by finding the optimal treatment policy for individual patients in a heterogeneous population.

Optimizing Patient Treatment Decisions in an Era of Rapid Technological Advances: The Case of Hepatitis C Treatment

PubMed Central

Liu, Shan; Goldhaber-Fiebert, Jeremy D.; Brandeau, Margaret L.

2015-01-01

How long should a patient with a treatable chronic disease wait for more effective treatments before accepting the best available treatment? We develop a framework to guide optimal treatment decisions for a deteriorating chronic disease when treatment technologies are improving over time. We formulate an optimal stopping problem using a discrete-time, finite-horizon Markov decision process. The goal is to maximize a patient’s quality-adjusted life expectancy. We derive structural properties of the model and analytically solve a three-period treatment decision problem. We illustrate the model with the example of treatment for chronic hepatitis C virus (HCV). Chronic HCV affects 3–4 million Americans and has been historically difficult to treat, but increasingly effective treatments have been commercialized in the past few years. We show that the optimal treatment decision is more likely to be to accept currently available treatment—despite expectations for future treatment improvement—for patients who have high-risk history, who are older, or who have more comorbidities. Insights from this study can guide HCV treatment decisions for individual patients. More broadly, our model can guide treatment decisions for curable chronic diseases by finding the optimal treatment policy for individual patients in a heterogeneous population. PMID:26188961

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

Entropy production rate as a criterion for inconsistency in decision theory

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-05-01

Individual and group decisions are complex, often involving choosing an apt alternative from a multitude of options. Evaluating pairwise comparisons breaks down such complex decision problems into tractable ones. Pairwise comparison matrices (PCMs) are regularly used to solve multiple-criteria decision-making problems, for example, using Saaty’s analytic hierarchy process (AHP) framework. However, there are two significant drawbacks of using PCMs. First, humans evaluate PCMs in an inconsistent manner. Second, not all entries of a large PCM can be reliably filled by human decision makers. We address these two issues by first establishing a novel connection between PCMs and time-irreversible Markov processes. Specifically, we show that every PCM induces a family of dissipative maximum path entropy random walks (MERW) over the set of alternatives. We show that only ‘consistent’ PCMs correspond to detailed balanced MERWs. We identify the non-equilibrium entropy production in the induced MERWs as a metric of inconsistency of the underlying PCMs. Notably, the entropy production satisfies all of the recently laid out criteria for reasonable consistency indices. We also propose an approach to use incompletely filled PCMs in AHP. Potential future avenues are discussed as well.

Markov Decision Process Measurement Model.

PubMed

LaMar, Michelle M

2018-03-01

Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.

Markov Chain Estimation of Avian Seasonal Fecundity

EPA Science Inventory

To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...

Robust path planning for flexible needle insertion using Markov decision processes.

PubMed

Tan, Xiaoyu; Yu, Pengqian; Lim, Kah-Bin; Chui, Chee-Kong

2018-05-11

Flexible needle has the potential to accurately navigate to a treatment region in the least invasive manner. We propose a new planning method using Markov decision processes (MDPs) for flexible needle navigation that can perform robust path planning and steering under the circumstance of complex tissue-needle interactions. This method enhances the robustness of flexible needle steering from three different perspectives. First, the method considers the problem caused by soft tissue deformation. The method then resolves the common needle penetration failure caused by patterns of targets, while the last solution addresses the uncertainty issues in flexible needle motion due to complex and unpredictable tissue-needle interaction. Computer simulation and phantom experimental results show that the proposed method can perform robust planning and generate a secure control policy for flexible needle steering. Compared with a traditional method using MDPs, the proposed method achieves higher accuracy and probability of success in avoiding obstacles under complicated and uncertain tissue-needle interactions. Future work will involve experiment with biological tissue in vivo. The proposed robust path planning method can securely steer flexible needle within soft phantom tissues and achieve high adaptability in computer simulation.

Agent-Centric Approach for Cybersecurity Decision-Support with Partial Observability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tipireddy, Ramakrishna; Chatterjee, Samrat; Paulson, Patrick R.

Generating automated cyber resilience policies for real-world settings is a challenging research problem that must account for uncertainties in system state over time and dynamics between attackers and defenders. In addition to understanding attacker and defender motives and tools, and identifying “relevant” system and attack data, it is also critical to develop rigorous mathematical formulations representing the defender’s decision-support problem under uncertainty. Game-theoretic approaches involving cyber resource allocation optimization with Markov decision processes (MDP) have been previously proposed in the literature. Moreover, advancements in reinforcement learning approaches have motivated the development of partially observable stochastic games (POSGs) in various multi-agentmore » problem domains with partial information. Recent advances in cyber-system state space modeling have also generated interest in potential applicability of POSGs for cybersecurity. However, as is the case in strategic card games such as poker, research challenges using game-theoretic approaches for practical cyber defense applications include: 1) solving for equilibrium and designing efficient algorithms for large-scale, general problems; 2) establishing mathematical guarantees that equilibrium exists; 3) handling possible existence of multiple equilibria; and 4) exploitation of opponent weaknesses. Inspired by advances in solving strategic card games while acknowledging practical challenges associated with the use of game-theoretic approaches in cyber settings, this paper proposes an agent-centric approach for cybersecurity decision-support with partial system state observability.« less

MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes

USGS Publications Warehouse

Williams, B.K.

1988-01-01

Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.

Dynamic Routing of Aircraft in the Presence of Adverse Weather Using a POMDP Framework

NASA Technical Reports Server (NTRS)

Balaban, Edward; Roychoudhury, Indranil; Spirkovska, Lilly; Sankararaman, Shankar; Kulkarni, Chetan; Arnon, Tomer

2017-01-01

Each year weather-related airline delays result in hundreds of millions of dollars in additional fuel burn, maintenance, and lost revenue, not to mention passenger inconvenience. The current approaches for aircraft route planning in the presence of adverse weather still mainly rely on deterministic methods. In contrast, this work aims to deal with the problem using a Partially Observable Markov Decision Processes (POMDPs) framework, which allows for reasoning over uncertainty (including uncertainty in weather evolution over time) and results in solutions that are more robust to disruptions. The POMDP-based decision support system is demonstrated on several scenarios involving convective weather cells and is benchmarked against a deterministic planning system with functionality similar to those currently in use or under development.

Sensitivity Analysis in Sequential Decision Models.

PubMed

Chen, Qiushi; Ayer, Turgay; Chhatwal, Jagpreet

2017-02-01

Sequential decision problems are frequently encountered in medical decision making, which are commonly solved using Markov decision processes (MDPs). Modeling guidelines recommend conducting sensitivity analyses in decision-analytic models to assess the robustness of the model results against the uncertainty in model parameters. However, standard methods of conducting sensitivity analyses cannot be directly applied to sequential decision problems because this would require evaluating all possible decision sequences, typically in the order of trillions, which is not practically feasible. As a result, most MDP-based modeling studies do not examine confidence in their recommended policies. In this study, we provide an approach to estimate uncertainty and confidence in the results of sequential decision models. First, we provide a probabilistic univariate method to identify the most sensitive parameters in MDPs. Second, we present a probabilistic multivariate approach to estimate the overall confidence in the recommended optimal policy considering joint uncertainty in the model parameters. We provide a graphical representation, which we call a policy acceptability curve, to summarize the confidence in the optimal policy by incorporating stakeholders' willingness to accept the base case policy. For a cost-effectiveness analysis, we provide an approach to construct a cost-effectiveness acceptability frontier, which shows the most cost-effective policy as well as the confidence in that for a given willingness to pay threshold. We demonstrate our approach using a simple MDP case study. We developed a method to conduct sensitivity analysis in sequential decision models, which could increase the credibility of these models among stakeholders.

Allocating conservation resources between areas where persistence of a species is uncertain.

PubMed

McDonald-Madden, Eve; Chadès, Iadine; McCarthy, Michael A; Linkie, Matthew; Possingham, Hugh P

2011-04-01

Research on the allocation of resources to manage threatened species typically assumes that the state of the system is completely observable; for example whether a species is present or not. The majority of this research has converged on modeling problems as Markov decision processes (MDP), which give an optimal strategy driven by the current state of the system being managed. However, the presence of threatened species in an area can be uncertain. Typically, resource allocation among multiple conservation areas has been based on the biggest expected benefit (return on investment) but fails to incorporate the risk of imperfect detection. We provide the first decision-making framework for confronting the trade-off between information and return on investment, and we illustrate the approach for populations of the Sumatran tiger (Panthera tigris sumatrae) in Kerinci Seblat National Park. The problem is posed as a partially observable Markov decision process (POMDP), which extends MDP to incorporate incomplete detection and allows decisions based on our confidence in particular states. POMDP has previously been used for making optimal management decisions for a single population of a threatened species. We extend this work by investigating two populations, enabling us to explore the importance of variation in expected return on investment between populations on how we should act. We compare the performance of optimal strategies derived assuming complete (MDP) and incomplete (POMDP) observability. We find that uncertainty about the presence of a species affects how we should act. Further, we show that assuming full knowledge of a species presence will deliver poorer strategic outcomes than if uncertainty about a species status is explicitly considered. MDP solutions perform up to 90% worse than the POMDP for highly cryptic species, and they only converge in performance when we are certain of observing the species during management: an unlikely scenario for many threatened species. This study illustrates an approach to allocating limited resources to threatened species where the conservation status of the species in different areas is uncertain. The results highlight the importance of including partial observability in future models of optimal species management when the species of concern is cryptic in nature.

Reduced-order dynamic output feedback control of uncertain discrete-time Markov jump linear systems

NASA Astrophysics Data System (ADS)

Morais, Cecília F.; Braga, Márcio F.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

2017-11-01

This paper deals with the problem of designing reduced-order robust dynamic output feedback controllers for discrete-time Markov jump linear systems (MJLS) with polytopic state space matrices and uncertain transition probabilities. Starting from a full order, mode-dependent and polynomially parameter-dependent dynamic output feedback controller, sufficient linear matrix inequality based conditions are provided for the existence of a robust reduced-order dynamic output feedback stabilising controller with complete, partial or none mode dependency assuring an upper bound to the ? or the ? norm of the closed-loop system. The main advantage of the proposed method when compared to the existing approaches is the fact that the dynamic controllers are exclusively expressed in terms of the decision variables of the problem. In other words, the matrices that define the controller realisation do not depend explicitly on the state space matrices associated with the modes of the MJLS. As a consequence, the method is specially suitable to handle order reduction or cluster availability constraints in the context of ? or ? dynamic output feedback control of discrete-time MJLS. Additionally, as illustrated by means of numerical examples, the proposed approach can provide less conservative results than other conditions in the literature.

Decision analysis with cumulative prospect theory.

PubMed

Bayoumi, A M; Redelmeier, D A

2000-01-01

Individuals sometimes express preferences that do not follow expected utility theory. Cumulative prospect theory adjusts for some phenomena by using decision weights rather than probabilities when analyzing a decision tree. The authors examined how probability transformations from cumulative prospect theory might alter a decision analysis of a prophylactic therapy in AIDS, eliciting utilities from patients with HIV infection (n = 75) and calculating expected outcomes using an established Markov model. They next focused on transformations of three sets of probabilities: 1) the probabilities used in calculating standard-gamble utility scores; 2) the probabilities of being in discrete Markov states; 3) the probabilities of transitioning between Markov states. The same prophylaxis strategy yielded the highest quality-adjusted survival under all transformations. For the average patient, prophylaxis appeared relatively less advantageous when standard-gamble utilities were transformed. Prophylaxis appeared relatively more advantageous when state probabilities were transformed and relatively less advantageous when transition probabilities were transformed. Transforming standard-gamble and transition probabilities simultaneously decreased the gain from prophylaxis by almost half. Sensitivity analysis indicated that even near-linear probability weighting transformations could substantially alter quality-adjusted survival estimates. The magnitude of benefit estimated in a decision-analytic model can change significantly after using cumulative prospect theory. Incorporating cumulative prospect theory into decision analysis can provide a form of sensitivity analysis and may help describe when people deviate from expected utility theory.

Mode identification using stochastic hybrid models with applications to conflict detection and resolution

NASA Astrophysics Data System (ADS)

Naseri Kouzehgarani, Asal

2009-12-01

Most models of aircraft trajectories are non-linear and stochastic in nature; and their internal parameters are often poorly defined. The ability to model, simulate and analyze realistic air traffic management conflict detection scenarios in a scalable, composable, multi-aircraft fashion is an extremely difficult endeavor. Accurate techniques for aircraft mode detection are critical in order to enable the precise projection of aircraft conflicts, and for the enactment of altitude separation resolution strategies. Conflict detection is an inherently probabilistic endeavor; our ability to detect conflicts in a timely and accurate manner over a fixed time horizon is traded off against the increased human workload created by false alarms---that is, situations that would not develop into an actual conflict, or would resolve naturally in the appropriate time horizon-thereby introducing a measure of probabilistic uncertainty in any decision aid fashioned to assist air traffic controllers. The interaction of the continuous dynamics of the aircraft, used for prediction purposes, with the discrete conflict detection logic gives rise to the hybrid nature of the overall system. The introduction of the probabilistic element, common to decision alerting and aiding devices, places the conflict detection and resolution problem in the domain of probabilistic hybrid phenomena. A hidden Markov model (HMM) has two stochastic components: a finite-state Markov chain and a finite set of output probability distributions. In other words an unobservable stochastic process (hidden) that can only be observed through another set of stochastic processes that generate the sequence of observations. The problem of self separation in distributed air traffic management reduces to the ability of aircraft to communicate state information to neighboring aircraft, as well as model the evolution of aircraft trajectories between communications, in the presence of probabilistic uncertain dynamics as well as partially observable and uncertain data. We introduce the Hybrid Hidden Markov Modeling (HHMM) formalism to enable the prediction of the stochastic aircraft states (and thus, potential conflicts), by combining elements of the probabilistic timed input output automaton and the partially observable Markov decision process frameworks, along with the novel addition of a Markovian scheduler to remove the non-deterministic elements arising from the enabling of several actions simultaneously. Comparisons of aircraft in level, climbing/descending and turning flight are performed, and unknown flight track data is evaluated probabilistically against the tuned model in order to assess the effectiveness of the model in detecting the switch between multiple flight modes for a given aircraft. This also allows for the generation of probabilistic distribution over the execution traces of the hybrid hidden Markov model, which then enables the prediction of the states of aircraft based on partially observable and uncertain data. Based on the composition properties of the HHMM, we study a decentralized air traffic system where aircraft are moving along streams and can perform cruise, accelerate, climb and turn maneuvers. We develop a common decentralized policy for conflict avoidance with spatially distributed agents (aircraft in the sky) and assure its safety properties via correctness proofs.

Artificial intelligence framework for simulating clinical decision-making: a Markov decision process approach.

PubMed

Bennett, Casey C; Hauser, Kris

2013-01-01

In the modern healthcare system, rapidly expanding costs/complexity, the growing myriad of treatment options, and exploding information streams that often do not effectively reach the front lines hinder the ability to choose optimal treatment decisions over time. The goal in this paper is to develop a general purpose (non-disease-specific) computational/artificial intelligence (AI) framework to address these challenges. This framework serves two potential functions: (1) a simulation environment for exploring various healthcare policies, payment methodologies, etc., and (2) the basis for clinical artificial intelligence - an AI that can "think like a doctor". This approach combines Markov decision processes and dynamic decision networks to learn from clinical data and develop complex plans via simulation of alternative sequential decision paths while capturing the sometimes conflicting, sometimes synergistic interactions of various components in the healthcare system. It can operate in partially observable environments (in the case of missing observations or data) by maintaining belief states about patient health status and functions as an online agent that plans and re-plans as actions are performed and new observations are obtained. This framework was evaluated using real patient data from an electronic health record. The results demonstrate the feasibility of this approach; such an AI framework easily outperforms the current treatment-as-usual (TAU) case-rate/fee-for-service models of healthcare. The cost per unit of outcome change (CPUC) was $189 vs. $497 for AI vs. TAU (where lower is considered optimal) - while at the same time the AI approach could obtain a 30-35% increase in patient outcomes. Tweaking certain AI model parameters could further enhance this advantage, obtaining approximately 50% more improvement (outcome change) for roughly half the costs. Given careful design and problem formulation, an AI simulation framework can approximate optimal decisions even in complex and uncertain environments. Future work is described that outlines potential lines of research and integration of machine learning algorithms for personalized medicine. Copyright © 2012 Elsevier B.V. All rights reserved.

Microsimulation Modeling for Health Decision Sciences Using R: A Tutorial.

PubMed

Krijkamp, Eline M; Alarid-Escudero, Fernando; Enns, Eva A; Jalal, Hawre J; Hunink, M G Myriam; Pechlivanoglou, Petros

2018-04-01

Microsimulation models are becoming increasingly common in the field of decision modeling for health. Because microsimulation models are computationally more demanding than traditional Markov cohort models, the use of computer programming languages in their development has become more common. R is a programming language that has gained recognition within the field of decision modeling. It has the capacity to perform microsimulation models more efficiently than software commonly used for decision modeling, incorporate statistical analyses within decision models, and produce more transparent models and reproducible results. However, no clear guidance for the implementation of microsimulation models in R exists. In this tutorial, we provide a step-by-step guide to build microsimulation models in R and illustrate the use of this guide on a simple, but transferable, hypothetical decision problem. We guide the reader through the necessary steps and provide generic R code that is flexible and can be adapted for other models. We also show how this code can be extended to address more complex model structures and provide an efficient microsimulation approach that relies on vectorization solutions.

Policy Transfer via Markov Logic Networks

NASA Astrophysics Data System (ADS)

Torrey, Lisa; Shavlik, Jude

We propose using a statistical-relational model, the Markov Logic Network, for knowledge transfer in reinforcement learning. Our goal is to extract relational knowledge from a source task and use it to speed up learning in a related target task. We show that Markov Logic Networks are effective models for capturing both source-task Q-functions and source-task policies. We apply them via demonstration, which involves using them for decision making in an initial stage of the target task before continuing to learn. Through experiments in the RoboCup simulated-soccer domain, we show that transfer via Markov Logic Networks can significantly improve early performance in complex tasks, and that transferring policies is more effective than transferring Q-functions.

A Self-Organizing Incremental Spatiotemporal Associative Memory Networks Model for Problems with Hidden State

PubMed Central

2016-01-01

Identifying the hidden state is important for solving problems with hidden state. We prove any deterministic partially observable Markov decision processes (POMDP) can be represented by a minimal, looping hidden state transition model and propose a heuristic state transition model constructing algorithm. A new spatiotemporal associative memory network (STAMN) is proposed to realize the minimal, looping hidden state transition model. STAMN utilizes the neuroactivity decay to realize the short-term memory, connection weights between different nodes to represent long-term memory, presynaptic potentials, and synchronized activation mechanism to complete identifying and recalling simultaneously. Finally, we give the empirical illustrations of the STAMN and compare the performance of the STAMN model with that of other methods. PMID:27891146

Navigating complex decision spaces: Problems and paradigms in sequential choice

PubMed Central

Walsh, Matthew M.; Anderson, John R.

2015-01-01

To behave adaptively, we must learn from the consequences of our actions. Doing so is difficult when the consequences of an action follow a delay. This introduces the problem of temporal credit assignment. When feedback follows a sequence of decisions, how should the individual assign credit to the intermediate actions that comprise the sequence? Research in reinforcement learning provides two general solutions to this problem: model-free reinforcement learning and model-based reinforcement learning. In this review, we examine connections between stimulus-response and cognitive learning theories, habitual and goal-directed control, and model-free and model-based reinforcement learning. We then consider a range of problems related to temporal credit assignment. These include second-order conditioning and secondary reinforcers, latent learning and detour behavior, partially observable Markov decision processes, actions with distributed outcomes, and hierarchical learning. We ask whether humans and animals, when faced with these problems, behave in a manner consistent with reinforcement learning techniques. Throughout, we seek to identify neural substrates of model-free and model-based reinforcement learning. The former class of techniques is understood in terms of the neurotransmitter dopamine and its effects in the basal ganglia. The latter is understood in terms of a distributed network of regions including the prefrontal cortex, medial temporal lobes cerebellum, and basal ganglia. Not only do reinforcement learning techniques have a natural interpretation in terms of human and animal behavior, but they also provide a useful framework for understanding neural reward valuation and action selection. PMID:23834192

Assessing the Value of Frost Forecasts to Orchardists: A Dynamic Decision-Making Approach.

NASA Astrophysics Data System (ADS)

Katz, Richard W.; Murphy, Allan H.; Winkler, Robert L.

1982-04-01

The methodology of decision analysis is used to investigate the economic value of frost (i.e., minimum temperature) forecasts to orchardists. First, the fruit-frost situation and previous studies of the value of minimum temperature forecasts in this context are described. Then, after a brief overview of decision analysis, a decision-making model for the fruit-frost problem is presented. The model involves identifying the relevant actions and events (or outcomes), specifying the effect of taking protective action, and describing the relationships among temperature, bud loss, and yield loss. A bivariate normal distribution is used to model the relationship between forecast and observed temperatures, thereby characterizing the quality of different types of information. Since the orchardist wants to minimize expenses (or maximize payoffs) over the entire frost-protection season and since current actions and outcomes at any point in the season are related to both previous and future actions and outcomes, the decision-making problem is inherently dynamic in nature. As a result, a class of dynamic models known as Markov decision processes is considered. A computational technique called dynamic programming is used in conjunction with these models to determine the optimal actions and to estimate the value of meteorological information.Some results concerning the value of frost forecasts to orchardists in the Yakima Valley of central Washington are presented for the cases of red delicious apples, bartlett pears, and elberta peaches. Estimates of the parameter values in the Markov decision process are obtained from relevant physical and economic data. Twenty years of National Weather Service forecast and observed temperatures for the Yakima key station are used to estimate the quality of different types of information, including perfect forecasts, current forecasts, and climatological information. The orchardist's optimal actions over the frost-protection season and the expected expenses associated with the use of such information are determined using a dynamic programming algorithm. The value of meteorological information is defined as the difference between the expected expense for the information of interest and the expected expense for climatological information. Over the entire frost-protection season, the value estimates (in 1977 dollars) for current forecasts were $808 per acre for red delicious apples, $492 per acre for bartlett pears, and $270 per acre for elberta peaches. These amounts account for 66, 63, and 47%, respectively, of the economic value associated with decisions based on perfect forecasts. Varying the quality of the minimum temperature forecasts reveals that the relationship between the accuracy and value of such forecasts is nonlinear and that improvements in current forecasts would not be as significant in terms of economic value as were comparable improvements in the past.Several possible extensions of this study of the value of frost forecasts to orchardists are briefly described. Finally, the application of the dynamic model formulated in this paper to other decision-making problems involving the use of meteorological information is mentioned.

Numerical methods in Markov chain modeling

NASA Technical Reports Server (NTRS)

Philippe, Bernard; Saad, Youcef; Stewart, William J.

1989-01-01

Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.

Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states.

PubMed

Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew

2016-07-01

Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling

PubMed Central

Williams, Claire; Lewsey, James D.; Mackay, Daniel F.; Briggs, Andrew H.

2016-01-01

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results. PMID:27698003

Estimation of Survival Probabilities for Use in Cost-effectiveness Analyses: A Comparison of a Multi-state Modeling Survival Analysis Approach with Partitioned Survival and Markov Decision-Analytic Modeling.

PubMed

Williams, Claire; Lewsey, James D; Mackay, Daniel F; Briggs, Andrew H

2017-05-01

Modeling of clinical-effectiveness in a cost-effectiveness analysis typically involves some form of partitioned survival or Markov decision-analytic modeling. The health states progression-free, progression and death and the transitions between them are frequently of interest. With partitioned survival, progression is not modeled directly as a state; instead, time in that state is derived from the difference in area between the overall survival and the progression-free survival curves. With Markov decision-analytic modeling, a priori assumptions are often made with regard to the transitions rather than using the individual patient data directly to model them. This article compares a multi-state modeling survival regression approach to these two common methods. As a case study, we use a trial comparing rituximab in combination with fludarabine and cyclophosphamide v. fludarabine and cyclophosphamide alone for the first-line treatment of chronic lymphocytic leukemia. We calculated mean Life Years and QALYs that involved extrapolation of survival outcomes in the trial. We adapted an existing multi-state modeling approach to incorporate parametric distributions for transition hazards, to allow extrapolation. The comparison showed that, due to the different assumptions used in the different approaches, a discrepancy in results was evident. The partitioned survival and Markov decision-analytic modeling deemed the treatment cost-effective with ICERs of just over £16,000 and £13,000, respectively. However, the results with the multi-state modeling were less conclusive, with an ICER of just over £29,000. This work has illustrated that it is imperative to check whether assumptions are realistic, as different model choices can influence clinical and cost-effectiveness results.

Metrics for Labeled Markov Systems

NASA Technical Reports Server (NTRS)

Desharnais, Josee; Jagadeesan, Radha; Gupta, Vineet; Panangaden, Prakash

1999-01-01

Partial Labeled Markov Chains are simultaneously generalizations of process algebra and of traditional Markov chains. They provide a foundation for interacting discrete probabilistic systems, the interaction being synchronization on labels as in process algebra. Existing notions of process equivalence are too sensitive to the exact probabilities of various transitions. This paper addresses contextual reasoning principles for reasoning about more robust notions of "approximate" equivalence between concurrent interacting probabilistic systems. The present results indicate that:We develop a family of metrics between partial labeled Markov chains to formalize the notion of distance between processes. We show that processes at distance zero are bisimilar. We describe a decision procedure to compute the distance between two processes. We show that reasoning about approximate equivalence can be done compositionally by showing that process combinators do not increase distance. We introduce an asymptotic metric to capture asymptotic properties of Markov chains; and show that parallel composition does not increase asymptotic distance.

An intelligent, knowledge-based multiple criteria decision making advisor for systems design

NASA Astrophysics Data System (ADS)

Li, Yongchang

In systems engineering, design and operation of systems are two main problems which always attract researcher's attentions. The accomplishment of activities in these problems often requires proper decisions to be made so that the desired goal can be achieved, thus, decision making needs to be carefully fulfilled in the design and operation of systems. Design is a decision making process which permeates through out the design process, and is at the core of all design activities. In modern aircraft design, more and more attention is paid to the conceptual and preliminary design phases so as to increase the odds of choosing a design that will ultimately be successful at the completion of the design process, therefore, decisions made during these early design stages play a critical role in determining the success of a design. Since aerospace systems are complex systems with interacting disciplines and technologies, the Decision Makers (DMs) dealing with such design problems are involved in balancing the multiple, potentially conflicting attributes/criteria, transforming a large amount of customer supplied guidelines into a solidly defined set of requirement definitions. Thus, one could state with confidence that modern aerospace system design is a Multiple Criteria Decision Making (MCDM) process. A variety of existing decision making methods are available to deal with this type of decision problems. The selection of the most appropriate decision making method is of particular importance since inappropriate decision methods are likely causes of misleading engineering design decisions. With no sufficient knowledge about each of the methods, it is usually difficult for the DMs to find an appropriate analytical model capable of solving their problems. In addition, with the complexity of the decision problem and the demand for more capable methods increasing, new decision making methods are emerging with time. These various methods exacerbate the difficulty of the selection of an appropriate decision making method. Furthermore, some DMs may be exclusively using one or two specific methods which they are familiar with or trust and not realizing that they may be inappropriate to handle certain classes of the problems, thus yielding erroneous results. These issues reveal that in order to ensure a good decision a suitable decision method should be chosen before the decision making process proceeds. The first part of this dissertation proposes an MCDM process supported by an intelligent, knowledge-based advisor system referred to as Multi-Criteria Interactive Decision-Making Advisor and Synthesis process (MIDAS), which is able to facilitate the selection of the most appropriate decision making method and which provides insight to the user for fulfilling different preferences. The second part of this dissertation presents an autonomous decision making advisor which is capable of dealing with ever-evolving real time information and making autonomous decisions under uncertain conditions. The advisor encompasses a Markov Decision Process (MDP) formulation which takes uncertainty into account when determines the best action for each system state. (Abstract shortened by UMI.)

Tracking Problem Solving by Multivariate Pattern Analysis and Hidden Markov Model Algorithms

ERIC Educational Resources Information Center

Anderson, John R.

2012-01-01

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application…

Optimizing model: insemination, replacement, seasonal production, and cash flow.

PubMed

DeLorenzo, M A; Spreen, T H; Bryan, G R; Beede, D K; Van Arendonk, J A

1992-03-01

Dynamic programming to solve the Markov decision process problem of optimal insemination and replacement decisions was adapted to address large dairy herd management decision problems in the US. Expected net present values of cow states (151,200) were used to determine the optimal policy. States were specified by class of parity (n = 12), production level (n = 15), month of calving (n = 12), month of lactation (n = 16), and days open (n = 7). Methodology optimized decisions based on net present value of an individual cow and all replacements over a 20-yr decision horizon. Length of decision horizon was chosen to ensure that optimal policies were determined for an infinite planning horizon. Optimization took 286 s of central processing unit time. The final probability transition matrix was determined, in part, by the optimal policy. It was estimated iteratively to determine post-optimization steady state herd structure, milk production, replacement, feed inputs and costs, and resulting cash flow on a calendar month and annual basis if optimal policies were implemented. Implementation of the model included seasonal effects on lactation curve shapes, estrus detection rates, pregnancy rates, milk prices, replacement costs, cull prices, and genetic progress. Other inputs included calf values, values of dietary TDN and CP per kilogram, and discount rate. Stochastic elements included conception (and, thus, subsequent freshening), cow milk production level within herd, and survival. Validation of optimized solutions was by separate simulation model, which implemented policies on a simulated herd and also described herd dynamics during transition to optimized structure.

Generation of intervention strategy for a genetic regulatory network represented by a family of Markov Chains.

PubMed

Berlow, Noah; Pal, Ranadip

2011-01-01

Genetic Regulatory Networks (GRNs) are frequently modeled as Markov Chains providing the transition probabilities of moving from one state of the network to another. The inverse problem of inference of the Markov Chain from noisy and limited experimental data is an ill posed problem and often generates multiple model possibilities instead of a unique one. In this article, we address the issue of intervention in a genetic regulatory network represented by a family of Markov Chains. The purpose of intervention is to alter the steady state probability distribution of the GRN as the steady states are considered to be representative of the phenotypes. We consider robust stationary control policies with best expected behavior. The extreme computational complexity involved in search of robust stationary control policies is mitigated by using a sequential approach to control policy generation and utilizing computationally efficient techniques for updating the stationary probability distribution of a Markov chain following a rank one perturbation.

H2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

NASA Astrophysics Data System (ADS)

Figueiredo, Danilo Zucolli; Costa, Oswaldo Luiz do Valle

2017-10-01

This paper deals with the H2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space ?. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H2-norm of the closed-loop system is minimised. It is shown that the H2-norm can be written as the sum of two H2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space ? considering the infinite time horizon case.

LECTURES ON GAME THEORY, MARKOV CHAINS, AND RELATED TOPICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thompson, G L

1958-03-01

Notes on nine lectures delivered at Sandin Corporation in August 1957 are given. Part one contains the manuscript of a paper concerning a judging problem. Part two is concerned with finite Markov-chain theory amd discusses regular Markov chains, absorbing Markov chains, the classification of states, application to the Leontief input-output model, and semimartingales. Part three contains notes on game theory and covers matrix games, the effect of psychological attitudes on the outcomes of games, extensive games, amd matrix theory applied to mathematical economics. (auth)

Decentralized Patrolling Under Constraints in Dynamic Environments.

PubMed

Shaofei Chen; Feng Wu; Lincheng Shen; Jing Chen; Ramchurn, Sarvapali D

2016-12-01

We investigate a decentralized patrolling problem for dynamic environments where information is distributed alongside threats. In this problem, agents obtain information at a location, but may suffer attacks from the threat at that location. In a decentralized fashion, each agent patrols in a designated area of the environment and interacts with a limited number of agents. Therefore, the goal of these agents is to coordinate to gather as much information as possible while limiting the damage incurred. Hence, we model this class of problem as a transition-decoupled partially observable Markov decision process with health constraints. Furthermore, we propose scalable decentralized online algorithms based on Monte Carlo tree search and a factored belief vector. We empirically evaluate our algorithms on decentralized patrolling problems and benchmark them against the state-of-the-art online planning solver. The results show that our approach outperforms the state-of-the-art by more than 56% for six agents patrolling problems and can scale up to 24 agents in reasonable time.

Affective State Level Recognition in Naturalistic Facial and Vocal Expressions.

PubMed

Meng, Hongying; Bianchi-Berthouze, Nadia

2014-03-01

Naturalistic affective expressions change at a rate much slower than the typical rate at which video or audio is recorded. This increases the probability that consecutive recorded instants of expressions represent the same affective content. In this paper, we exploit such a relationship to improve the recognition performance of continuous naturalistic affective expressions. Using datasets of naturalistic affective expressions (AVEC 2011 audio and video dataset, PAINFUL video dataset) continuously labeled over time and over different dimensions, we analyze the transitions between levels of those dimensions (e.g., transitions in pain intensity level). We use an information theory approach to show that the transitions occur very slowly and hence suggest modeling them as first-order Markov models. The dimension levels are considered to be the hidden states in the Hidden Markov Model (HMM) framework. Their discrete transition and emission matrices are trained by using the labels provided with the training set. The recognition problem is converted into a best path-finding problem to obtain the best hidden states sequence in HMMs. This is a key difference from previous use of HMMs as classifiers. Modeling of the transitions between dimension levels is integrated in a multistage approach, where the first level performs a mapping between the affective expression features and a soft decision value (e.g., an affective dimension level), and further classification stages are modeled as HMMs that refine that mapping by taking into account the temporal relationships between the output decision labels. The experimental results for each of the unimodal datasets show overall performance to be significantly above that of a standard classification system that does not take into account temporal relationships. In particular, the results on the AVEC 2011 audio dataset outperform all other systems presented at the international competition.

Evaluation of linearly solvable Markov decision process with dynamic model learning in a mobile robot navigation task.

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

Linearly solvable Markov Decision Process (LMDP) is a class of optimal control problem in which the Bellman's equation can be converted into a linear equation by an exponential transformation of the state value function (Todorov, 2009b). In an LMDP, the optimal value function and the corresponding control policy are obtained by solving an eigenvalue problem in a discrete state space or an eigenfunction problem in a continuous state using the knowledge of the system dynamics and the action, state, and terminal cost functions. In this study, we evaluate the effectiveness of the LMDP framework in real robot control, in which the dynamics of the body and the environment have to be learned from experience. We first perform a simulation study of a pole swing-up task to evaluate the effect of the accuracy of the learned dynamics model on the derived the action policy. The result shows that a crude linear approximation of the non-linear dynamics can still allow solution of the task, despite with a higher total cost. We then perform real robot experiments of a battery-catching task using our Spring Dog mobile robot platform. The state is given by the position and the size of a battery in its camera view and two neck joint angles. The action is the velocities of two wheels, while the neck joints were controlled by a visual servo controller. We test linear and bilinear dynamic models in tasks with quadratic and Guassian state cost functions. In the quadratic cost task, the LMDP controller derived from a learned linear dynamics model performed equivalently with the optimal linear quadratic regulator (LQR). In the non-quadratic task, the LMDP controller with a linear dynamics model showed the best performance. The results demonstrate the usefulness of the LMDP framework in real robot control even when simple linear models are used for dynamics learning.

Analysing grouping of nucleotides in DNA sequences using lumped processes constructed from Markov chains.

PubMed

Guédon, Yann; d'Aubenton-Carafa, Yves; Thermes, Claude

2006-03-01

The most commonly used models for analysing local dependencies in DNA sequences are (high-order) Markov chains. Incorporating knowledge relative to the possible grouping of the nucleotides enables to define dedicated sub-classes of Markov chains. The problem of formulating lumpability hypotheses for a Markov chain is therefore addressed. In the classical approach to lumpability, this problem can be formulated as the determination of an appropriate state space (smaller than the original state space) such that the lumped chain defined on this state space retains the Markov property. We propose a different perspective on lumpability where the state space is fixed and the partitioning of this state space is represented by a one-to-many probabilistic function within a two-level stochastic process. Three nested classes of lumped processes can be defined in this way as sub-classes of first-order Markov chains. These lumped processes enable parsimonious reparameterizations of Markov chains that help to reveal relevant partitions of the state space. Characterizations of the lumped processes on the original transition probability matrix are derived. Different model selection methods relying either on hypothesis testing or on penalized log-likelihood criteria are presented as well as extensions to lumped processes constructed from high-order Markov chains. The relevance of the proposed approach to lumpability is illustrated by the analysis of DNA sequences. In particular, the use of lumped processes enables to highlight differences between intronic sequences and gene untranslated region sequences.

A simple formulation and solution to the replacement problem: a practical tool to assess the economic cow value, the value of a new pregnancy, and the cost of a pregnancy loss.

PubMed

Cabrera, V E

2012-08-01

This study contributes to the research literature by providing a new formulation for the cow replacement problem, and it also contributes to the Extension deliverables by providing a user-friendly decision support system tool that would more likely be adopted and applied for practical decision making. The cow value, its related values of a new pregnancy and a pregnancy loss, and their associated replacement policies determine profitability in dairy farming. One objective of this study was to present a simple, interactive, dynamic, and robust formulation of the cow value and the replacement problem, including expectancy of the future production of the cow and the genetic gain of the replacement. The proven hypothesis of this study was that all the above requirements could be achieved by using a Markov chain algorithm. The Markov chain model allowed (1) calculation of a forward expected value of a studied cow and its replacement; (2) use of a single model (the Markov chain) to calculate both the replacement policies and the herd statistics; (3) use of a predefined, preestablished farm reproductive replacement policy; (4) inclusion of a farmer's assessment of the expected future performance of a cow; (5) inclusion of a farmer's assessment of genetic gain with a replacement; and (6) use of a simple spreadsheet or an online system to implement the decision support system. Results clearly demonstrated that the decision policies found with the Markov chain model were consistent with more complex dynamic programming models. The final user-friendly decision support tool is available at http://dairymgt.info/ → Tools → The Economic Value of a Dairy Cow. This tool calculates the cow value instantaneously and is highly interactive, dynamic, and robust. When a Wisconsin dairy farm was studied using the model, the solution policy called for replacing nonpregnant cows 11 mo after calving or months in milk (MIM) if in the first lactation and 9 MIM if in later lactations. The cow value for an average second-lactation cow was as follows: (1) when nonpregnant, (a) $897 in MIM = 1 and (b) $68 in MIM = 8; (2) when the cow just became pregnant,(a) $889 for a pregnancy in MIM = 3 and (b) $298 for a pregnancy in MIM = 8; and (3) the value of a pregnancy loss when a cow became pregnant in MIM = 5 was (a) $221 when the loss was in the first month of pregnancy and (b) $897 when the loss was in the ninth month of pregnancy. The cow value indicated pregnant cows should be kept. The expected future production of a cow with respect to a similar average cow was an important determinant in the cow replacement decision. The expected production in the rest of the lactation was more important for nonpregnant cows, and the expected production in successive lactations was more important for pregnant cows. A 120% expected milk production for a cow with MIM = 16 and 6 mo pregnant in the present lactation or in successive lactations determined between 1.52 and 6.48 times the cow value, respectively, of an average production cow. The cow value decreased by $211 for every 1 percentage point of expected genetic gain of the replacement. A break-even analysis of the cow value with respect to expected milk production of an average second-parity cow indicated that (1) nonpregnant cows in MIM = 1 and 8 could still remain in the herd if they produced at least 84 and 98% in the present lactation or if they produced at least 78 and 97% in future lactations, respectively; and (2) cows becoming pregnant in MIM = 5 would require at least 64% of milk production in the rest of the lactation or 93% in successive lactations to remain in the herd. Copyright © 2012 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.

Hidden Markov models for character recognition.

PubMed

Vlontzos, J A; Kung, S Y

1992-01-01

A hierarchical system for character recognition with hidden Markov model knowledge sources which solve both the context sensitivity problem and the character instantiation problem is presented. The system achieves 97-99% accuracy using a two-level architecture and has been implemented using a systolic array, thus permitting real-time (1 ms per character) multifont and multisize printed character recognition as well as handwriting recognition.

Evaluation of Markov-Decision Model for Instructional Sequence Optimization. Semi-Annual Technical Report for the period 1 July-31 December 1975. Technical Report No. 76.

ERIC Educational Resources Information Center

Wollmer, Richard D.; Bond, Nicholas A.

Two computer-assisted instruction programs were written in electronics and trigonometry to test the Wollmer Markov Model for optimizing hierarchial learning; calibration samples totalling 110 students completed these programs. Since the model postulated that transfer effects would be a function of the amount of practice, half of the students were…

Optimal throughput for cognitive radio with energy harvesting in fading wireless channel.

PubMed

Vu-Van, Hiep; Koo, Insoo

2014-01-01

Energy resource management is a crucial problem of a device with a finite capacity battery. In this paper, cognitive radio is considered to be a device with an energy harvester that can harvest energy from a non-RF energy resource while performing other actions of cognitive radio. Harvested energy will be stored in a finite capacity battery. At the start of the time slot of cognitive radio, the radio needs to determine if it should remain silent or carry out spectrum sensing based on the idle probability of the primary user and the remaining energy in order to maximize the throughput of the cognitive radio system. In addition, optimal sensing energy and adaptive transmission power control are also investigated in this paper to effectively utilize the limited energy of cognitive radio. Finding an optimal approach is formulated as a partially observable Markov decision process. The simulation results show that the proposed optimal decision scheme outperforms the myopic scheme in which current throughput is only considered when making a decision.

Discriminative Learning with Markov Logic Networks

DTIC Science & Technology

2009-10-01

Discriminative Learning with Markov Logic Networks Tuyen N. Huynh Department of Computer Sciences University of Texas at Austin Austin, TX 78712...emerging area of research that addresses the problem of learning from noisy structured/relational data. Markov logic networks (MLNs), sets of weighted...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) University of Texas at Austin,Department of Computer

Making the Impossible Possible: Strategies for Fast POMDP Monitoring

NASA Technical Reports Server (NTRS)

Washington, Richard; Lau, Sonie (Technical Monitor)

1998-01-01

Systems modeled as partially observable Markov decision processes (POMDPs) can be tracked quickly with three restrictions: all actions are grouped together, the out-degree of each system state is bounded by a constant, and the number of non-zero elements in the belief state is bounded by a (different) constant. With these restrictions, the tracking algorithm operates in constant time and linear space. The first restriction assumes that the action itself is unobservable. The second restriction defines a subclass of POMDPs that covers however a wide range of problems. The third restriction is an approximation technique that can lead to a potentially vexing problem: an observation may be received that has probability according to the restricted belief state. This problem of impossibility will cause the belief state to collapse. In this paper we discuss the tradeoffs between the constant bound on the belief state and the quality of the solution. We concentrate on strategies for overcoming the impossibility problem and demonstrate initial experimental results that indicate promising directions.

Continuous-Time Semi-Markov Models in Health Economic Decision Making: An Illustrative Example in Heart Failure Disease Management.

PubMed

Cao, Qi; Buskens, Erik; Feenstra, Talitha; Jaarsma, Tiny; Hillege, Hans; Postmus, Douwe

2016-01-01

Continuous-time state transition models may end up having large unwieldy structures when trying to represent all relevant stages of clinical disease processes by means of a standard Markov model. In such situations, a more parsimonious, and therefore easier-to-grasp, model of a patient's disease progression can often be obtained by assuming that the future state transitions do not depend only on the present state (Markov assumption) but also on the past through time since entry in the present state. Despite that these so-called semi-Markov models are still relatively straightforward to specify and implement, they are not yet routinely applied in health economic evaluation to assess the cost-effectiveness of alternative interventions. To facilitate a better understanding of this type of model among applied health economic analysts, the first part of this article provides a detailed discussion of what the semi-Markov model entails and how such models can be specified in an intuitive way by adopting an approach called vertical modeling. In the second part of the article, we use this approach to construct a semi-Markov model for assessing the long-term cost-effectiveness of 3 disease management programs for heart failure. Compared with a standard Markov model with the same disease states, our proposed semi-Markov model fitted the observed data much better. When subsequently extrapolating beyond the clinical trial period, these relatively large differences in goodness-of-fit translated into almost a doubling in mean total cost and a 60-d decrease in mean survival time when using the Markov model instead of the semi-Markov model. For the disease process considered in our case study, the semi-Markov model thus provided a sensible balance between model parsimoniousness and computational complexity. © The Author(s) 2015.

Handling target obscuration through Markov chain observations

NASA Astrophysics Data System (ADS)

Kouritzin, Michael A.; Wu, Biao

2008-04-01

Target Obscuration, including foliage or building obscuration of ground targets and landscape or horizon obscuration of airborne targets, plagues many real world filtering problems. In particular, ground moving target identification Doppler radar, mounted on a surveillance aircraft or unattended airborne vehicle, is used to detect motion consistent with targets of interest. However, these targets try to obscure themselves (at least partially) by, for example, traveling along the edge of a forest or around buildings. This has the effect of creating random blockages in the Doppler radar image that move dynamically and somewhat randomly through this image. Herein, we address tracking problems with target obscuration by building memory into the observations, eschewing the usual corrupted, distorted partial measurement assumptions of filtering in favor of dynamic Markov chain assumptions. In particular, we assume the observations are a Markov chain whose transition probabilities depend upon the signal. The state of the observation Markov chain attempts to depict the current obscuration and the Markov chain dynamics are used to handle the evolution of the partially obscured radar image. Modifications of the classical filtering equations that allow observation memory (in the form of a Markov chain) are given. We use particle filters to estimate the position of the moving targets. Moreover, positive proof-of-concept simulations are included.

Applying Probabilistic Decision Models to Clinical Trial Design

PubMed Central

Smith, Wade P; Phillips, Mark H

2018-01-01

Clinical trial design most often focuses on a single or several related outcomes with corresponding calculations of statistical power. We consider a clinical trial to be a decision problem, often with competing outcomes. Using a current controversy in the treatment of HPV-positive head and neck cancer, we apply several different probabilistic methods to help define the range of outcomes given different possible trial designs. Our model incorporates the uncertainties in the disease process and treatment response and the inhomogeneities in the patient population. Instead of expected utility, we have used a Markov model to calculate quality adjusted life expectancy as a maximization objective. Monte Carlo simulations over realistic ranges of parameters are used to explore different trial scenarios given the possible ranges of parameters. This modeling approach can be used to better inform the initial trial design so that it will more likely achieve clinical relevance. PMID:29888075

Recommendation System for Adaptive Learning.

PubMed

Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang

2018-01-01

An adaptive learning system aims at providing instruction tailored to the current status of a learner, differing from the traditional classroom experience. The latest advances in technology make adaptive learning possible, which has the potential to provide students with high-quality learning benefit at a low cost. A key component of an adaptive learning system is a recommendation system, which recommends the next material (video lectures, practices, and so on, on different skills) to the learner, based on the psychometric assessment results and possibly other individual characteristics. An important question then follows: How should recommendations be made? To answer this question, a mathematical framework is proposed that characterizes the recommendation process as a Markov decision problem, for which decisions are made based on the current knowledge of the learner and that of the learning materials. In particular, two plain vanilla systems are introduced, for which the optimal recommendation at each stage can be obtained analytically.

State-dependent resource harvesting with lagged information about system states

USGS Publications Warehouse

Johnson, Fred A.; Fackler, Paul L.; Boomer, G Scott; Zimmerman, Guthrie S.; Williams, Byron K.; Nichols, James D.; Dorazio, Robert

2016-01-01

Markov decision processes (MDPs), which involve a temporal sequence of actions conditioned on the state of the managed system, are increasingly being applied in natural resource management. This study focuses on the modification of a traditional MDP to account for those cases in which an action must be chosen after a significant time lag in observing system state, but just prior to a new observation. In order to calculate an optimal decision policy under these conditions, possible actions must be conditioned on the previous observed system state and action taken. We show how to solve these problems when the state transition structure is known and when it is uncertain. Our focus is on the latter case, and we show how actions must be conditioned not only on the previous system state and action, but on the probabilities associated with alternative models of system dynamics. To demonstrate this framework, we calculated and simulated optimal, adaptive policies for MDPs with lagged states for the problem of deciding annual harvest regulations for mallards (Anas platyrhynchos) in the United States. In this particular example, changes in harvest policy induced by the use of lagged information about system state were sufficient to maintain expected management performance (e.g. population size, harvest) even in the face of an uncertain system state at the time of a decision.

Markov logic network based complex event detection under uncertainty

NASA Astrophysics Data System (ADS)

Lu, Jingyang; Jia, Bin; Chen, Genshe; Chen, Hua-mei; Sullivan, Nichole; Pham, Khanh; Blasch, Erik

2018-05-01

In a cognitive reasoning system, the four-stage Observe-Orient-Decision-Act (OODA) reasoning loop is of interest. The OODA loop is essential for the situational awareness especially in heterogeneous data fusion. Cognitive reasoning for making decisions can take advantage of different formats of information such as symbolic observations, various real-world sensor readings, or the relationship between intelligent modalities. Markov Logic Network (MLN) provides mathematically sound technique in presenting and fusing data at multiple levels of abstraction, and across multiple intelligent sensors to conduct complex decision-making tasks. In this paper, a scenario about vehicle interaction is investigated, in which uncertainty is taken into consideration as no systematic approaches can perfectly characterize the complex event scenario. MLNs are applied to the terrestrial domain where the dynamic features and relationships among vehicles are captured through multiple sensors and information sources regarding the data uncertainty.

When to stop managing or surveying cryptic threatened species

PubMed Central

Chadès, Iadine; McDonald-Madden, Eve; McCarthy, Michael A.; Wintle, Brendan; Linkie, Matthew; Possingham, Hugh P.

2008-01-01

Threatened species become increasingly difficult to detect as their populations decline. Managers of such cryptic threatened species face several dilemmas: if they are not sure the species is present, should they continue to manage for that species or invest the limited resources in surveying? We find optimal solutions to this problem using a Partially Observable Markov Decision Process and rules of thumb derived from an analytical approximation. We discover that managing a protected area for a cryptic threatened species can be optimal even if we are not sure the species is present. The more threatened and valuable the species is, relative to the costs of management, the more likely we are to manage this species without determining its continued persistence by using surveys. If a species remains unseen, our belief in the persistence of the species declines to a point where the optimal strategy is to shift resources from saving the species to surveying for it. Finally, when surveys lead to a sufficiently low belief that the species is extant, we surrender resources to other conservation actions. We illustrate our findings with a case study using parameters based on the critically endangered Sumatran tiger (Panthera tigris sumatrae), and we generate rules of thumb on how to allocate conservation effort for any cryptic species. Using Partially Observable Markov Decision Processes in conservation science, we determine the conditions under which it is better to abandon management for that species because our belief that it continues to exist is too low. PMID:18779594

When to stop managing or surveying cryptic threatened species.

PubMed

Chadès, Iadine; McDonald-Madden, Eve; McCarthy, Michael A; Wintle, Brendan; Linkie, Matthew; Possingham, Hugh P

2008-09-16

Threatened species become increasingly difficult to detect as their populations decline. Managers of such cryptic threatened species face several dilemmas: if they are not sure the species is present, should they continue to manage for that species or invest the limited resources in surveying? We find optimal solutions to this problem using a Partially Observable Markov Decision Process and rules of thumb derived from an analytical approximation. We discover that managing a protected area for a cryptic threatened species can be optimal even if we are not sure the species is present. The more threatened and valuable the species is, relative to the costs of management, the more likely we are to manage this species without determining its continued persistence by using surveys. If a species remains unseen, our belief in the persistence of the species declines to a point where the optimal strategy is to shift resources from saving the species to surveying for it. Finally, when surveys lead to a sufficiently low belief that the species is extant, we surrender resources to other conservation actions. We illustrate our findings with a case study using parameters based on the critically endangered Sumatran tiger (Panthera tigris sumatrae), and we generate rules of thumb on how to allocate conservation effort for any cryptic species. Using Partially Observable Markov Decision Processes in conservation science, we determine the conditions under which it is better to abandon management for that species because our belief that it continues to exist is too low.

Numerical research of the optimal control problem in the semi-Markov inventory model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorshenin, Andrey K.; Belousov, Vasily V.; Shnourkoff, Peter V.

2015-03-10

This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China☆

PubMed Central

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-01-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology. PMID:23554632

Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China.

PubMed

Peng, Zhihang; Bao, Changjun; Zhao, Yang; Yi, Honggang; Xia, Letian; Yu, Hao; Shen, Hongbing; Chen, Feng

2010-05-01

This paper first applies the sequential cluster method to set up the classification standard of infectious disease incidence state based on the fact that there are many uncertainty characteristics in the incidence course. Then the paper presents a weighted Markov chain, a method which is used to predict the future incidence state. This method assumes the standardized self-coefficients as weights based on the special characteristics of infectious disease incidence being a dependent stochastic variable. It also analyzes the characteristics of infectious diseases incidence via the Markov chain Monte Carlo method to make the long-term benefit of decision optimal. Our method is successfully validated using existing incidents data of infectious diseases in Jiangsu Province. In summation, this paper proposes ways to improve the accuracy of the weighted Markov chain, specifically in the field of infection epidemiology.

VAMPnets for deep learning of molecular kinetics.

PubMed

Mardt, Andreas; Pasquali, Luca; Wu, Hao; Noé, Frank

2018-01-02

There is an increasing demand for computing the relevant structures, equilibria, and long-timescale kinetics of biomolecular processes, such as protein-drug binding, from high-throughput molecular dynamics simulations. Current methods employ transformation of simulated coordinates into structural features, dimension reduction, clustering the dimension-reduced data, and estimation of a Markov state model or related model of the interconversion rates between molecular structures. This handcrafted approach demands a substantial amount of modeling expertise, as poor decisions at any step will lead to large modeling errors. Here we employ the variational approach for Markov processes (VAMP) to develop a deep learning framework for molecular kinetics using neural networks, dubbed VAMPnets. A VAMPnet encodes the entire mapping from molecular coordinates to Markov states, thus combining the whole data processing pipeline in a single end-to-end framework. Our method performs equally or better than state-of-the-art Markov modeling methods and provides easily interpretable few-state kinetic models.

An Application of Markov Chains and a Monte-Carlo Simulation to Decision-Making Behavior of an Educational Administrator

ERIC Educational Resources Information Center

Yoda, Koji

1973-01-01

Develops models to systematically forecast the tendency of an educational administrator in charge of personnel selection processes to shift from one decision strategy to another under generally stable environmental conditions. Urges further research on these processes by educational planners. (JF)

Current recommendations on the estimation of transition probabilities in Markov cohort models for use in health care decision-making: a targeted literature review.

PubMed

Olariu, Elena; Cadwell, Kevin K; Hancock, Elizabeth; Trueman, David; Chevrou-Severac, Helene

2017-01-01

Although Markov cohort models represent one of the most common forms of decision-analytic models used in health care decision-making, correct implementation of such models requires reliable estimation of transition probabilities. This study sought to identify consensus statements or guidelines that detail how such transition probability matrices should be estimated. A literature review was performed to identify relevant publications in the following databases: Medline, Embase, the Cochrane Library, and PubMed. Electronic searches were supplemented by manual-searches of health technology assessment (HTA) websites in Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and the UK. One reviewer assessed studies for eligibility. Of the 1,931 citations identified in the electronic searches, no studies met the inclusion criteria for full-text review, and no guidelines on transition probabilities in Markov models were identified. Manual-searching of the websites of HTA agencies identified ten guidelines on economic evaluations (Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and UK). All identified guidelines provided general guidance on how to develop economic models, but none provided guidance on the calculation of transition probabilities. One relevant publication was identified following review of the reference lists of HTA agency guidelines: the International Society for Pharmacoeconomics and Outcomes Research taskforce guidance. This provided limited guidance on the use of rates and probabilities. There is limited formal guidance available on the estimation of transition probabilities for use in decision-analytic models. Given the increasing importance of cost-effectiveness analysis in the decision-making processes of HTA bodies and other medical decision-makers, there is a need for additional guidance to inform a more consistent approach to decision-analytic modeling. Further research should be done to develop more detailed guidelines on the estimation of transition probabilities.

Unifying Temporal and Structural Credit Assignment Problems

NASA Technical Reports Server (NTRS)

Agogino, Adrian K.; Tumer, Kagan

2004-01-01

Single-agent reinforcement learners in time-extended domains and multi-agent systems share a common dilemma known as the credit assignment problem. Multi-agent systems have the structural credit assignment problem of determining the contributions of a particular agent to a common task. Instead, time-extended single-agent systems have the temporal credit assignment problem of determining the contribution of a particular action to the quality of the full sequence of actions. Traditionally these two problems are considered different and are handled in separate ways. In this article we show how these two forms of the credit assignment problem are equivalent. In this unified frame-work, a single-agent Markov decision process can be broken down into a single-time-step multi-agent process. Furthermore we show that Monte-Carlo estimation or Q-learning (depending on whether the values of resulting actions in the episode are known at the time of learning) are equivalent to different agent utility functions in a multi-agent system. This equivalence shows how an often neglected issue in multi-agent systems is equivalent to a well-known deficiency in multi-time-step learning and lays the basis for solving time-extended multi-agent problems, where both credit assignment problems are present.

A dynamic multi-scale Markov model based methodology for remaining life prediction

NASA Astrophysics Data System (ADS)

Yan, Jihong; Guo, Chaozhong; Wang, Xing

2011-05-01

The ability to accurately predict the remaining life of partially degraded components is crucial in prognostics. In this paper, a performance degradation index is designed using multi-feature fusion techniques to represent deterioration severities of facilities. Based on this indicator, an improved Markov model is proposed for remaining life prediction. Fuzzy C-Means (FCM) algorithm is employed to perform state division for Markov model in order to avoid the uncertainty of state division caused by the hard division approach. Considering the influence of both historical and real time data, a dynamic prediction method is introduced into Markov model by a weighted coefficient. Multi-scale theory is employed to solve the state division problem of multi-sample prediction. Consequently, a dynamic multi-scale Markov model is constructed. An experiment is designed based on a Bently-RK4 rotor testbed to validate the dynamic multi-scale Markov model, experimental results illustrate the effectiveness of the methodology.

Network Security Risk Assessment System Based on Attack Graph and Markov Chain

NASA Astrophysics Data System (ADS)

Sun, Fuxiong; Pi, Juntao; Lv, Jin; Cao, Tian

2017-10-01

Network security risk assessment technology can be found in advance of the network problems and related vulnerabilities, it has become an important means to solve the problem of network security. Based on attack graph and Markov chain, this paper provides a Network Security Risk Assessment Model (NSRAM). Based on the network infiltration tests, NSRAM generates the attack graph by the breadth traversal algorithm. Combines with the international standard CVSS, the attack probability of atomic nodes are counted, and then the attack transition probabilities of ones are calculated by Markov chain. NSRAM selects the optimal attack path after comprehensive measurement to assessment network security risk. The simulation results show that NSRAM can reflect the actual situation of network security objectively.

Sequential planning of flood protection infrastructure under limited historic flood record and climate change uncertainty

NASA Astrophysics Data System (ADS)

Dittes, Beatrice; Špačková, Olga; Straub, Daniel

2017-04-01

Flood protection is often designed to safeguard people and property following regulations and standards, which specify a target design flood protection level, such as the 100-year flood level prescribed in Germany (DWA, 2011). In practice, the magnitude of such an event is only known within a range of uncertainty, which is caused by limited historic records and uncertain climate change impacts, among other factors (Hall & Solomatine, 2008). As more observations and improved climate projections become available in the future, the design flood estimate changes and the capacity of the flood protection may be deemed insufficient at a future point in time. This problem can be mitigated by the implementation of flexible flood protection systems (that can easily be adjusted in the future) and/or by adding an additional reserve to the flood protection, i.e. by applying a safety factor to the design. But how high should such a safety factor be? And how much should the decision maker be willing to pay to make the system flexible, i.e. what is the Value of Flexibility (Špačková & Straub, 2017)? We propose a decision model that identifies cost-optimal decisions on flood protection capacity in the face of uncertainty (Dittes et al. 2017). It considers sequential adjustments of the protection system during its lifetime, taking into account its flexibility. The proposed framework is based on pre-posterior Bayesian decision analysis, using Decision Trees and Markov Decision Processes, and is fully quantitative. It can include a wide range of uncertainty components such as uncertainty associated with limited historic record or uncertain climate or socio-economic change. It is shown that since flexible systems are less costly to adjust when flood estimates are changing, they justify initially lower safety factors. Investigation on the Value of Flexibility (VoF) demonstrates that VoF depends on the type and degree of uncertainty, on the learning effect (i.e. kind and quality of information that we will gather in the future) and on the formulation of the optimization problem (risk-based vs. rule-based approach). The application of the framework is demonstrated on catchments in Germany. References: DWA (Deutsche Vereinigung für Wasserwirtschaft Abwasser und Abfall eV.) 2011. Merkblatt DWA-M 507-1: Deiche an Fließgewässern. (A. Bieberstein, Ed.). Hennef: DWA Deutsche Vereinigung für Wasserwirtschaft, Abwasser und Abfall e. V. Hall, J., & Solomatine, D. 2008. A framework for uncertainty analysis in flood risk management decisions. International Journal of River Basin Management, 6(2), 85-98. http://doi.org/10.1080/15715124.2008.9635339 Špačková, O. & Straub, D. 2017. Long-term adaption decisions via fully and partially observable Markov decision processes. Sustainable and Resilient Infrastructure. In print.

Resolvent-Techniques for Multiple Exercise Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christensen, Sören, E-mail: christensen@math.uni-kiel.de; Lempa, Jukka, E-mail: jukka.lempa@hioa.no

2015-02-15

We study optimal multiple stopping of strong Markov processes with random refraction periods. The refraction periods are assumed to be exponentially distributed with a common rate and independent of the underlying dynamics. Our main tool is using the resolvent operator. In the first part, we reduce infinite stopping problems to ordinary ones in a general strong Markov setting. This leads to explicit solutions for wide classes of such problems. Starting from this result, we analyze problems with finitely many exercise rights and explain solution methods for some classes of problems with underlying Lévy and diffusion processes, where the optimal characteristicsmore » of the problems can be identified more explicitly. We illustrate the main results with explicit examples.« less

An Approach for Dynamic Optimization of Prevention Program Implementation in Stochastic Environments

NASA Astrophysics Data System (ADS)

Kang, Yuncheol; Prabhu, Vittal

The science of preventing youth problems has significantly advanced in developing evidence-based prevention program (EBP) by using randomized clinical trials. Effective EBP can reduce delinquency, aggression, violence, bullying and substance abuse among youth. Unfortunately the outcomes of EBP implemented in natural settings usually tend to be lower than in clinical trials, which has motivated the need to study EBP implementations. In this paper we propose to model EBP implementations in natural settings as stochastic dynamic processes. Specifically, we propose Markov Decision Process (MDP) for modeling and dynamic optimization of such EBP implementations. We illustrate these concepts using simple numerical examples and discuss potential challenges in using such approaches in practice.

Efficient Learning of Continuous-Time Hidden Markov Models for Disease Progression

PubMed Central

Liu, Yu-Ying; Li, Shuang; Li, Fuxin; Song, Le; Rehg, James M.

2016-01-01

The Continuous-Time Hidden Markov Model (CT-HMM) is an attractive approach to modeling disease progression due to its ability to describe noisy observations arriving irregularly in time. However, the lack of an efficient parameter learning algorithm for CT-HMM restricts its use to very small models or requires unrealistic constraints on the state transitions. In this paper, we present the first complete characterization of efficient EM-based learning methods for CT-HMM models. We demonstrate that the learning problem consists of two challenges: the estimation of posterior state probabilities and the computation of end-state conditioned statistics. We solve the first challenge by reformulating the estimation problem in terms of an equivalent discrete time-inhomogeneous hidden Markov model. The second challenge is addressed by adapting three approaches from the continuous time Markov chain literature to the CT-HMM domain. We demonstrate the use of CT-HMMs with more than 100 states to visualize and predict disease progression using a glaucoma dataset and an Alzheimer’s disease dataset. PMID:27019571

A Markovian state-space framework for integrating flexibility into space system design decisions

NASA Astrophysics Data System (ADS)

Lafleur, Jarret M.

The past decades have seen the state of the art in aerospace system design progress from a scope of simple optimization to one including robustness, with the objective of permitting a single system to perform well even in off-nominal future environments. Integrating flexibility, or the capability to easily modify a system after it has been fielded in response to changing environments, into system design represents a further step forward. One challenge in accomplishing this rests in that the decision-maker must consider not only the present system design decision, but also sequential future design and operation decisions. Despite extensive interest in the topic, the state of the art in designing flexibility into aerospace systems, and particularly space systems, tends to be limited to analyses that are qualitative, deterministic, single-objective, and/or limited to consider a single future time period. To address these gaps, this thesis develops a stochastic, multi-objective, and multi-period framework for integrating flexibility into space system design decisions. Central to the framework are five steps. First, system configuration options are identified and costs of switching from one configuration to another are compiled into a cost transition matrix. Second, probabilities that demand on the system will transition from one mission to another are compiled into a mission demand Markov chain. Third, one performance matrix for each design objective is populated to describe how well the identified system configurations perform in each of the identified mission demand environments. The fourth step employs multi-period decision analysis techniques, including Markov decision processes from the field of operations research, to find efficient paths and policies a decision-maker may follow. The final step examines the implications of these paths and policies for the primary goal of informing initial system selection. Overall, this thesis unifies state-centric concepts of flexibility from economics and engineering literature with sequential decision-making techniques from operations research. The end objective of this thesis’ framework and its supporting tools is to enable selection of the next-generation space systems today, tailored to decision-maker budget and performance preferences, that will be best able to adapt and perform in a future of changing environments and requirements. Following extensive theoretical development, the framework and its steps are applied to space system planning problems of (1) DARPA-motivated multiple- or distributed-payload satellite selection and (2) NASA human space exploration architecture selection.

Economic Evaluations of Multicomponent Disease Management Programs with Markov Models: A Systematic Review.

PubMed

Kirsch, Florian

2016-12-01

Disease management programs (DMPs) for chronic diseases are being increasingly implemented worldwide. To present a systematic overview of the economic effects of DMPs with Markov models. The quality of the models is assessed, the method by which the DMP intervention is incorporated into the model is examined, and the differences in the structure and data used in the models are considered. A literature search was conducted; the Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement was followed to ensure systematic selection of the articles. Study characteristics e.g. results, the intensity of the DMP and usual care, model design, time horizon, discount rates, utility measures, and cost-of-illness were extracted from the reviewed studies. Model quality was assessed by two researchers with two different appraisals: one proposed by Philips et al. (Good practice guidelines for decision-analytic modelling in health technology assessment: a review and consolidation of quality asessment. Pharmacoeconomics 2006;24:355-71) and the other proposed by Caro et al. (Questionnaire to assess relevance and credibility of modeling studies for informing health care decision making: an ISPOR-AMCP-NPC Good Practice Task Force report. Value Health 2014;17:174-82). A total of 16 studies (9 on chronic heart disease, 2 on asthma, and 5 on diabetes) met the inclusion criteria. Five studies reported cost savings and 11 studies reported additional costs. In the quality, the overall score of the models ranged from 39% to 65%, it ranged from 34% to 52%. Eleven models integrated effectiveness derived from a clinical trial or a meta-analysis of complete DMPs and only five models combined intervention effects from different sources into a DMP. The main limitations of the models are bad reporting practice and the variation in the selection of input parameters. Eleven of the 14 studies reported cost-effectiveness results of less than $30,000 per quality-adjusted life-year and the remaining two studies less than $30,000 per life-year gained. Nevertheless, if the reporting and selection of data problems are addressed, then Markov models should provide more reliable information for decision makers, because understanding under what circumstances a DMP is cost-effective is an important determinant of efficient resource allocation. Copyright © 2016 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Enrollment Planning Using Computer Decision Model: A Case Study at Grambling State University.

ERIC Educational Resources Information Center

Ghosh, Kalyan; Lundy, Harold W.

Achieving enrollment goals continues to be a major administrative concern in higher education. Enrollment management can be assisted through the use of computerized planning and forecast models. Although commercially available Markov transition type curve fitting models have been developed and used, a microcomputer-based decision planning model…

A baker's dozen of new particle flows for nonlinear filters, Bayesian decisions and transport

NASA Astrophysics Data System (ADS)

Daum, Fred; Huang, Jim

2015-05-01

We describe a baker's dozen of new particle flows to compute Bayes' rule for nonlinear filters, Bayesian decisions and learning as well as transport. Several of these new flows were inspired by transport theory, but others were inspired by physics or statistics or Markov chain Monte Carlo methods.

Hierarchical structure for audio-video based semantic classification of sports video sequences

NASA Astrophysics Data System (ADS)

Kolekar, M. H.; Sengupta, S.

2005-07-01

A hierarchical structure for sports event classification based on audio and video content analysis is proposed in this paper. Compared to the event classifications in other games, those of cricket are very challenging and yet unexplored. We have successfully solved cricket video classification problem using a six level hierarchical structure. The first level performs event detection based on audio energy and Zero Crossing Rate (ZCR) of short-time audio signal. In the subsequent levels, we classify the events based on video features using a Hidden Markov Model implemented through Dynamic Programming (HMM-DP) using color or motion as a likelihood function. For some of the game-specific decisions, a rule-based classification is also performed. Our proposed hierarchical structure can easily be applied to any other sports. Our results are very promising and we have moved a step forward towards addressing semantic classification problems in general.

Algorithms for Discovery of Multiple Markov Boundaries

PubMed Central

Statnikov, Alexander; Lytkin, Nikita I.; Lemeire, Jan; Aliferis, Constantin F.

2013-01-01

Algorithms for Markov boundary discovery from data constitute an important recent development in machine learning, primarily because they offer a principled solution to the variable/feature selection problem and give insight on local causal structure. Over the last decade many sound algorithms have been proposed to identify a single Markov boundary of the response variable. Even though faithful distributions and, more broadly, distributions that satisfy the intersection property always have a single Markov boundary, other distributions/data sets may have multiple Markov boundaries of the response variable. The latter distributions/data sets are common in practical data-analytic applications, and there are several reasons why it is important to induce multiple Markov boundaries from such data. However, there are currently no sound and efficient algorithms that can accomplish this task. This paper describes a family of algorithms TIE* that can discover all Markov boundaries in a distribution. The broad applicability as well as efficiency of the new algorithmic family is demonstrated in an extensive benchmarking study that involved comparison with 26 state-of-the-art algorithms/variants in 15 data sets from a diversity of application domains. PMID:25285052

Reinforcement learning for resource allocation in LEO satellite networks.

PubMed

Usaha, Wipawee; Barria, Javier A

2007-06-01

In this paper, we develop and assess online decision-making algorithms for call admission and routing for low Earth orbit (LEO) satellite networks. It has been shown in a recent paper that, in a LEO satellite system, a semi-Markov decision process formulation of the call admission and routing problem can achieve better performance in terms of an average revenue function than existing routing methods. However, the conventional dynamic programming (DP) numerical solution becomes prohibited as the problem size increases. In this paper, two solution methods based on reinforcement learning (RL) are proposed in order to circumvent the computational burden of DP. The first method is based on an actor-critic method with temporal-difference (TD) learning. The second method is based on a critic-only method, called optimistic TD learning. The algorithms enhance performance in terms of requirements in storage, computational complexity and computational time, and in terms of an overall long-term average revenue function that penalizes blocked calls. Numerical studies are carried out, and the results obtained show that the RL framework can achieve up to 56% higher average revenue over existing routing methods used in LEO satellite networks with reasonable storage and computational requirements.

Phasic Triplet Markov Chains.

PubMed

El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar

2014-11-01

Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.

Invited commentary: Lost in estimation--searching for alternatives to markov chains to fit complex Bayesian models.

PubMed

Molitor, John

2012-03-01

Bayesian methods have seen an increase in popularity in a wide variety of scientific fields, including epidemiology. One of the main reasons for their widespread application is the power of the Markov chain Monte Carlo (MCMC) techniques generally used to fit these models. As a result, researchers often implicitly associate Bayesian models with MCMC estimation procedures. However, Bayesian models do not always require Markov-chain-based methods for parameter estimation. This is important, as MCMC estimation methods, while generally quite powerful, are complex and computationally expensive and suffer from convergence problems related to the manner in which they generate correlated samples used to estimate probability distributions for parameters of interest. In this issue of the Journal, Cole et al. (Am J Epidemiol. 2012;175(5):368-375) present an interesting paper that discusses non-Markov-chain-based approaches to fitting Bayesian models. These methods, though limited, can overcome some of the problems associated with MCMC techniques and promise to provide simpler approaches to fitting Bayesian models. Applied researchers will find these estimation approaches intuitively appealing and will gain a deeper understanding of Bayesian models through their use. However, readers should be aware that other non-Markov-chain-based methods are currently in active development and have been widely published in other fields.

Hidden Markov models and other machine learning approaches in computational molecular biology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldi, P.

1995-12-31

This tutorial was one of eight tutorials selected to be presented at the Third International Conference on Intelligent Systems for Molecular Biology which was held in the United Kingdom from July 16 to 19, 1995. Computational tools are increasingly needed to process the massive amounts of data, to organize and classify sequences, to detect weak similarities, to separate coding from non-coding regions, and reconstruct the underlying evolutionary history. The fundamental problem in machine learning is the same as in scientific reasoning in general, as well as statistical modeling: to come up with a good model for the data. In thismore » tutorial four classes of models are reviewed. They are: Hidden Markov models; artificial Neural Networks; Belief Networks; and Stochastic Grammars. When dealing with DNA and protein primary sequences, Hidden Markov models are one of the most flexible and powerful alignments and data base searches. In this tutorial, attention is focused on the theory of Hidden Markov Models, and how to apply them to problems in molecular biology.« less

A clustering-based graph Laplacian framework for value function approximation in reinforcement learning.

PubMed

Xu, Xin; Huang, Zhenhua; Graves, Daniel; Pedrycz, Witold

2014-12-01

In order to deal with the sequential decision problems with large or continuous state spaces, feature representation and function approximation have been a major research topic in reinforcement learning (RL). In this paper, a clustering-based graph Laplacian framework is presented for feature representation and value function approximation (VFA) in RL. By making use of clustering-based techniques, that is, K-means clustering or fuzzy C-means clustering, a graph Laplacian is constructed by subsampling in Markov decision processes (MDPs) with continuous state spaces. The basis functions for VFA can be automatically generated from spectral analysis of the graph Laplacian. The clustering-based graph Laplacian is integrated with a class of approximation policy iteration algorithms called representation policy iteration (RPI) for RL in MDPs with continuous state spaces. Simulation and experimental results show that, compared with previous RPI methods, the proposed approach needs fewer sample points to compute an efficient set of basis functions and the learning control performance can be improved for a variety of parameter settings.

Timing of testing and treatment for asymptomatic diseases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kırkızlar, Eser; Faissol, Daniel M.; Griffin, Paul M.

2010-07-01

Many papers in the medical literature analyze the cost-effectiveness of screening for diseases by comparing a limited number of a priori testing policies under estimated problem parameters. However, this may be insufficient to determine the best timing of the tests or incorporate changes over time. In this paper, we develop and solve a Markov Decision Process (MDP) model for a simple class of asymptomatic diseases in order to provide the building blocks for analysis of a more general class of diseases. We provide a computationally efficient method for determining a cost-effective dynamic intervention strategy that takes into account (i) themore » results of the previous test for each individual and (ii) the change in the individual’s behavior based on awareness of the disease. We demonstrate the usefulness of the approach by applying the results to screening decisions for Hepatitis C (HCV) using medical data, and compare our findings to current HCV screening recommendations.« less

Probabilistic sensitivity analysis for decision trees with multiple branches: use of the Dirichlet distribution in a Bayesian framework.

PubMed

Briggs, Andrew H; Ades, A E; Price, Martin J

2003-01-01

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Current guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately represents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

A Hidden Markov Model Approach to the Problem of Heuristic Selection in Hyper-Heuristics with a Case Study in High School Timetabling Problems.

PubMed

Kheiri, Ahmed; Keedwell, Ed

2017-01-01

Operations research is a well-established field that uses computational systems to support decisions in business and public life. Good solutions to operations research problems can make a large difference to the efficient running of businesses and organisations and so the field often searches for new methods to improve these solutions. The high school timetabling problem is an example of an operations research problem and is a challenging task which requires assigning events and resources to time slots subject to a set of constraints. In this article, a new sequence-based selection hyper-heuristic is presented that produces excellent results on a suite of high school timetabling problems. In this study, we present an easy-to-implement, easy-to-maintain, and effective sequence-based selection hyper-heuristic to solve high school timetabling problems using a benchmark of unified real-world instances collected from different countries. We show that with sequence-based methods, it is possible to discover new best known solutions for a number of the problems in the timetabling domain. Through this investigation, the usefulness of sequence-based selection hyper-heuristics has been demonstrated and the capability of these methods has been shown to exceed the state of the art.

Modeling the value for money of changing clinical practice change: a stochastic application in diabetes care.

PubMed

Hoomans, Ties; Abrams, Keith R; Ament, Andre J H A; Evers, Silvia M A A; Severens, Johan L

2009-10-01

Decision making about resource allocation for guideline implementation to change clinical practice is inevitably undertaken in a context of uncertainty surrounding the cost-effectiveness of both clinical guidelines and implementation strategies. Adopting a total net benefit approach, a model was recently developed to overcome problems with the use of combined ratio statistics when analyzing decision uncertainty. To demonstrate the stochastic application of the model for informing decision making about the adoption of an audit and feedback strategy for implementing a guideline recommending intensive blood glucose control in type 2 diabetes in primary care in the Netherlands. An integrated Bayesian approach to decision modeling and evidence synthesis is adopted, using Markov Chain Monte Carlo simulation in WinBUGs. Data on model parameters is gathered from various sources, with effectiveness of implementation being estimated using pooled, random-effects meta-analysis. Decision uncertainty is illustrated using cost-effectiveness acceptability curves and frontier. Decisions about whether to adopt intensified glycemic control and whether to adopt audit and feedback alter for the maximum values that decision makers are willing to pay for health gain. Through simultaneously incorporating uncertain economic evidence on both guidance and implementation strategy, the cost-effectiveness acceptability curves and cost-effectiveness acceptability frontier show an increase in decision uncertainty concerning guideline implementation. The stochastic application in diabetes care demonstrates that the model provides a simple and useful tool for quantifying and exploring the (combined) uncertainty associated with decision making about adopting guidelines and implementation strategies and, therefore, for informing decisions about efficient resource allocation to change clinical practice.

Markov and non-Markov processes in complex systems by the dynamical information entropy

NASA Astrophysics Data System (ADS)

Yulmetyev, R. M.; Gafarov, F. M.

1999-12-01

We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.

Markov chains for testing redundant software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1988-01-01

A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.

Counting of oligomers in sequences generated by markov chains for DNA motif discovery.

PubMed

Shan, Gao; Zheng, Wei-Mou

2009-02-01

By means of the technique of the imbedded Markov chain, an efficient algorithm is proposed to exactly calculate first, second moments of word counts and the probability for a word to occur at least once in random texts generated by a Markov chain. A generating function is introduced directly from the imbedded Markov chain to derive asymptotic approximations for the problem. Two Z-scores, one based on the number of sequences with hits and the other on the total number of word hits in a set of sequences, are examined for discovery of motifs on a set of promoter sequences extracted from A. thaliana genome. Source code is available at http://www.itp.ac.cn/zheng/oligo.c.

Robust Satisficing Decision Making for Unmanned Aerial Vehicle Complex Missions under Severe Uncertainty

PubMed Central

Ji, Xiaoting; Niu, Yifeng; Shen, Lincheng

2016-01-01

This paper presents a robust satisficing decision-making method for Unmanned Aerial Vehicles (UAVs) executing complex missions in an uncertain environment. Motivated by the info-gap decision theory, we formulate this problem as a novel robust satisficing optimization problem, of which the objective is to maximize the robustness while satisfying some desired mission requirements. Specifically, a new info-gap based Markov Decision Process (IMDP) is constructed to abstract the uncertain UAV system and specify the complex mission requirements with the Linear Temporal Logic (LTL). A robust satisficing policy is obtained to maximize the robustness to the uncertain IMDP while ensuring a desired probability of satisfying the LTL specifications. To this end, we propose a two-stage robust satisficing solution strategy which consists of the construction of a product IMDP and the generation of a robust satisficing policy. In the first stage, a product IMDP is constructed by combining the IMDP with an automaton representing the LTL specifications. In the second, an algorithm based on robust dynamic programming is proposed to generate a robust satisficing policy, while an associated robustness evaluation algorithm is presented to evaluate the robustness. Finally, through Monte Carlo simulation, the effectiveness of our algorithms is demonstrated on an UAV search mission under severe uncertainty so that the resulting policy can maximize the robustness while reaching the desired performance level. Furthermore, by comparing the proposed method with other robust decision-making methods, it can be concluded that our policy can tolerate higher uncertainty so that the desired performance level can be guaranteed, which indicates that the proposed method is much more effective in real applications. PMID:27835670

Robust Satisficing Decision Making for Unmanned Aerial Vehicle Complex Missions under Severe Uncertainty.

PubMed

Ji, Xiaoting; Niu, Yifeng; Shen, Lincheng

2016-01-01

This paper presents a robust satisficing decision-making method for Unmanned Aerial Vehicles (UAVs) executing complex missions in an uncertain environment. Motivated by the info-gap decision theory, we formulate this problem as a novel robust satisficing optimization problem, of which the objective is to maximize the robustness while satisfying some desired mission requirements. Specifically, a new info-gap based Markov Decision Process (IMDP) is constructed to abstract the uncertain UAV system and specify the complex mission requirements with the Linear Temporal Logic (LTL). A robust satisficing policy is obtained to maximize the robustness to the uncertain IMDP while ensuring a desired probability of satisfying the LTL specifications. To this end, we propose a two-stage robust satisficing solution strategy which consists of the construction of a product IMDP and the generation of a robust satisficing policy. In the first stage, a product IMDP is constructed by combining the IMDP with an automaton representing the LTL specifications. In the second, an algorithm based on robust dynamic programming is proposed to generate a robust satisficing policy, while an associated robustness evaluation algorithm is presented to evaluate the robustness. Finally, through Monte Carlo simulation, the effectiveness of our algorithms is demonstrated on an UAV search mission under severe uncertainty so that the resulting policy can maximize the robustness while reaching the desired performance level. Furthermore, by comparing the proposed method with other robust decision-making methods, it can be concluded that our policy can tolerate higher uncertainty so that the desired performance level can be guaranteed, which indicates that the proposed method is much more effective in real applications.

A Modularized Efficient Framework for Non-Markov Time Series Estimation

NASA Astrophysics Data System (ADS)

Schamberg, Gabriel; Ba, Demba; Coleman, Todd P.

2018-06-01

We present a compartmentalized approach to finding the maximum a-posteriori (MAP) estimate of a latent time series that obeys a dynamic stochastic model and is observed through noisy measurements. We specifically consider modern signal processing problems with non-Markov signal dynamics (e.g. group sparsity) and/or non-Gaussian measurement models (e.g. point process observation models used in neuroscience). Through the use of auxiliary variables in the MAP estimation problem, we show that a consensus formulation of the alternating direction method of multipliers (ADMM) enables iteratively computing separate estimates based on the likelihood and prior and subsequently "averaging" them in an appropriate sense using a Kalman smoother. As such, this can be applied to a broad class of problem settings and only requires modular adjustments when interchanging various aspects of the statistical model. Under broad log-concavity assumptions, we show that the separate estimation problems are convex optimization problems and that the iterative algorithm converges to the MAP estimate. As such, this framework can capture non-Markov latent time series models and non-Gaussian measurement models. We provide example applications involving (i) group-sparsity priors, within the context of electrophysiologic specrotemporal estimation, and (ii) non-Gaussian measurement models, within the context of dynamic analyses of learning with neural spiking and behavioral observations.

Quicker Q-Learning in Multi-Agent Systems

NASA Technical Reports Server (NTRS)

Agogino, Adrian K.; Tumer, Kagan

2005-01-01

Multi-agent learning in Markov Decisions Problems is challenging because of the presence ot two credit assignment problems: 1) How to credit an action taken at time step t for rewards received at t' greater than t; and 2) How to credit an action taken by agent i considering the system reward is a function of the actions of all the agents. The first credit assignment problem is typically addressed with temporal difference methods such as Q-learning OK TD(lambda) The second credit assi,onment problem is typically addressed either by hand-crafting reward functions that assign proper credit to an agent, or by making certain independence assumptions about an agent's state-space and reward function. To address both credit assignment problems simultaneously, we propose the Q Updates with Immediate Counterfactual Rewards-learning (QUICR-learning) designed to improve both the convergence properties and performance of Q-learning in large multi-agent problems. Instead of assuming that an agent s value function can be made independent of other agents, this method suppresses the impact of other agents using counterfactual rewards. Results on multi-agent grid-world problems over multiple topologies show that QUICR-learning can achieve up to thirty fold improvements in performance over both conventional and local Q-learning in the largest tested systems.

Variable context Markov chains for HIV protease cleavage site prediction.

PubMed

Oğul, Hasan

2009-06-01

Deciphering the knowledge of HIV protease specificity and developing computational tools for detecting its cleavage sites in protein polypeptide chain are very desirable for designing efficient and specific chemical inhibitors to prevent acquired immunodeficiency syndrome. In this study, we developed a generative model based on a generalization of variable order Markov chains (VOMC) for peptide sequences and adapted the model for prediction of their cleavability by certain proteases. The new method, called variable context Markov chains (VCMC), attempts to identify the context equivalence based on the evolutionary similarities between individual amino acids. It was applied for HIV-1 protease cleavage site prediction problem and shown to outperform existing methods in terms of prediction accuracy on a common dataset. In general, the method is a promising tool for prediction of cleavage sites of all proteases and encouraged to be used for any kind of peptide classification problem as well.

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Tracking problem solving by multivariate pattern analysis and Hidden Markov Model algorithms.

PubMed

Anderson, John R

2012-03-01

Multivariate pattern analysis can be combined with Hidden Markov Model algorithms to track the second-by-second thinking as people solve complex problems. Two applications of this methodology are illustrated with a data set taken from children as they interacted with an intelligent tutoring system for algebra. The first "mind reading" application involves using fMRI activity to track what students are doing as they solve a sequence of algebra problems. The methodology achieves considerable accuracy at determining both what problem-solving step the students are taking and whether they are performing that step correctly. The second "model discovery" application involves using statistical model evaluation to determine how many substates are involved in performing a step of algebraic problem solving. This research indicates that different steps involve different numbers of substates and these substates are associated with different fluency in algebra problem solving. Copyright © 2011 Elsevier Ltd. All rights reserved.

Nonparametric model validations for hidden Markov models with applications in financial econometrics.

PubMed

Zhao, Zhibiao

2011-06-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise.

Markov Chain Model with Catastrophe to Determine Mean Time to Default of Credit Risky Assets

NASA Astrophysics Data System (ADS)

Dharmaraja, Selvamuthu; Pasricha, Puneet; Tardelli, Paola

2017-11-01

This article deals with the problem of probabilistic prediction of the time distance to default for a firm. To model the credit risk, the dynamics of an asset is described as a function of a homogeneous discrete time Markov chain subject to a catastrophe, the default. The behaviour of the Markov chain is investigated and the mean time to the default is expressed in a closed form. The methodology to estimate the parameters is given. Numerical results are provided to illustrate the applicability of the proposed model on real data and their analysis is discussed.

Markov Chains for Investigating and Predicting Migration: A Case from Southwestern China

NASA Astrophysics Data System (ADS)

Qin, Bo; Wang, Yiyu; Xu, Haoming

2018-03-01

In order to accurately predict the population’s happiness, this paper conducted two demographic surveys on a new district of a city in western China, and carried out a dynamic analysis using related mathematical methods. This paper argues that the migration of migrants in the city will change the pattern of spatial distribution of human resources in the city and thus affect the social and economic development in all districts. The migration status of the population will change randomly with the passage of time, so it can be predicted and analyzed through the Markov process. The Markov process provides the local government and decision-making bureau a valid basis for the dynamic analysis of the mobility of migrants in the city as well as the ways for promoting happiness of local people’s lives.

Radiative transfer calculated from a Markov chain formalism

NASA Technical Reports Server (NTRS)

Esposito, L. W.; House, L. L.

1978-01-01

The theory of Markov chains is used to formulate the radiative transport problem in a general way by modeling the successive interactions of a photon as a stochastic process. Under the minimal requirement that the stochastic process is a Markov chain, the determination of the diffuse reflection or transmission from a scattering atmosphere is equivalent to the solution of a system of linear equations. This treatment is mathematically equivalent to, and thus has many of the advantages of, Monte Carlo methods, but can be considerably more rapid than Monte Carlo algorithms for numerical calculations in particular applications. We have verified the speed and accuracy of this formalism for the standard problem of finding the intensity of scattered light from a homogeneous plane-parallel atmosphere with an arbitrary phase function for scattering. Accurate results over a wide range of parameters were obtained with computation times comparable to those of a standard 'doubling' routine. The generality of this formalism thus allows fast, direct solutions to problems that were previously soluble only by Monte Carlo methods. Some comparisons are made with respect to integral equation methods.

Block-accelerated aggregation multigrid for Markov chains with application to PageRank problems

NASA Astrophysics Data System (ADS)

Shen, Zhao-Li; Huang, Ting-Zhu; Carpentieri, Bruno; Wen, Chun; Gu, Xian-Ming

2018-06-01

Recently, the adaptive algebraic aggregation multigrid method has been proposed for computing stationary distributions of Markov chains. This method updates aggregates on every iterative cycle to keep high accuracies of coarse-level corrections. Accordingly, its fast convergence rate is well guaranteed, but often a large proportion of time is cost by aggregation processes. In this paper, we show that the aggregates on each level in this method can be utilized to transfer the probability equation of that level into a block linear system. Then we propose a Block-Jacobi relaxation that deals with the block system on each level to smooth error. Some theoretical analysis of this technique is presented, meanwhile it is also adapted to solve PageRank problems. The purpose of this technique is to accelerate the adaptive aggregation multigrid method and its variants for solving Markov chains and PageRank problems. It also attempts to shed some light on new solutions for making aggregation processes more cost-effective for aggregation multigrid methods. Numerical experiments are presented to illustrate the effectiveness of this technique.

Markov Chains For Testing Redundant Software

NASA Technical Reports Server (NTRS)

White, Allan L.; Sjogren, Jon A.

1990-01-01

Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.

Pavement maintenance optimization model using Markov Decision Processes

NASA Astrophysics Data System (ADS)

Mandiartha, P.; Duffield, C. F.; Razelan, I. S. b. M.; Ismail, A. b. H.

2017-09-01

This paper presents an optimization model for selection of pavement maintenance intervention using a theory of Markov Decision Processes (MDP). There are some particular characteristics of the MDP developed in this paper which distinguish it from other similar studies or optimization models intended for pavement maintenance policy development. These unique characteristics include a direct inclusion of constraints into the formulation of MDP, the use of an average cost method of MDP, and the policy development process based on the dual linear programming solution. The limited information or discussions that are available on these matters in terms of stochastic based optimization model in road network management motivates this study. This paper uses a data set acquired from road authorities of state of Victoria, Australia, to test the model and recommends steps in the computation of MDP based stochastic optimization model, leading to the development of optimum pavement maintenance policy.

A methodology for stochastic analysis of share prices as Markov chains with finite states.

PubMed

Mettle, Felix Okoe; Quaye, Enoch Nii Boi; Laryea, Ravenhill Adjetey

2014-01-01

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

The fusion of large scale classified side-scan sonar image mosaics.

PubMed

Reed, Scott; Tena, Ruiz Ioseba; Capus, Chris; Petillot, Yvan

2006-07-01

This paper presents a unified framework for the creation of classified maps of the seafloor from sonar imagery. Significant challenges in photometric correction, classification, navigation and registration, and image fusion are addressed. The techniques described are directly applicable to a range of remote sensing problems. Recent advances in side-scan data correction are incorporated to compensate for the sonar beam pattern and motion of the acquisition platform. The corrected images are segmented using pixel-based textural features and standard classifiers. In parallel, the navigation of the sonar device is processed using Kalman filtering techniques. A simultaneous localization and mapping framework is adopted to improve the navigation accuracy and produce georeferenced mosaics of the segmented side-scan data. These are fused within a Markovian framework and two fusion models are presented. The first uses a voting scheme regularized by an isotropic Markov random field and is applicable when the reliability of each information source is unknown. The Markov model is also used to inpaint regions where no final classification decision can be reached using pixel level fusion. The second model formally introduces the reliability of each information source into a probabilistic model. Evaluation of the two models using both synthetic images and real data from a large scale survey shows significant quantitative and qualitative improvement using the fusion approach.

GMDPtoolbox: A Matlab library for designing spatial management policies. Application to the long-term collective management of an airborne disease

PubMed Central

Aubertot, Jean-Noël; Peyrard, Nathalie; Sabbadin, Régis

2017-01-01

Designing management policies in ecology and agroecology is complex. Several components must be managed together while they strongly interact spatially. Decision choices must be made under uncertainty on the results of the actions and on the system dynamics. Furthermore, the objectives pursued when managing ecological systems or agroecosystems are usually long term objectives, such as biodiversity conservation or sustainable crop production. The framework of Graph-Based Markov Decision Processes (GMDP) is well adapted to the qualitative modeling of such problems of sequential decision under uncertainty. Spatial interactions are easily modeled and integrated control policies (combining several action levers) can be designed through optimization. The provided policies are adaptive, meaning that management actions are decided at each time step (for instance yearly) and the chosen actions depend on the current system state. This framework has already been successfully applied to forest management and invasive species management. However, up to now, no “easy-to-use” implementation of this framework was available. We present GMDPtoolbox, a Matlab toolbox which can be used both for the design of new management policies and for comparing policies by simulation. We provide an illustration of the use of the toolbox on a realistic crop disease management problem: the design of long term management policy of blackleg of canola using an optimal combination of three possible cultural levers. This example shows how GMDPtoolbox can be used as a tool to support expert thinking. PMID:28982151

GMDPtoolbox: A Matlab library for designing spatial management policies. Application to the long-term collective management of an airborne disease.

PubMed

Cros, Marie-Josée; Aubertot, Jean-Noël; Peyrard, Nathalie; Sabbadin, Régis

2017-01-01

Designing management policies in ecology and agroecology is complex. Several components must be managed together while they strongly interact spatially. Decision choices must be made under uncertainty on the results of the actions and on the system dynamics. Furthermore, the objectives pursued when managing ecological systems or agroecosystems are usually long term objectives, such as biodiversity conservation or sustainable crop production. The framework of Graph-Based Markov Decision Processes (GMDP) is well adapted to the qualitative modeling of such problems of sequential decision under uncertainty. Spatial interactions are easily modeled and integrated control policies (combining several action levers) can be designed through optimization. The provided policies are adaptive, meaning that management actions are decided at each time step (for instance yearly) and the chosen actions depend on the current system state. This framework has already been successfully applied to forest management and invasive species management. However, up to now, no "easy-to-use" implementation of this framework was available. We present GMDPtoolbox, a Matlab toolbox which can be used both for the design of new management policies and for comparing policies by simulation. We provide an illustration of the use of the toolbox on a realistic crop disease management problem: the design of long term management policy of blackleg of canola using an optimal combination of three possible cultural levers. This example shows how GMDPtoolbox can be used as a tool to support expert thinking.

Resolving structural uncertainty in natural resources management using POMDP approaches

USGS Publications Warehouse

Williams, B.K.

2011-01-01

In recent years there has been a growing focus on the uncertainties of natural resources management, and the importance of accounting for uncertainty in assessing management effectiveness. This paper focuses on uncertainty in resource management in terms of discrete-state Markov decision processes (MDP) under structural uncertainty and partial observability. It describes the treatment of structural uncertainty with approaches developed for partially observable resource systems. In particular, I show how value iteration for partially observable MDPs (POMDP) can be extended to structurally uncertain MDPs. A key difference between these process classes is that structurally uncertain MDPs require the tracking of system state as well as a probability structure for the structure uncertainty, whereas with POMDPs require only a probability structure for the observation uncertainty. The added complexity of the optimization problem under structural uncertainty is compensated by reduced dimensionality in the search for optimal strategy. A solution algorithm for structurally uncertain processes is outlined for a simple example in conservation biology. By building on the conceptual framework developed for POMDPs, natural resource analysts and decision makers who confront structural uncertainties in natural resources can take advantage of the rapid growth in POMDP methods and approaches, and thereby produce better conservation strategies over a larger class of resource problems. ?? 2011.

Solving problems by interrogating sets of knowledge systems: Toward a theory of multiple knowledge systems

NASA Technical Reports Server (NTRS)

Dekorvin, Andre

1989-01-01

The main purpose is to develop a theory for multiple knowledge systems. A knowledge system could be a sensor or an expert system, but it must specialize in one feature. The problem is that we have an exhaustive list of possible answers to some query (such as what object is it). By collecting different feature values, in principle, it should be possible to give an answer to the query, or at least narrow down the list. Since a sensor, or for that matter an expert system, does not in most cases yield a precise value for the feature, uncertainty must be built into the model. Also, researchers must have a formal mechanism to be able to put the information together. Researchers chose to use the Dempster-Shafer approach to handle the problems mentioned above. Researchers introduce the concept of a state of recognition and point out that there is a relation between receiving updates and defining a set valued Markov Chain. Also, deciding what the value of the next set valued variable is can be phrased in terms of classical decision making theory such as minimizing the maximum regret. Other related problems are examined.

Benchmarking for Bayesian Reinforcement Learning

PubMed Central

Ernst, Damien; Couëtoux, Adrien

2016-01-01

In the Bayesian Reinforcement Learning (BRL) setting, agents try to maximise the collected rewards while interacting with their environment while using some prior knowledge that is accessed beforehand. Many BRL algorithms have already been proposed, but the benchmarks used to compare them are only relevant for specific cases. The paper addresses this problem, and provides a new BRL comparison methodology along with the corresponding open source library. In this methodology, a comparison criterion that measures the performance of algorithms on large sets of Markov Decision Processes (MDPs) drawn from some probability distributions is defined. In order to enable the comparison of non-anytime algorithms, our methodology also includes a detailed analysis of the computation time requirement of each algorithm. Our library is released with all source code and documentation: it includes three test problems, each of which has two different prior distributions, and seven state-of-the-art RL algorithms. Finally, our library is illustrated by comparing all the available algorithms and the results are discussed. PMID:27304891

Benchmarking for Bayesian Reinforcement Learning.

PubMed

Castronovo, Michael; Ernst, Damien; Couëtoux, Adrien; Fonteneau, Raphael

2016-01-01

In the Bayesian Reinforcement Learning (BRL) setting, agents try to maximise the collected rewards while interacting with their environment while using some prior knowledge that is accessed beforehand. Many BRL algorithms have already been proposed, but the benchmarks used to compare them are only relevant for specific cases. The paper addresses this problem, and provides a new BRL comparison methodology along with the corresponding open source library. In this methodology, a comparison criterion that measures the performance of algorithms on large sets of Markov Decision Processes (MDPs) drawn from some probability distributions is defined. In order to enable the comparison of non-anytime algorithms, our methodology also includes a detailed analysis of the computation time requirement of each algorithm. Our library is released with all source code and documentation: it includes three test problems, each of which has two different prior distributions, and seven state-of-the-art RL algorithms. Finally, our library is illustrated by comparing all the available algorithms and the results are discussed.

Markov modeling for the neurosurgeon: a review of the literature and an introduction to cost-effectiveness research.

PubMed

Wali, Arvin R; Brandel, Michael G; Santiago-Dieppa, David R; Rennert, Robert C; Steinberg, Jeffrey A; Hirshman, Brian R; Murphy, James D; Khalessi, Alexander A

2018-05-01

OBJECTIVE Markov modeling is a clinical research technique that allows competing medical strategies to be mathematically assessed in order to identify the optimal allocation of health care resources. The authors present a review of the recently published neurosurgical literature that employs Markov modeling and provide a conceptual framework with which to evaluate, critique, and apply the findings generated from health economics research. METHODS The PubMed online database was searched to identify neurosurgical literature published from January 2010 to December 2017 that had utilized Markov modeling for neurosurgical cost-effectiveness studies. Included articles were then assessed with regard to year of publication, subspecialty of neurosurgery, decision analytical techniques utilized, and source information for model inputs. RESULTS A total of 55 articles utilizing Markov models were identified across a broad range of neurosurgical subspecialties. Sixty-five percent of the papers were published within the past 3 years alone. The majority of models derived health transition probabilities, health utilities, and cost information from previously published studies or publicly available information. Only 62% of the studies incorporated indirect costs. Ninety-three percent of the studies performed a 1-way or 2-way sensitivity analysis, and 67% performed a probabilistic sensitivity analysis. A review of the conceptual framework of Markov modeling and an explanation of the different terminology and methodology are provided. CONCLUSIONS As neurosurgeons continue to innovate and identify novel treatment strategies for patients, Markov modeling will allow for better characterization of the impact of these interventions on a patient and societal level. The aim of this work is to equip the neurosurgical readership with the tools to better understand, critique, and apply findings produced from cost-effectiveness research.

Limiting Distributions of Functionals of Markov Chains.

DTIC Science & Technology

1984-08-01

limiting distributions; periodic * nonhomoger.,!ous Poisson processes . 19 ANS? MACY IConuui oe nonoe’ee if necorglooy and edern thty by block numbers...homogeneous Poisson processes is of interest in itself. The problem considered in this paper is of interest in the theory of partially observable...where we obtain the limiting distribution of the interevent times. Key Words: Markov Chains, Limiting Distributions, Periodic Nonhomogeneous Poisson

An abstract specification language for Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, R. W.

1985-01-01

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

An abstract language for specifying Markov reliability models

NASA Technical Reports Server (NTRS)

Butler, Ricky W.

1986-01-01

Markov models can be used to compute the reliability of virtually any fault tolerant system. However, the process of delineating all of the states and transitions in a model of complex system can be devastatingly tedious and error-prone. An approach to this problem is presented utilizing an abstract model definition language. This high level language is described in a nonformal manner and illustrated by example.

Nonparametric model validations for hidden Markov models with applications in financial econometrics

PubMed Central

Zhao, Zhibiao

2011-01-01

We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametric density estimate is contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the hidden states. Our approach is applicable for continuous time diffusion models, stochastic volatility models, nonlinear time series models, and models with market microstructure noise. PMID:21750601

QoS Differential Scheduling in Cognitive-Radio-Based Smart Grid Networks: An Adaptive Dynamic Programming Approach.

PubMed

Yu, Rong; Zhong, Weifeng; Xie, Shengli; Zhang, Yan; Zhang, Yun

2016-02-01

As the next-generation power grid, smart grid will be integrated with a variety of novel communication technologies to support the explosive data traffic and the diverse requirements of quality of service (QoS). Cognitive radio (CR), which has the favorable ability to improve the spectrum utilization, provides an efficient and reliable solution for smart grid communications networks. In this paper, we study the QoS differential scheduling problem in the CR-based smart grid communications networks. The scheduler is responsible for managing the spectrum resources and arranging the data transmissions of smart grid users (SGUs). To guarantee the differential QoS, the SGUs are assigned to have different priorities according to their roles and their current situations in the smart grid. Based on the QoS-aware priority policy, the scheduler adjusts the channels allocation to minimize the transmission delay of SGUs. The entire transmission scheduling problem is formulated as a semi-Markov decision process and solved by the methodology of adaptive dynamic programming. A heuristic dynamic programming (HDP) architecture is established for the scheduling problem. By the online network training, the HDP can learn from the activities of primary users and SGUs, and adjust the scheduling decision to achieve the purpose of transmission delay minimization. Simulation results illustrate that the proposed priority policy ensures the low transmission delay of high priority SGUs. In addition, the emergency data transmission delay is also reduced to a significantly low level, guaranteeing the differential QoS in smart grid.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

Active inference, evidence accumulation and the urn task

PubMed Central

FitzGerald, Thomas HB; Schwartenbeck, Philipp; Moutoussis, Michael; Dolan, Raymond J; Friston, Karl

2015-01-01

Deciding how much evidence to accumulate before making a decision is a problem we and other animals often face, but one which is not completely understood. This issue is particularly important because a tendency to sample less information (often known as reflection impulsivity) is a feature in several psychopathologies, such as psychosis. A formal understanding information sampling may therefore clarify the computational anatomy of psychopathology. In this theoretical paper, we consider evidence accumulation in terms of active (Bayesian) inference using a generic model of Markov decision processes. Here, agents are equipped with beliefs about their own behaviour – in this case, that they will make informed decisions. Normative decision-making is then modelled using variational Bayes to minimise surprise about choice outcomes. Under this scheme, different facets of belief updating map naturally onto the functional anatomy of the brain (at least at a heuristic level). Of particular interest is the key role played by the expected precision of beliefs about control, which we have previously suggested may be encoded by dopaminergic neurons in the midbrain. We show that manipulating expected precision strongly affects how much information an agent characteristically samples, and thus provides a possible link between impulsivity and dopaminergic dysfunction. Our study therefore represents a step towards understanding evidence accumulation in terms of neurobiologically plausible Bayesian inference, and may cast light on why this process is disordered in psychopathology. PMID:25514108

Projection methods for the numerical solution of Markov chain models

NASA Technical Reports Server (NTRS)

Saad, Youcef

1989-01-01

Projection methods for computing stationary probability distributions for Markov chain models are presented. A general projection method is a method which seeks an approximation from a subspace of small dimension to the original problem. Thus, the original matrix problem of size N is approximated by one of dimension m, typically much smaller than N. A particularly successful class of methods based on this principle is that of Krylov subspace methods which utilize subspaces of the form span(v,av,...,A(exp m-1)v). These methods are effective in solving linear systems and eigenvalue problems (Lanczos, Arnoldi,...) as well as nonlinear equations. They can be combined with more traditional iterative methods such as successive overrelaxation, symmetric successive overrelaxation, or with incomplete factorization methods to enhance convergence.

Modeling rheumatoid arthritis using different techniques - a review of model construction and results.

PubMed

Scholz, Stefan; Mittendorf, Thomas

2014-12-01

Rheumatoid arthritis (RA) is a chronic, inflammatory disease with severe effects on the functional ability of patients. Due to the prevalence of 0.5 to 1.0 percent in western countries, new treatment options are a major concern for decision makers with regard to their budget impact. In this context, cost-effectiveness analyses are a helpful tool to evaluate new treatment options for reimbursement schemes. To analyze and compare decision analytic modeling techniques and to explore their use in RA with regard to their advantages and shortcomings. A systematic literature review was conducted in PubMED and 58 studies reporting health economics decision models were analyzed with regard to the modeling technique used. From the 58 reviewed publications, we found 13 reporting decision tree-analysis, 25 (cohort) Markov models, 13 publications on individual sampling methods (ISM) and seven discrete event simulations (DES). Thereby 26 studies were identified as presenting independently developed models and 32 models as adoptions. The modeling techniques used were found to differ in their complexity and in the number of treatment options compared. Methodological features are presented in the article and a comprehensive overview of the cost-effectiveness estimates is given in Additional files 1 and 2. When compared to the other modeling techniques, ISM and DES have advantages in the coverage of patient heterogeneity and, additionally, DES is capable to model more complex treatment sequences and competing risks in RA-patients. Nevertheless, the availability of sufficient data is necessary to avoid assumptions in ISM and DES exercises, thereby enabling biased results. Due to the different settings, time frames and interventions in the reviewed publications, no direct comparison of modeling techniques was applicable. The results from other indications suggest that incremental cost-effective ratios (ICERs) do not differ significantly between Markov and DES models, but DES is able to report more outcome parameters. Given a sufficient data supply, DES is the modeling technique of choice when modeling cost-effectiveness in RA. Otherwise transparency on the data inputs is crucial for valid results and to inform decision makers about possible biases. With regard to ICERs, Markov models might provide similar estimates as more advanced modeling techniques.

Neoadjuvant therapy versus upfront surgical strategies in resectable pancreatic cancer: A Markov decision analysis.

PubMed

de Geus, S W L; Evans, D B; Bliss, L A; Eskander, M F; Smith, J K; Wolff, R A; Miksad, R A; Weinstein, M C; Tseng, J F

2016-10-01

Neoadjuvant therapy is gaining acceptance as a valid treatment option for borderline resectable pancreatic cancer; however, its value for clearly resectable pancreatic cancer remains controversial. The aim of this study was to use a Markov decision analysis model, in the absence of adequately powered randomized trials, to compare the life expectancy (LE) and quality-adjusted life expectancy (QALE) of neoadjuvant therapy to conventional upfront surgical strategies in resectable pancreatic cancer patients. A Markov decision model was created to compare two strategies: attempted pancreatic resection followed by adjuvant chemoradiotherapy and neoadjuvant chemoradiotherapy followed by restaging with, if appropriate, attempted pancreatic resection. Data obtained through a comprehensive systematic search in PUBMED of the literature from 2000 to 2015 were used to estimate the probabilities used in the model. Deterministic and probabilistic sensitivity analyses were performed. Of the 786 potentially eligible studies identified, 22 studies met the inclusion criteria and were used to extract the probabilities used in the model. Base case analyses of the model showed a higher LE (32.2 vs. 26.7 months) and QALE (25.5 vs. 20.8 quality-adjusted life months) for patients in the neoadjuvant therapy arm compared to upfront surgery. Probabilistic sensitivity analyses for LE and QALE revealed that neoadjuvant therapy is favorable in 59% and 60% of the cases respectively. Although conceptual, these data suggest that neoadjuvant therapy offers substantial benefit in LE and QALE for resectable pancreatic cancer patients. These findings highlight the value of further prospective randomized trials comparing neoadjuvant therapy to conventional upfront surgical strategies. Copyright © 2016 Elsevier Ltd, BASO ~ The Association for Cancer Surgery, and the European Society of Surgical Oncology. All rights reserved.

Estimation of sojourn time in chronic disease screening without data on interval cases.

PubMed

Chen, T H; Kuo, H S; Yen, M F; Lai, M S; Tabar, L; Duffy, S W

2000-03-01

Estimation of the sojourn time on the preclinical detectable period in disease screening or transition rates for the natural history of chronic disease usually rely on interval cases (diagnosed between screens). However, to ascertain such cases might be difficult in developing countries due to incomplete registration systems and difficulties in follow-up. To overcome this problem, we propose three Markov models to estimate parameters without using interval cases. A three-state Markov model, a five-state Markov model related to regional lymph node spread, and a five-state Markov model pertaining to tumor size are applied to data on breast cancer screening in female relatives of breast cancer cases in Taiwan. Results based on a three-state Markov model give mean sojourn time (MST) 1.90 (95% CI: 1.18-4.86) years for this high-risk group. Validation of these models on the basis of data on breast cancer screening in the age groups 50-59 and 60-69 years from the Swedish Two-County Trial shows the estimates from a three-state Markov model that does not use interval cases are very close to those from previous Markov models taking interval cancers into account. For the five-state Markov model, a reparameterized procedure using auxiliary information on clinically detected cancers is performed to estimate relevant parameters. A good fit of internal and external validation demonstrates the feasibility of using these models to estimate parameters that have previously required interval cancers. This method can be applied to other screening data in which there are no data on interval cases.

A Lagrangian Transport Eulerian Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport

NASA Astrophysics Data System (ADS)

Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi

2017-11-01

Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a Lagrangian framework, while in others an Eulerian might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a Lagrangian closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a LAgrangian Transport Eulerian Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the Lagrangian Spatial Markov model and maps concentrations to an Eulerian grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the Eulerian reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.

A New Framework for Analysis of Coevolutionary Systems-Directed Graph Representation and Random Walks.

PubMed

Chong, Siang Yew; Tiňo, Peter; He, Jun; Yao, Xin

2017-11-20

Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains-random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

Asynchronous Gossip for Averaging and Spectral Ranking

NASA Astrophysics Data System (ADS)

Borkar, Vivek S.; Makhijani, Rahul; Sundaresan, Rajesh

2014-08-01

We consider two variants of the classical gossip algorithm. The first variant is a version of asynchronous stochastic approximation. We highlight a fundamental difficulty associated with the classical asynchronous gossip scheme, viz., that it may not converge to a desired average, and suggest an alternative scheme based on reinforcement learning that has guaranteed convergence to the desired average. We then discuss a potential application to a wireless network setting with simultaneous link activation constraints. The second variant is a gossip algorithm for distributed computation of the Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant draws upon a reinforcement learning algorithm for an average cost controlled Markov decision problem, the second variant draws upon a reinforcement learning algorithm for risk-sensitive control. We then discuss potential applications of the second variant to ranking schemes, reputation networks, and principal component analysis.

Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration

PubMed Central

Doss, Hani; Tan, Aixin

2017-01-01

In the classical biased sampling problem, we have k densities π1(·), …, πk(·), each known up to a normalizing constant, i.e. for l = 1, …, k, πl(·) = νl(·)/ml, where νl(·) is a known function and ml is an unknown constant. For each l, we have an iid sample from πl,·and the problem is to estimate the ratios ml/ms for all l and all s. This problem arises frequently in several situations in both frequentist and Bayesian inference. An estimate of the ratios was developed and studied by Vardi and his co-workers over two decades ago, and there has been much subsequent work on this problem from many different perspectives. In spite of this, there are no rigorous results in the literature on how to estimate the standard error of the estimate. We present a class of estimates of the ratios of normalizing constants that are appropriate for the case where the samples from the πl’s are not necessarily iid sequences, but are Markov chains. We also develop an approach based on regenerative simulation for obtaining standard errors for the estimates of ratios of normalizing constants. These standard error estimates are valid for both the iid case and the Markov chain case. PMID:28706463

Estimates and Standard Errors for Ratios of Normalizing Constants from Multiple Markov Chains via Regeneration.

PubMed

Doss, Hani; Tan, Aixin

2014-09-01

In the classical biased sampling problem, we have k densities π 1 (·), …, π k (·), each known up to a normalizing constant, i.e. for l = 1, …, k , π l (·) = ν l (·)/ m l , where ν l (·) is a known function and m l is an unknown constant. For each l , we have an iid sample from π l , · and the problem is to estimate the ratios m l /m s for all l and all s . This problem arises frequently in several situations in both frequentist and Bayesian inference. An estimate of the ratios was developed and studied by Vardi and his co-workers over two decades ago, and there has been much subsequent work on this problem from many different perspectives. In spite of this, there are no rigorous results in the literature on how to estimate the standard error of the estimate. We present a class of estimates of the ratios of normalizing constants that are appropriate for the case where the samples from the π l 's are not necessarily iid sequences, but are Markov chains. We also develop an approach based on regenerative simulation for obtaining standard errors for the estimates of ratios of normalizing constants. These standard error estimates are valid for both the iid case and the Markov chain case.

A Markov Model Analysis of Problem-Solving Progress.

ERIC Educational Resources Information Center

Vendlinski, Terry

This study used a computerized simulation and problem-solving tool along with artificial neural networks (ANN) as pattern recognizers to identify the common types of strategies high school and college undergraduate chemistry students would use to solve qualitative chemistry problems. Participants were 134 high school chemistry students who used…

A systematic review of the quality of economic models comparing thrombosis inhibitors in patients with acute coronary syndrome undergoing percutaneous coronary intervention.

PubMed

Hatz, Maximilian H M; Leidl, Reiner; Yates, Nichola A; Stollenwerk, Björn

2014-04-01

Thrombosis inhibitors can be used to treat acute coronary syndromes (ACS). However, there are various alternative treatment strategies, of which some have been compared using health economic decision models. To assess the quality of health economic decision models comparing thrombosis inhibitors in patients with ACS undergoing percutaneous coronary intervention, and to identify areas for quality improvement. The literature databases MEDLINE, EMBASE, EconLit, National Health Service Economic Evaluation Database (NHS EED), Database of Abstracts of Reviews of Effects (DARE) and Health Technology Assessment (HTA). A review of the quality of health economic decision models was conducted by two independent reviewers, using the Philips checklist. Twenty-one relevant studies were identified. Differences were apparent regarding the model type (six decision trees, four Markov models, eight combinations, three undefined models), the model structure (types of events, Markov states) and the incorporation of data (efficacy, cost and utility data). Critical issues were the absence of particular events (e.g. thrombocytopenia, stroke) and questionable usage of utility values within some studies. As we restricted our search to health economic decision models comparing thrombosis inhibitors, interesting aspects related to the quality of studies of adjacent medical areas that compared stents or procedures could have been missed. This review identified areas where recommendations are indicated regarding the quality of future ACS decision models. For example, all critical events and relevant treatment options should be included. Models also need to allow for changing event probabilities to correctly reflect ACS and to incorporate appropriate, age-specific utility values and decrements when conducting cost-utility analyses.

The application of mean field theory to image motion estimation.

PubMed

Zhang, J; Hanauer, G G

1995-01-01

Previously, Markov random field (MRF) model-based techniques have been proposed for image motion estimation. Since motion estimation is usually an ill-posed problem, various constraints are needed to obtain a unique and stable solution. The main advantage of the MRF approach is its capacity to incorporate such constraints, for instance, motion continuity within an object and motion discontinuity at the boundaries between objects. In the MRF approach, motion estimation is often formulated as an optimization problem, and two frequently used optimization methods are simulated annealing (SA) and iterative-conditional mode (ICM). Although the SA is theoretically optimal in the sense of finding the global optimum, it usually takes many iterations to converge. The ICM, on the other hand, converges quickly, but its results are often unsatisfactory due to its "hard decision" nature. Previously, the authors have applied the mean field theory to image segmentation and image restoration problems. It provides results nearly as good as SA but with much faster convergence. The present paper shows how the mean field theory can be applied to MRF model-based motion estimation. This approach is demonstrated on both synthetic and real-world images, where it produced good motion estimates.

Learning Grasp Strategies Composed of Contact Relative Motions

NASA Technical Reports Server (NTRS)

Platt, Robert, Jr.

2007-01-01

Of central importance to grasp synthesis algorithms are the assumptions made about the object to be grasped and the sensory information that is available. Many approaches avoid the issue of sensing entirely by assuming that complete information is available. In contrast, this paper proposes an approach to grasp synthesis expressed in terms of units of control that simultaneously change the contact configuration and sense information about the object and the relative manipulator-object pose. These units of control, known as contact relative motions (CRMs), allow the grasp synthesis problem to be recast as an optimal control problem where the goal is to find a strategy for executing CRMs that leads to a grasp in the shortest number of steps. An experiment is described that uses Robonaut, the NASA-JSC space humanoid, to show that CRMs are a viable means of synthesizing grasps. However, because of the limited amount of information that a single CRM can sense, the optimal control problem may be partially observable. This paper proposes expressing the problem as a k-order Markov Decision Process (MDP) and solving it using Reinforcement Learning. This approach is tested in a simulation of a two-contact manipulator that learns to grasp an object. Grasp strategies learned in simulation are tested on the physical Robonaut platform and found to lead to grasp configurations consistently.

The cutoff phenomenon in finite Markov chains.

PubMed Central

Diaconis, P

1996-01-01

Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to symmetry) is explored. Examples are given where the symmetry is broken but the cutoff phenomenon persists. PMID:11607633

Markov State Models of gene regulatory networks.

PubMed

Chu, Brian K; Tse, Margaret J; Sato, Royce R; Read, Elizabeth L

2017-02-06

Gene regulatory networks with dynamics characterized by multiple stable states underlie cell fate-decisions. Quantitative models that can link molecular-level knowledge of gene regulation to a global understanding of network dynamics have the potential to guide cell-reprogramming strategies. Networks are often modeled by the stochastic Chemical Master Equation, but methods for systematic identification of key properties of the global dynamics are currently lacking. The method identifies the number, phenotypes, and lifetimes of long-lived states for a set of common gene regulatory network models. Application of transition path theory to the constructed Markov State Model decomposes global dynamics into a set of dominant transition paths and associated relative probabilities for stochastic state-switching. In this proof-of-concept study, we found that the Markov State Model provides a general framework for analyzing and visualizing stochastic multistability and state-transitions in gene networks. Our results suggest that this framework-adopted from the field of atomistic Molecular Dynamics-can be a useful tool for quantitative Systems Biology at the network scale.

Operations and support cost modeling using Markov chains

NASA Technical Reports Server (NTRS)

Unal, Resit

1989-01-01

Systems for future missions will be selected with life cycle costs (LCC) as a primary evaluation criterion. This reflects the current realization that only systems which are considered affordable will be built in the future due to the national budget constaints. Such an environment calls for innovative cost modeling techniques which address all of the phases a space system goes through during its life cycle, namely: design and development, fabrication, operations and support; and retirement. A significant portion of the LCC for reusable systems are generated during the operations and support phase (OS). Typically, OS costs can account for 60 to 80 percent of the total LCC. Clearly, OS costs are wholly determined or at least strongly influenced by decisions made during the design and development phases of the project. As a result OS costs need to be considered and estimated early in the conceptual phase. To be effective, an OS cost estimating model needs to account for actual instead of ideal processes by associating cost elements with probabilities. One approach that may be suitable for OS cost modeling is the use of the Markov Chain Process. Markov chains are an important method of probabilistic analysis for operations research analysts but they are rarely used for life cycle cost analysis. This research effort evaluates the use of Markov Chains in LCC analysis by developing OS cost model for a hypothetical reusable space transportation vehicle (HSTV) and suggests further uses of the Markov Chain process as a design-aid tool.

Stochastic control approaches for sensor management in search and exploitation

NASA Astrophysics Data System (ADS)

Hitchings, Darin Chester

Recent improvements in the capabilities of autonomous vehicles have motivated their increased use in such applications as defense, homeland security, environmental monitoring, and surveillance. To enhance performance in these applications, new algorithms are required to control teams of robots autonomously and through limited interactions with human operators. In this dissertation we develop new algorithms for control of robots performing information-seeking missions in unknown environments. These missions require robots to control their sensors in order to discover the presence of objects, keep track of the objects, and learn what these objects are, given a fixed sensing budget. Initially, we investigate control of multiple sensors, with a finite set of sensing options and finite-valued measurements, to locate and classify objects given a limited resource budget. The control problem is formulated as a Partially Observed Markov Decision Problem (POMDP), but its exact solution requires excessive computation. Under the assumption that sensor error statistics are independent and time-invariant, we develop a class of algorithms using Lagrangian Relaxation techniques to obtain optimal mixed strategies using performance bounds developed in previous research. We investigate alternative Receding Horizon (RH) controllers to convert the mixed strategies to feasible adaptive-sensing strategies and evaluate the relative performance of these controllers in simulation. The resulting controllers provide superior performance to alternative algorithms proposed in the literature and obtain solutions to large-scale POMDP problems several orders of magnitude faster than optimal Dynamic Programming (DP) approaches with comparable performance quality. We extend our results for finite action, finite measurement sensor control to scenarios with moving objects. We use Hidden Markov Models (HMMs) for the evolution of objects, according to the dynamics of a birth-death process. We develop a new lower bound on the performance of adaptive controllers in these scenarios, develop algorithms for computing solutions to this lower bound, and use these algorithms as part of a RH controller for sensor allocation in the presence of moving objects We also consider an adaptive Search problem where sensing actions are continuous and the underlying measurement space is also continuous. We extend our previous hierarchical decomposition approach based on performance bounds to this problem and develop novel implementations of Stochastic Dynamic Programming (SDP) techniques to solve this problem. Our algorithms are nearly two orders of magnitude faster than previously proposed approaches and yield solutions of comparable quality. For supervisory control, we discuss how human operators can work with and augment robotic teams performing these tasks. Our focus is on how tasks are partitioned among teams of robots and how a human operator can make intelligent decisions for task partitioning. We explore these questions through the design of a game that involves robot automata controlled by our algorithms and a human supervisor that partitions tasks based on different levels of support information. This game can be used with human subject experiments to explore the effect of information on quality of supervisory control.

Image segmentation using hidden Markov Gauss mixture models.

PubMed

Pyun, Kyungsuk; Lim, Johan; Won, Chee Sun; Gray, Robert M

2007-07-01

Image segmentation is an important tool in image processing and can serve as an efficient front end to sophisticated algorithms and thereby simplify subsequent processing. We develop a multiclass image segmentation method using hidden Markov Gauss mixture models (HMGMMs) and provide examples of segmentation of aerial images and textures. HMGMMs incorporate supervised learning, fitting the observation probability distribution given each class by a Gauss mixture estimated using vector quantization with a minimum discrimination information (MDI) distortion. We formulate the image segmentation problem using a maximum a posteriori criteria and find the hidden states that maximize the posterior density given the observation. We estimate both the hidden Markov parameter and hidden states using a stochastic expectation-maximization algorithm. Our results demonstrate that HMGMM provides better classification in terms of Bayes risk and spatial homogeneity of the classified objects than do several popular methods, including classification and regression trees, learning vector quantization, causal hidden Markov models (HMMs), and multiresolution HMMs. The computational load of HMGMM is similar to that of the causal HMM.

Automated Guidance from Physiological Sensing to Reduce Thermal-Work Strain Levels on a Novel Task

USDA-ARS?s Scientific Manuscript database

This experiment demonstrated that automated pace guidance generated from real-time physiological monitoring allowed least stressful completion of a timed (60 minute limit) 5 mile treadmill exercise. An optimal pacing policy was estimated from a Markov decision process that balanced the goals of the...

Unsupervised MDP Value Selection for Automating ITS Capabilities

ERIC Educational Resources Information Center

Stamper, John; Barnes, Tiffany

2009-01-01

We seek to simplify the creation of intelligent tutors by using student data acquired from standard computer aided instruction (CAI) in conjunction with educational data mining methods to automatically generate adaptive hints. In our previous work, we have automatically generated hints for logic tutoring by constructing a Markov Decision Process…

A quantum probability explanation for violations of ‘rational’ decision theory

PubMed Central

Pothos, Emmanuel M.; Busemeyer, Jerome R.

2009-01-01

Two experimental tasks in psychology, the two-stage gambling game and the Prisoner's Dilemma game, show that people violate the sure thing principle of decision theory. These paradoxical findings have resisted explanation by classical decision theory for over a decade. A quantum probability model, based on a Hilbert space representation and Schrödinger's equation, provides a simple and elegant explanation for this behaviour. The quantum model is compared with an equivalent Markov model and it is shown that the latter is unable to account for violations of the sure thing principle. Accordingly, it is argued that quantum probability provides a better framework for modelling human decision-making. PMID:19324743

A model of interaction between anticorruption authority and corruption groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Neverova, Elena G.; Malafeyef, Oleg A.

The paper provides a model of interaction between anticorruption unit and corruption groups. The main policy functions of the anticorruption unit involve reducing corrupt practices in some entities through an optimal approach to resource allocation and effective anticorruption policy. We develop a model based on Markov decision-making process and use Howard’s policy-improvement algorithm for solving an optimal decision strategy. We examine the assumption that corruption groups retaliate against the anticorruption authority to protect themselves. This model was implemented through stochastic game.

Optimal inventories for overhaul of repairable redundant systems - A Markov decision model

NASA Technical Reports Server (NTRS)

Schaefer, M. K.

1984-01-01

A Markovian decision model was developed to calculate the optimal inventory of repairable spare parts for an avionics control system for commercial aircraft. Total expected shortage costs, repair costs, and holding costs are minimized for a machine containing a single system of redundant parts. Transition probabilities are calculated for each repair state and repair rate, and optimal spare parts inventory and repair strategies are determined through linear programming. The linear programming solutions are given in a table.

Parallel algorithms for simulating continuous time Markov chains

NASA Technical Reports Server (NTRS)

Nicol, David M.; Heidelberger, Philip

1992-01-01

We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.

Women's views of two interventions designed to assist in the prophylactic oophorectomy decision: a qualitative pilot evaluation

PubMed Central

Bhavnani, Vanita; Clarke, Aileen; Dowie, Jack; Kennedy, Andrew; Pell, Ian

2002-01-01

Abstract Introduction  A qualitative pilot evaluation of two different decision interventions for the prophylactic oophorectomy (PO) decision: a Decision Chart and a computerized clinical guidance programme (CGP) was undertaken. The Decision Chart, representing current practice in decision interventions, presents population‐based information. The CGP elicits individual values to allow for quality‐adjusted life years to be calculated and an explicit guidance statement is given. Prophylactic oophorectomy involves removal of the ovaries as an adjunct to hysterectomy to prevent ovarian cancer. The decision is complex because the operation can affect a number of long‐term outcomes including breast cancer, coronary heart disease and osteoporosis. Methods  Both interventions were based on the evidence and were administered by a facilitator. The Decision Chart is a file, which progressively reveals information in the form of bar charts. The CGP is a decision‐analysis based program integrating the results from a cluster of Markov cycle trees. The research evidence is incorporated with woman's individual risk factors, values and preferences. A purposive sample of 19 women awaiting hysterectomy used the decision interventions (10 CGP, nine Decision Chart). In‐depth semi‐structured interviews were undertaken. Interviews were transcribed and analysed to derive themes. Results  Reactions to the different decision interventions were mixed. Both were seen as clarifying the decision. Some women found some of the tasks difficult (e.g. rating health status). Some were surprised by the ‘individualized’ guidance, which the CGP offered. The Decision Chart provided some with a sense of empowerment, although some found that it provided too much information. Conclusions  Women were able to use both decision interventions. Both provided decision clarification. Problems were evident with both interventions, which give useful pointers for future development. These included the possibility for women to see how their individual risks of different outcomes are affected in the Decision Chart and enhanced explanation of the CGP tasks. Future design and evaluation of decision aids, will need to accommodate differences between patients in the desire for amount and type of information and level of involvement in the decision‐making process. PMID:12031056

Parametric inference for biological sequence analysis.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

One of the major successes in computational biology has been the unification, by using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied to these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems that are associated with different statistical models. This article introduces the polytope propagation algorithm for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.

Providing guidance for genomics-based cancer treatment decisions: insights from stakeholder engagement for post-prostatectomy radiation therapy.

PubMed

Abe, James; Lobo, Jennifer M; Trifiletti, Daniel M; Showalter, Timothy N

2017-08-24

Despite the emergence of genomics-based risk prediction tools in oncology, there is not yet an established framework for communication of test results to cancer patients to support shared decision-making. We report findings from a stakeholder engagement program that aimed to develop a framework for using Markov models with individualized model inputs, including genomics-based estimates of cancer recurrence probability, to generate personalized decision aids for prostate cancer patients faced with radiation therapy treatment decisions after prostatectomy. We engaged a total of 22 stakeholders, including: prostate cancer patients, urological surgeons, radiation oncologists, genomic testing industry representatives, and biomedical informatics faculty. Slides were at each meeting to provide background information regarding the analytical framework. Participants were invited to provide feedback during the meeting, including revising the overall project aims. Stakeholder meeting content was reviewed and summarized by stakeholder group and by theme. The majority of stakeholder suggestions focused on aspects of decision aid design and formatting. Stakeholders were enthusiastic about the potential value of using decision analysis modeling with personalized model inputs for cancer recurrence risk, as well as competing risks from age and comorbidities, to generate a patient-centered tool to assist decision-making. Stakeholders did not view privacy considerations as a major barrier to the proposed decision aid program. A common theme was that decision aids should be portable across multiple platforms (electronic and paper), should allow for interaction by the user to adjust model inputs iteratively, and available to patients both before and during consult appointments. Emphasis was placed on the challenge of explaining the model's composite result of quality-adjusted life years. A range of stakeholders provided valuable insights regarding the design of a personalized decision aid program, based upon Markov modeling with individualized model inputs, to provide a patient-centered framework to support for genomic-based treatment decisions for cancer patients. The guidance provided by our stakeholders may be broadly applicable to the communication of genomic test results to patients in a patient-centered fashion that supports effective shared decision-making that represents a spectrum of personal factors such as age, medical comorbidities, and individual priorities and values.

Some Work and Some Play: Microscopic and Macroscopic Approaches to Labor and Leisure

PubMed Central

Niyogi, Ritwik K.; Shizgal, Peter; Dayan, Peter

2014-01-01

Given the option, humans and other animals elect to distribute their time between work and leisure, rather than choosing all of one and none of the other. Traditional accounts of partial allocation have characterised behavior on a macroscopic timescale, reporting and studying the mean times spent in work or leisure. However, averaging over the more microscopic processes that govern choices is known to pose tricky theoretical problems, and also eschews any possibility of direct contact with the neural computations involved. We develop a microscopic framework, formalized as a semi-Markov decision process with possibly stochastic choices, in which subjects approximately maximise their expected returns by making momentary commitments to one or other activity. We show macroscopic utilities that arise from microscopic ones, and demonstrate how facets such as imperfect substitutability can arise in a more straightforward microscopic manner. PMID:25474151

On the optimal use of a slow server in two-stage queueing systems

NASA Astrophysics Data System (ADS)

Papachristos, Ioannis; Pandelis, Dimitrios G.

2017-07-01

We consider two-stage tandem queueing systems with a dedicated server in each queue and a slower flexible server that can attend both queues. We assume Poisson arrivals and exponential service times, and linear holding costs for jobs present in the system. We study the optimal dynamic assignment of servers to jobs assuming that two servers cannot collaborate to work on the same job and preemptions are not allowed. We formulate the problem as a Markov decision process and derive properties of the optimal allocation for the dedicated (fast) servers. Specifically, we show that the one downstream should not idle, and the same is true for the one upstream when holding costs are larger there. The optimal allocation of the slow server is investigated through extensive numerical experiments that lead to conjectures on the structure of the optimal policy.

Learning a Markov Logic network for supervised gene regulatory network inference

PubMed Central

2013-01-01

Background Gene regulatory network inference remains a challenging problem in systems biology despite the numerous approaches that have been proposed. When substantial knowledge on a gene regulatory network is already available, supervised network inference is appropriate. Such a method builds a binary classifier able to assign a class (Regulation/No regulation) to an ordered pair of genes. Once learnt, the pairwise classifier can be used to predict new regulations. In this work, we explore the framework of Markov Logic Networks (MLN) that combine features of probabilistic graphical models with the expressivity of first-order logic rules. Results We propose to learn a Markov Logic network, e.g. a set of weighted rules that conclude on the predicate “regulates”, starting from a known gene regulatory network involved in the switch proliferation/differentiation of keratinocyte cells, a set of experimental transcriptomic data and various descriptions of genes all encoded into first-order logic. As training data are unbalanced, we use asymmetric bagging to learn a set of MLNs. The prediction of a new regulation can then be obtained by averaging predictions of individual MLNs. As a side contribution, we propose three in silico tests to assess the performance of any pairwise classifier in various network inference tasks on real datasets. A first test consists of measuring the average performance on balanced edge prediction problem; a second one deals with the ability of the classifier, once enhanced by asymmetric bagging, to update a given network. Finally our main result concerns a third test that measures the ability of the method to predict regulations with a new set of genes. As expected, MLN, when provided with only numerical discretized gene expression data, does not perform as well as a pairwise SVM in terms of AUPR. However, when a more complete description of gene properties is provided by heterogeneous sources, MLN achieves the same performance as a black-box model such as a pairwise SVM while providing relevant insights on the predictions. Conclusions The numerical studies show that MLN achieves very good predictive performance while opening the door to some interpretability of the decisions. Besides the ability to suggest new regulations, such an approach allows to cross-validate experimental data with existing knowledge. PMID:24028533

Learning a Markov Logic network for supervised gene regulatory network inference.

PubMed

Brouard, Céline; Vrain, Christel; Dubois, Julie; Castel, David; Debily, Marie-Anne; d'Alché-Buc, Florence

2013-09-12

Gene regulatory network inference remains a challenging problem in systems biology despite the numerous approaches that have been proposed. When substantial knowledge on a gene regulatory network is already available, supervised network inference is appropriate. Such a method builds a binary classifier able to assign a class (Regulation/No regulation) to an ordered pair of genes. Once learnt, the pairwise classifier can be used to predict new regulations. In this work, we explore the framework of Markov Logic Networks (MLN) that combine features of probabilistic graphical models with the expressivity of first-order logic rules. We propose to learn a Markov Logic network, e.g. a set of weighted rules that conclude on the predicate "regulates", starting from a known gene regulatory network involved in the switch proliferation/differentiation of keratinocyte cells, a set of experimental transcriptomic data and various descriptions of genes all encoded into first-order logic. As training data are unbalanced, we use asymmetric bagging to learn a set of MLNs. The prediction of a new regulation can then be obtained by averaging predictions of individual MLNs. As a side contribution, we propose three in silico tests to assess the performance of any pairwise classifier in various network inference tasks on real datasets. A first test consists of measuring the average performance on balanced edge prediction problem; a second one deals with the ability of the classifier, once enhanced by asymmetric bagging, to update a given network. Finally our main result concerns a third test that measures the ability of the method to predict regulations with a new set of genes. As expected, MLN, when provided with only numerical discretized gene expression data, does not perform as well as a pairwise SVM in terms of AUPR. However, when a more complete description of gene properties is provided by heterogeneous sources, MLN achieves the same performance as a black-box model such as a pairwise SVM while providing relevant insights on the predictions. The numerical studies show that MLN achieves very good predictive performance while opening the door to some interpretability of the decisions. Besides the ability to suggest new regulations, such an approach allows to cross-validate experimental data with existing knowledge.

Modeling Search Behaviors during the Acquisition of Expertise in a Sequential Decision-Making Task.

PubMed

Moënne-Loccoz, Cristóbal; Vergara, Rodrigo C; López, Vladimir; Mery, Domingo; Cosmelli, Diego

2017-01-01

Our daily interaction with the world is plagued of situations in which we develop expertise through self-motivated repetition of the same task. In many of these interactions, and especially when dealing with computer and machine interfaces, we must deal with sequences of decisions and actions. For instance, when drawing cash from an ATM machine, choices are presented in a step-by-step fashion and a specific sequence of choices must be performed in order to produce the expected outcome. But, as we become experts in the use of such interfaces, is it possible to identify specific search and learning strategies? And if so, can we use this information to predict future actions? In addition to better understanding the cognitive processes underlying sequential decision making, this could allow building adaptive interfaces that can facilitate interaction at different moments of the learning curve. Here we tackle the question of modeling sequential decision-making behavior in a simple human-computer interface that instantiates a 4-level binary decision tree (BDT) task. We record behavioral data from voluntary participants while they attempt to solve the task. Using a Hidden Markov Model-based approach that capitalizes on the hierarchical structure of behavior, we then model their performance during the interaction. Our results show that partitioning the problem space into a small set of hierarchically related stereotyped strategies can potentially capture a host of individual decision making policies. This allows us to follow how participants learn and develop expertise in the use of the interface. Moreover, using a Mixture of Experts based on these stereotyped strategies, the model is able to predict the behavior of participants that master the task.

Strategic level proton therapy patient admission planning: a Markov decision process modeling approach.

PubMed

Gedik, Ridvan; Zhang, Shengfan; Rainwater, Chase

2017-06-01

A relatively new consideration in proton therapy planning is the requirement that the mix of patients treated from different categories satisfy desired mix percentages. Deviations from these percentages and their impacts on operational capabilities are of particular interest to healthcare planners. In this study, we investigate intelligent ways of admitting patients to a proton therapy facility that maximize the total expected number of treatment sessions (fractions) delivered to patients in a planning period with stochastic patient arrivals and penalize the deviation from the patient mix restrictions. We propose a Markov Decision Process (MDP) model that provides very useful insights in determining the best patient admission policies in the case of an unexpected opening in the facility (i.e., no-shows, appointment cancellations, etc.). In order to overcome the curse of dimensionality for larger and more realistic instances, we propose an aggregate MDP model that is able to approximate optimal patient admission policies using the worded weight aggregation technique. Our models are applicable to healthcare treatment facilities throughout the United States, but are motivated by collaboration with the University of Florida Proton Therapy Institute (UFPTI).

Markov Chain Monte Carlo Inference of Parametric Dictionaries for Sparse Bayesian Approximations

PubMed Central

Chaspari, Theodora; Tsiartas, Andreas; Tsilifis, Panagiotis; Narayanan, Shrikanth

2016-01-01

Parametric dictionaries can increase the ability of sparse representations to meaningfully capture and interpret the underlying signal information, such as encountered in biomedical problems. Given a mapping function from the atom parameter space to the actual atoms, we propose a sparse Bayesian framework for learning the atom parameters, because of its ability to provide full posterior estimates, take uncertainty into account and generalize on unseen data. Inference is performed with Markov Chain Monte Carlo, that uses block sampling to generate the variables of the Bayesian problem. Since the parameterization of dictionary atoms results in posteriors that cannot be analytically computed, we use a Metropolis-Hastings-within-Gibbs framework, according to which variables with closed-form posteriors are generated with the Gibbs sampler, while the remaining ones with the Metropolis Hastings from appropriate candidate-generating densities. We further show that the corresponding Markov Chain is uniformly ergodic ensuring its convergence to a stationary distribution independently of the initial state. Results on synthetic data and real biomedical signals indicate that our approach offers advantages in terms of signal reconstruction compared to previously proposed Steepest Descent and Equiangular Tight Frame methods. This paper demonstrates the ability of Bayesian learning to generate parametric dictionaries that can reliably represent the exemplar data and provides the foundation towards inferring the entire variable set of the sparse approximation problem for signal denoising, adaptation and other applications. PMID:28649173

Emotion and decision-making: affect-driven belief systems in anxiety and depression.

PubMed

Paulus, Martin P; Yu, Angela J

2012-09-01

Emotion processing and decision-making are integral aspects of daily life. However, our understanding of the interaction between these constructs is limited. In this review, we summarize theoretical approaches that link emotion and decision-making, and focus on research with anxious or depressed individuals to show how emotions can interfere with decision-making. We integrate the emotional framework based on valence and arousal with a Bayesian approach to decision-making in terms of probability and value processing. We discuss how studies of individuals with emotional dysfunctions provide evidence that alterations of decision-making can be viewed in terms of altered probability and value computation. We argue that the probabilistic representation of belief states in the context of partially observable Markov decision processes provides a useful approach to examine alterations in probability and value representation in individuals with anxiety and depression, and outline the broader implications of this approach. Copyright © 2012. Published by Elsevier Ltd.

Emotion and decision-making: affect-driven belief systems in anxiety and depression

PubMed Central

Paulus, Martin P.; Yu, Angela J.

2012-01-01

Emotion processing and decision-making are integral aspects of daily life. However, our understanding of the interaction between these constructs is limited. In this review, we summarize theoretical approaches to the link between emotion and decision-making, and focus on research with anxious or depressed individuals that reveals how emotions can interfere with decision-making. We integrate the emotional framework based on valence and arousal with a Bayesian approach to decision-making in terms of probability and value processing. We then discuss how studies of individuals with emotional dysfunctions provide evidence that alterations of decision-making can be viewed in terms of altered probability and value computation. We argue that the probabilistic representation of belief states in the context of partially observable Markov decision processes provides a useful approach to examine alterations in probability and value representation in individuals with anxiety and depression and outline the broader implications of this approach. PMID:22898207

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

NASA Astrophysics Data System (ADS)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of the plume in two-dimensional problems.

Protocol and practice in the adaptive management of waterfowl harvests

USGS Publications Warehouse

Johnson, F.; Williams, K.

1999-01-01

Waterfowl harvest management in North America, for all its success, historically has had several shortcomings, including a lack of well-defined objectives, a failure to account for uncertain management outcomes, and inefficient use of harvest regulations to understand the effects of management. To address these and other concerns, the U.S. Fish and Wildlife Service began implementation of adaptive harvest management in 1995. Harvest policies are now developed using a Markov decision process in which there is an explicit accounting for uncontrolled environmental variation, partial controllability of harvest, and structural uncertainty in waterfowl population dynamics. Current policies are passively adaptive, in the sense that any reduction in structural uncertainty is an unplanned by-product of the regulatory process. A generalization of the Markov decision process permits the calculation of optimal actively adaptive policies, but it is not yet clear how state-specific harvest actions differ between passive and active approaches. The Markov decision process also provides managers the ability to explore optimal levels of aggregation or "management scale" for regulating harvests in a system that exhibits high temporal, spatial, and organizational variability. Progress in institutionalizing adaptive harvest management has been remarkable, but some managers still perceive the process as a panacea, while failing to appreciate the challenges presented by this more explicit and methodical approach to harvest regulation. Technical hurdles include the need to develop better linkages between population processes and the dynamics of landscapes, and to model the dynamics of structural uncertainty in a more comprehensive fashion. From an institutional perspective, agreement on how to value and allocate harvests continues to be elusive, and there is some evidence that waterfowl managers have overestimated the importance of achievement-oriented factors in setting hunting regulations. Indeed, it is these unresolved value judgements, and the lack of an effective structure for organizing debate, that present the greatest threat to adaptive harvest management as a viable means for coping with management uncertainty. Copyright ?? 1999 by The Resilience Alliance.

Recursive recovery of Markov transition probabilities from boundary value data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patch, Sarah Kathyrn

1994-04-01

In an effort to mathematically describe the anisotropic diffusion of infrared radiation in biological tissue Gruenbaum posed an anisotropic diffusion boundary value problem in 1989. In order to accommodate anisotropy, he discretized the temporal as well as the spatial domain. The probabilistic interpretation of the diffusion equation is retained; radiation is assumed to travel according to a random walk (of sorts). In this random walk the probabilities with which photons change direction depend upon their previous as well as present location. The forward problem gives boundary value data as a function of the Markov transition probabilities. The inverse problem requiresmore » finding the transition probabilities from boundary value data. Problems in the plane are studied carefully in this thesis. Consistency conditions amongst the data are derived. These conditions have two effects: they prohibit inversion of the forward map but permit smoothing of noisy data. Next, a recursive algorithm which yields a family of solutions to the inverse problem is detailed. This algorithm takes advantage of all independent data and generates a system of highly nonlinear algebraic equations. Pluecker-Grassmann relations are instrumental in simplifying the equations. The algorithm is used to solve the 4 x 4 problem. Finally, the smallest nontrivial problem in three dimensions, the 2 x 2 x 2 problem, is solved.« less

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Passive synchronization for Markov jump genetic oscillator networks with time-varying delays.

PubMed

Lu, Li; He, Bing; Man, Chuntao; Wang, Shun

2015-04-01

In this paper, the synchronization problem of coupled Markov jump genetic oscillator networks with time-varying delays and external disturbances is investigated. By introducing the drive-response concept, a novel mode-dependent control scheme is proposed, which guarantees that the synchronization can be achieved. By applying the Lyapunov-Krasovskii functional method and stochastic analysis, sufficient conditions are established based on passivity theory in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of our theoretical results. Copyright © 2015 Elsevier Inc. All rights reserved.

RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

PubMed Central

Griego, R. J.; Hersh, R.

1969-01-01

Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new. PMID:16578690

A fast exact simulation method for a class of Markov jump processes.

PubMed

Li, Yao; Hu, Lili

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.

Quantitative risk stratification in Markov chains with limiting conditional distributions.

PubMed

Chan, David C; Pollett, Philip K; Weinstein, Milton C

2009-01-01

Many clinical decisions require patient risk stratification. The authors introduce the concept of limiting conditional distributions, which describe the equilibrium proportion of surviving patients occupying each disease state in a Markov chain with death. Such distributions can quantitatively describe risk stratification. The authors first establish conditions for the existence of a positive limiting conditional distribution in a general Markov chain and describe a framework for risk stratification using the limiting conditional distribution. They then apply their framework to a clinical example of a treatment indicated for high-risk patients, first to infer the risk of patients selected for treatment in clinical trials and then to predict the outcomes of expanding treatment to other populations of risk. For the general chain, a positive limiting conditional distribution exists only if patients in the earliest state have the lowest combined risk of progression or death. The authors show that in their general framework, outcomes and population risk are interchangeable. For the clinical example, they estimate that previous clinical trials have selected the upper quintile of patient risk for this treatment, but they also show that expanded treatment would weakly dominate this degree of targeted treatment, and universal treatment may be cost-effective. Limiting conditional distributions exist in most Markov models of progressive diseases and are well suited to represent risk stratification quantitatively. This framework can characterize patient risk in clinical trials and predict outcomes for other populations of risk.

Mathematical Analysis of Vehicle Delivery Scale of Bike-Sharing Rental Nodes

NASA Astrophysics Data System (ADS)

Zhai, Y.; Liu, J.; Liu, L.

2018-04-01

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

Music and Video Gaming during Breaks: Influence on Habitual versus Goal-Directed Decision Making.

PubMed

Liu, Shuyan; Schad, Daniel J; Kuschpel, Maxim S; Rapp, Michael A; Heinz, Andreas

2016-01-01

Different systems for habitual versus goal-directed control are thought to underlie human decision-making. Working memory is known to shape these decision-making systems and their interplay, and is known to support goal-directed decision making even under stress. Here, we investigated if and how decision systems are differentially influenced by breaks filled with diverse everyday life activities known to modulate working memory performance. We used a within-subject design where young adults listened to music and played a video game during breaks interleaved with trials of a sequential two-step Markov decision task, designed to assess habitual as well as goal-directed decision making. Based on a neurocomputational model of task performance, we observed that for individuals with a rather limited working memory capacity video gaming as compared to music reduced reliance on the goal-directed decision-making system, while a rather large working memory capacity prevented such a decline. Our findings suggest differential effects of everyday activities on key decision-making processes.

Music and Video Gaming during Breaks: Influence on Habitual versus Goal-Directed Decision Making

PubMed Central

Kuschpel, Maxim S.; Rapp, Michael A.; Heinz, Andreas

2016-01-01

Different systems for habitual versus goal-directed control are thought to underlie human decision-making. Working memory is known to shape these decision-making systems and their interplay, and is known to support goal-directed decision making even under stress. Here, we investigated if and how decision systems are differentially influenced by breaks filled with diverse everyday life activities known to modulate working memory performance. We used a within-subject design where young adults listened to music and played a video game during breaks interleaved with trials of a sequential two-step Markov decision task, designed to assess habitual as well as goal-directed decision making. Based on a neurocomputational model of task performance, we observed that for individuals with a rather limited working memory capacity video gaming as compared to music reduced reliance on the goal-directed decision-making system, while a rather large working memory capacity prevented such a decline. Our findings suggest differential effects of everyday activities on key decision-making processes. PMID:26982326

An Illustration of the Use of Markov Decision Processes to Represent Student Growth (Learning). Research Report. ETS RR-07-40

ERIC Educational Resources Information Center

Almond, Russell G.

2007-01-01

Over the course of instruction, instructors generally collect a great deal of information about each student. Integrating that information intelligently requires models for how a student's proficiency changes over time. Armed with such models, instructors can "filter" the data--more accurately estimate the student's current proficiency…

Testing the Efficiency of Markov Chain Monte Carlo with People Using Facial Affect Categories

ERIC Educational Resources Information Center

Martin, Jay B.; Griffiths, Thomas L.; Sanborn, Adam N.

2012-01-01

Exploring how people represent natural categories is a key step toward developing a better understanding of how people learn, form memories, and make decisions. Much research on categorization has focused on artificial categories that are created in the laboratory, since studying natural categories defined on high-dimensional stimuli such as…

[Decision modeling for economic evaluation of health technologies].

PubMed

de Soárez, Patrícia Coelho; Soares, Marta Oliveira; Novaes, Hillegonda Maria Dutilh

2014-10-01

Most economic evaluations that participate in decision-making processes for incorporation and financing of technologies of health systems use decision models to assess the costs and benefits of the compared strategies. Despite the large number of economic evaluations conducted in Brazil, there is a pressing need to conduct an in-depth methodological study of the types of decision models and their applicability in our setting. The objective of this literature review is to contribute to the knowledge and use of decision models in the national context of economic evaluations of health technologies. This article presents general definitions about models and concerns with their use; it describes the main models: decision trees, Markov chains, micro-simulation, simulation of discrete and dynamic events; it discusses the elements involved in the choice of model; and exemplifies the models addressed in national economic evaluation studies of diagnostic and therapeutic preventive technologies and health programs.

Non parametric, self organizing, scalable modeling of spatiotemporal inputs: the sign language paradigm.

PubMed

Caridakis, G; Karpouzis, K; Drosopoulos, A; Kollias, S

2012-12-01

Modeling and recognizing spatiotemporal, as opposed to static input, is a challenging task since it incorporates input dynamics as part of the problem. The vast majority of existing methods tackle the problem as an extension of the static counterpart, using dynamics, such as input derivatives, at feature level and adopting artificial intelligence and machine learning techniques originally designed for solving problems that do not specifically address the temporal aspect. The proposed approach deals with temporal and spatial aspects of the spatiotemporal domain in a discriminative as well as coupling manner. Self Organizing Maps (SOM) model the spatial aspect of the problem and Markov models its temporal counterpart. Incorporation of adjacency, both in training and classification, enhances the overall architecture with robustness and adaptability. The proposed scheme is validated both theoretically, through an error propagation study, and experimentally, on the recognition of individual signs, performed by different, native Greek Sign Language users. Results illustrate the architecture's superiority when compared to Hidden Markov Model techniques and variations both in terms of classification performance and computational cost. Copyright © 2012 Elsevier Ltd. All rights reserved.

Reverse engineering a social agent-based hidden markov model--visage.

PubMed

Chen, Hung-Ching Justin; Goldberg, Mark; Magdon-Ismail, Malik; Wallace, William A

2008-12-01

We present a machine learning approach to discover the agent dynamics that drives the evolution of the social groups in a community. We set up the problem by introducing an agent-based hidden Markov model for the agent dynamics: an agent's actions are determined by micro-laws. Nonetheless, We learn the agent dynamics from the observed communications without knowing state transitions. Our approach is to identify the appropriate micro-laws corresponding to an identification of the appropriate parameters in the model. The model identification problem is then formulated as a mixed optimization problem. To solve the problem, we develop a multistage learning process for determining the group structure, the group evolution, and the micro-laws of a community based on the observed set of communications among actors, without knowing the semantic contents. Finally, to test the quality of our approximations and the feasibility of the approach, we present the results of extensive experiments on synthetic data as well as the results on real communities, such as Enron email and Movie newsgroups. Insight into agent dynamics helps us understand the driving forces behind social evolution.

Decision-Making in Critical Limb Ischemia: A Markov Simulation.

PubMed

Deutsch, Aaron J; Jain, C Charles; Blumenthal, Kimberly G; Dickinson, Mark W; Neilan, Anne M

2017-11-01

Critical limb ischemia (CLI) is a feared complication of peripheral vascular disease that often requires surgical management and may require amputation of the affected limb. We developed a decision model to inform clinical management for a 63-year-old woman with CLI and multiple medical comorbidities, including advanced heart failure and diabetes. We developed a Markov decision model to evaluate 4 strategies: amputation, surgical bypass, endovascular therapy (e.g. stent or revascularization), and medical management. We measured the impact of parameter uncertainty using 1-way, 2-way, and multiway sensitivity analyses. In the base case, endovascular therapy yielded similar discounted quality-adjusted life months (26.50 QALMs) compared with surgical bypass (26.34 QALMs). Both endovascular and surgical therapies were superior to amputation (18.83 QALMs) and medical management (11.08 QALMs). This finding was robust to a wide range of periprocedural mortality weights and was most sensitive to long-term mortality associated with endovascular and surgical therapies. Utility weights were not stratified by patient comorbidities; nonetheless, our conclusion was robust to a range of utility weight values. For a patient with CLI, endovascular therapy and surgical bypass provided comparable clinical outcomes. However, this finding was sensitive to long-term mortality rates associated with each procedure. Both endovascular and surgical therapies were superior to amputation or medical management in a range of scenarios. Copyright © 2017 Elsevier Inc. All rights reserved.

Hidden Markov models for evolution and comparative genomics analysis.

PubMed

Bykova, Nadezda A; Favorov, Alexander V; Mironov, Andrey A

2013-01-01

The problem of reconstruction of ancestral states given a phylogeny and data from extant species arises in a wide range of biological studies. The continuous-time Markov model for the discrete states evolution is generally used for the reconstruction of ancestral states. We modify this model to account for a case when the states of the extant species are uncertain. This situation appears, for example, if the states for extant species are predicted by some program and thus are known only with some level of reliability; it is common for bioinformatics field. The main idea is formulation of the problem as a hidden Markov model on a tree (tree HMM, tHMM), where the basic continuous-time Markov model is expanded with the introduction of emission probabilities of observed data (e.g. prediction scores) for each underlying discrete state. Our tHMM decoding algorithm allows us to predict states at the ancestral nodes as well as to refine states at the leaves on the basis of quantitative comparative genomics. The test on the simulated data shows that the tHMM approach applied to the continuous variable reflecting the probabilities of the states (i.e. prediction score) appears to be more accurate then the reconstruction from the discrete states assignment defined by the best score threshold. We provide examples of applying our model to the evolutionary analysis of N-terminal signal peptides and transcription factor binding sites in bacteria. The program is freely available at http://bioinf.fbb.msu.ru/~nadya/tHMM and via web-service at http://bioinf.fbb.msu.ru/treehmmweb.

Information-Theoretic Performance Analysis of Sensor Networks via Markov Modeling of Time Series Data.

PubMed

Li, Yue; Jha, Devesh K; Ray, Asok; Wettergren, Thomas A; Yue Li; Jha, Devesh K; Ray, Asok; Wettergren, Thomas A; Wettergren, Thomas A; Li, Yue; Ray, Asok; Jha, Devesh K

2018-06-01

This paper presents information-theoretic performance analysis of passive sensor networks for detection of moving targets. The proposed method falls largely under the category of data-level information fusion in sensor networks. To this end, a measure of information contribution for sensors is formulated in a symbolic dynamics framework. The network information state is approximately represented as the largest principal component of the time series collected across the network. To quantify each sensor's contribution for generation of the information content, Markov machine models as well as x-Markov (pronounced as cross-Markov) machine models, conditioned on the network information state, are constructed; the difference between the conditional entropies of these machines is then treated as an approximate measure of information contribution by the respective sensors. The x-Markov models represent the conditional temporal statistics given the network information state. The proposed method has been validated on experimental data collected from a local area network of passive sensors for target detection, where the statistical characteristics of environmental disturbances are similar to those of the target signal in the sense of time scale and texture. A distinctive feature of the proposed algorithm is that the network decisions are independent of the behavior and identity of the individual sensors, which is desirable from computational perspectives. Results are presented to demonstrate the proposed method's efficacy to correctly identify the presence of a target with very low false-alarm rates. The performance of the underlying algorithm is compared with that of a recent data-driven, feature-level information fusion algorithm. It is shown that the proposed algorithm outperforms the other algorithm.

Multiscale modelling and analysis of collective decision making in swarm robotics.

PubMed

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable.

AN OPTIMAL MAINTENANCE MANAGEMENT MODEL FOR AIRPORT CONCRETE PAVEMENT

NASA Astrophysics Data System (ADS)

Shimomura, Taizo; Fujimori, Yuji; Kaito, Kiyoyuki; Obama, Kengo; Kobayashi, Kiyoshi

In this paper, an optimal management model is formulated for the performance-based rehabilitation/maintenance contract for airport concrete pavement, whereby two types of life cycle cost risks, i.e., ground consolidation risk and concrete depreciation risk, are explicitly considered. The non-homogenous Markov chain model is formulated to represent the deterioration processes of concrete pavement which are conditional upon the ground consolidation processes. The optimal non-homogenous Markov decision model with multiple types of risk is presented to design the optimal rehabilitation/maintenance plans. And the methodology to revise the optimal rehabilitation/maintenance plans based upon the monitoring data by the Bayesian up-to-dating rules. The validity of the methodology presented in this paper is examined based upon the case studies carried out for the H airport.

The Discounted Method and Equivalence of Average Criteria for Risk-Sensitive Markov Decision Processes on Borel Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cavazos-Cadena, Rolando, E-mail: rcavazos@uaaan.m; Salem-Silva, Francisco, E-mail: frsalem@uv.m

2010-04-15

This note concerns discrete-time controlled Markov chains with Borel state and action spaces. Given a nonnegative cost function, the performance of a control policy is measured by the superior limit risk-sensitive average criterion associated with a constant and positive risk sensitivity coefficient. Within such a framework, the discounted approach is used (a) to establish the existence of solutions for the corresponding optimality inequality, and (b) to show that, under mild conditions on the cost function, the optimal value functions corresponding to the superior and inferior limit average criteria coincide on a certain subset of the state space. The approach ofmore » the paper relies on standard dynamic programming ideas and on a simple analytical derivation of a Tauberian relation.« less

GIS, remote sensing and spatial modeling for conservation of stone forest landscape in Lunan, China

NASA Astrophysics Data System (ADS)

Zhang, Chuanrong

The Lunan Stone Forest is the World's premier pinnacle karst landscape, with considerable scientific and cultural importance. Because of its inherent ecological fragility and ongoing human disruption, especially recently burgeoning tourism development, the landscape is stressed and is in danger of being destroyed. Conservation policies have been implemented by the local and national governments, but many problems remain in the national park. For example, there is no accurate detailed map and no computer system to help authorities manage the natural resources. By integrating GIS, remote sensing and spatial modeling this dissertation investigates the issue of landscape conservation and develops some methodologies to assist in management of the natural resources in the national park. Four elements are involved: (1) To help decision-makers and residents understand the scope of resource exploitation and develop appropriate protective strategies, the dissertation documents how the landscape has been changed by human activities over the past 3 decades; (2) To help authorities scientifically designate different levels of protection in the park and to let the public actively participate in conservation decision making, a web-based Spatial Decision Support System for the conservation of the landscape was developed; (3) To make data sharing and integration easy in the future, a GML-based interoperable database for the park was implemented; and (4) To acquire more information and provide the uncertainty information to landscape conservation decision-makers, spatial land use patterns were modeled and the distributional uncertainty of land cover categories was assessed using a triplex Markov chain (TMC) model approach.

The exit-time problem for a Markov jump process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Phase unwrapping using region-based markov random field model.

PubMed

Dong, Ying; Ji, Jim

2010-01-01

Phase unwrapping is a classical problem in Magnetic Resonance Imaging (MRI), Interferometric Synthetic Aperture Radar and Sonar (InSAR/InSAS), fringe pattern analysis, and spectroscopy. Although many methods have been proposed to address this problem, robust and effective phase unwrapping remains a challenge. This paper presents a novel phase unwrapping method using a region-based Markov Random Field (MRF) model. Specifically, the phase image is segmented into regions within which the phase is not wrapped. Then, the phase image is unwrapped between different regions using an improved Highest Confidence First (HCF) algorithm to optimize the MRF model. The proposed method has desirable theoretical properties as well as an efficient implementation. Simulations and experimental results on MRI images show that the proposed method provides similar or improved phase unwrapping than Phase Unwrapping MAx-flow/min-cut (PUMA) method and ZpM method.

A fast exact simulation method for a class of Markov jump processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yao, E-mail: yaoli@math.umass.edu; Hu, Lili, E-mail: lilyhu86@gmail.com

2015-11-14

A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze itsmore » properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.« less

Sentiment classification technology based on Markov logic networks

NASA Astrophysics Data System (ADS)

He, Hui; Li, Zhigang; Yao, Chongchong; Zhang, Weizhe

2016-07-01

With diverse online media emerging, there is a growing concern of sentiment classification problem. At present, text sentiment classification mainly utilizes supervised machine learning methods, which feature certain domain dependency. On the basis of Markov logic networks (MLNs), this study proposed a cross-domain multi-task text sentiment classification method rooted in transfer learning. Through many-to-one knowledge transfer, labeled text sentiment classification, knowledge was successfully transferred into other domains, and the precision of the sentiment classification analysis in the text tendency domain was improved. The experimental results revealed the following: (1) the model based on a MLN demonstrated higher precision than the single individual learning plan model. (2) Multi-task transfer learning based on Markov logical networks could acquire more knowledge than self-domain learning. The cross-domain text sentiment classification model could significantly improve the precision and efficiency of text sentiment classification.

Stochastic Dynamics through Hierarchically Embedded Markov Chains

NASA Astrophysics Data System (ADS)

Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.

2017-02-01

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Stability Analysis of Multi-Sensor Kalman Filtering over Lossy Networks

PubMed Central

Gao, Shouwan; Chen, Pengpeng; Huang, Dan; Niu, Qiang

2016-01-01

This paper studies the remote Kalman filtering problem for a distributed system setting with multiple sensors that are located at different physical locations. Each sensor encapsulates its own measurement data into one single packet and transmits the packet to the remote filter via a lossy distinct channel. For each communication channel, a time-homogeneous Markov chain is used to model the normal operating condition of packet delivery and losses. Based on the Markov model, a necessary and sufficient condition is obtained, which can guarantee the stability of the mean estimation error covariance. Especially, the stability condition is explicitly expressed as a simple inequality whose parameters are the spectral radius of the system state matrix and transition probabilities of the Markov chains. In contrast to the existing related results, our method imposes less restrictive conditions on systems. Finally, the results are illustrated by simulation examples. PMID:27104541

Markov chain Monte Carlo techniques applied to parton distribution functions determination: Proof of concept

NASA Astrophysics Data System (ADS)

Gbedo, Yémalin Gabin; Mangin-Brinet, Mariane

2017-07-01

We present a new procedure to determine parton distribution functions (PDFs), based on Markov chain Monte Carlo (MCMC) methods. The aim of this paper is to show that we can replace the standard χ2 minimization by procedures grounded on statistical methods, and on Bayesian inference in particular, thus offering additional insight into the rich field of PDFs determination. After a basic introduction to these techniques, we introduce the algorithm we have chosen to implement—namely Hybrid (or Hamiltonian) Monte Carlo. This algorithm, initially developed for Lattice QCD, turns out to be very interesting when applied to PDFs determination by global analyses; we show that it allows us to circumvent the difficulties due to the high dimensionality of the problem, in particular concerning the acceptance. A first feasibility study is performed and presented, which indicates that Markov chain Monte Carlo can successfully be applied to the extraction of PDFs and of their uncertainties.

Stochastic Dynamics through Hierarchically Embedded Markov Chains.

PubMed

Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M

2017-02-03

Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.

Development of coffee maker service robot using speech and face recognition systems using POMDP

NASA Astrophysics Data System (ADS)

Budiharto, Widodo; Meiliana; Santoso Gunawan, Alexander Agung

2016-07-01

There are many development of intelligent service robot in order to interact with user naturally. This purpose can be done by embedding speech and face recognition ability on specific tasks to the robot. In this research, we would like to propose Intelligent Coffee Maker Robot which the speech recognition is based on Indonesian language and powered by statistical dialogue systems. This kind of robot can be used in the office, supermarket or restaurant. In our scenario, robot will recognize user's face and then accept commands from the user to do an action, specifically in making a coffee. Based on our previous work, the accuracy for speech recognition is about 86% and face recognition is about 93% in laboratory experiments. The main problem in here is to know the intention of user about how sweetness of the coffee. The intelligent coffee maker robot should conclude the user intention through conversation under unreliable automatic speech in noisy environment. In this paper, this spoken dialog problem is treated as a partially observable Markov decision process (POMDP). We describe how this formulation establish a promising framework by empirical results. The dialog simulations are presented which demonstrate significant quantitative outcome.

Exploring complex dynamics in multi agent-based intelligent systems: Theoretical and experimental approaches using the Multi Agent-based Behavioral Economic Landscape (MABEL) model

NASA Astrophysics Data System (ADS)

Alexandridis, Konstantinos T.

This dissertation adopts a holistic and detailed approach to modeling spatially explicit agent-based artificial intelligent systems, using the Multi Agent-based Behavioral Economic Landscape (MABEL) model. The research questions that addresses stem from the need to understand and analyze the real-world patterns and dynamics of land use change from a coupled human-environmental systems perspective. Describes the systemic, mathematical, statistical, socio-economic and spatial dynamics of the MABEL modeling framework, and provides a wide array of cross-disciplinary modeling applications within the research, decision-making and policy domains. Establishes the symbolic properties of the MABEL model as a Markov decision process, analyzes the decision-theoretic utility and optimization attributes of agents towards comprising statistically and spatially optimal policies and actions, and explores the probabilogic character of the agents' decision-making and inference mechanisms via the use of Bayesian belief and decision networks. Develops and describes a Monte Carlo methodology for experimental replications of agent's decisions regarding complex spatial parcel acquisition and learning. Recognizes the gap on spatially-explicit accuracy assessment techniques for complex spatial models, and proposes an ensemble of statistical tools designed to address this problem. Advanced information assessment techniques such as the Receiver-Operator Characteristic curve, the impurity entropy and Gini functions, and the Bayesian classification functions are proposed. The theoretical foundation for modular Bayesian inference in spatially-explicit multi-agent artificial intelligent systems, and the ensembles of cognitive and scenario assessment modular tools build for the MABEL model are provided. Emphasizes the modularity and robustness as valuable qualitative modeling attributes, and examines the role of robust intelligent modeling as a tool for improving policy-decisions related to land use change. Finally, the major contributions to the science are presented along with valuable directions for future research.

Service-Oriented Node Scheduling Scheme for Wireless Sensor Networks Using Markov Random Field Model

PubMed Central

Cheng, Hongju; Su, Zhihuang; Lloret, Jaime; Chen, Guolong

2014-01-01

Future wireless sensor networks are expected to provide various sensing services and energy efficiency is one of the most important criterions. The node scheduling strategy aims to increase network lifetime by selecting a set of sensor nodes to provide the required sensing services in a periodic manner. In this paper, we are concerned with the service-oriented node scheduling problem to provide multiple sensing services while maximizing the network lifetime. We firstly introduce how to model the data correlation for different services by using Markov Random Field (MRF) model. Secondly, we formulate the service-oriented node scheduling issue into three different problems, namely, the multi-service data denoising problem which aims at minimizing the noise level of sensed data, the representative node selection problem concerning with selecting a number of active nodes while determining the services they provide, and the multi-service node scheduling problem which aims at maximizing the network lifetime. Thirdly, we propose a Multi-service Data Denoising (MDD) algorithm, a novel multi-service Representative node Selection and service Determination (RSD) algorithm, and a novel MRF-based Multi-service Node Scheduling (MMNS) scheme to solve the above three problems respectively. Finally, extensive experiments demonstrate that the proposed scheme efficiently extends the network lifetime. PMID:25384005

On the Role of Situational Stressors in the Disruption of Global Neural Network Stability during Problem Solving.

PubMed

Liu, Mengting; Amey, Rachel C; Forbes, Chad E

2017-12-01

When individuals are placed in stressful situations, they are likely to exhibit deficits in cognitive capacity over and above situational demands. Despite this, individuals may still persevere and ultimately succeed in these situations. Little is known, however, about neural network properties that instantiate success or failure in both neutral and stressful situations, particularly with respect to regions integral for problem-solving processes that are necessary for optimal performance on more complex tasks. In this study, we outline how hidden Markov modeling based on multivoxel pattern analysis can be used to quantify unique brain states underlying complex network interactions that yield either successful or unsuccessful problem solving in more neutral or stressful situations. We provide evidence that brain network stability and states underlying synchronous interactions in regions integral for problem-solving processes are key predictors of whether individuals succeed or fail in stressful situations. Findings also suggested that individuals utilize discriminate neural patterns in successfully solving problems in stressful or neutral situations. Findings overall highlight how hidden Markov modeling can provide myriad possibilities for quantifying and better understanding the role of global network interactions in the problem-solving process and how the said interactions predict success or failure in different contexts.

Research on Learning Strategies and Hands-On Training in CAI. Final Report, 1 January 1975 to 30 September 1978.

ERIC Educational Resources Information Center

Towne, Douglas M.; And Others

This final report reviews research performed in two major areas--instructional theory, and development of a generalized maintenance trainer simulator. Five related research projects were carried out in the domain of instructional theory: (1) the effects of visual analogies of abstract concepts, (2) Markov decision models for instructional sequence…

Developmental changes in autonomic responses are associated with future reward/punishment expectations: A study of sympathetic skin responses in the Markov decision task.

PubMed

Hosaka, Hiromi; Aoyagi, Kakuro; Kaga, Yoshimi; Kanemura, Hideaki; Sugita, Kanji; Aihara, Masao

2017-08-01

Autonomic nervous system activity is recognized as a major component of emotional responses. Future reward/punishment expectations depend upon the process of decision making in the frontal lobe, which is considered to play an important role in executive function. The aim of this study was to investigate the relationship between autonomic responses and decision making during reinforcement tasks using sympathetic skin responses (SSR). Nine adult and 9 juvenile (mean age, 10.2years) volunteers were enrolled in this study. SSRs were measured during the Markov decision task (MDT), which is a reinforcement task. In this task, subjects must endure a small immediate loss to ultimately get a large reward. The subjects had to undergo three sets of tests and their scores in these tests were assessed and evaluated. All adults showed gradually increasing scores for the MDT from the first to third set. As the trial progressed from the first to second set in adults, SSR appearance ratios remarkably increased for both punishment and reward expectations. In comparison with adults, children showed decreasing scores from the first to second set. There were no significant inter-target differences in the SSR appearance ratio in the first and second set in children. In the third set, the SSR appearance ratio for reward expectations was higher than that in the neutral condition. In reinforcement tasks, such as MDT, autonomic responses play an important role in decision making. We assume that SSRs are elicited during efficient decision making tasks associated with future reward/punishment expectations, which demonstrates the importance of autonomic function. In contrast, in children around the age of 10years, the autonomic system does not react as an organized response specific to reward/punishment expectations. This suggests the immaturity of the future reward/punishment expectations process in children. Copyright © 2017 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.

Selecting a dynamic simulation modeling method for health care delivery research-part 2: report of the ISPOR Dynamic Simulation Modeling Emerging Good Practices Task Force.

PubMed

Marshall, Deborah A; Burgos-Liz, Lina; IJzerman, Maarten J; Crown, William; Padula, William V; Wong, Peter K; Pasupathy, Kalyan S; Higashi, Mitchell K; Osgood, Nathaniel D

2015-03-01

In a previous report, the ISPOR Task Force on Dynamic Simulation Modeling Applications in Health Care Delivery Research Emerging Good Practices introduced the fundamentals of dynamic simulation modeling and identified the types of health care delivery problems for which dynamic simulation modeling can be used more effectively than other modeling methods. The hierarchical relationship between the health care delivery system, providers, patients, and other stakeholders exhibits a level of complexity that ought to be captured using dynamic simulation modeling methods. As a tool to help researchers decide whether dynamic simulation modeling is an appropriate method for modeling the effects of an intervention on a health care system, we presented the System, Interactions, Multilevel, Understanding, Loops, Agents, Time, Emergence (SIMULATE) checklist consisting of eight elements. This report builds on the previous work, systematically comparing each of the three most commonly used dynamic simulation modeling methods-system dynamics, discrete-event simulation, and agent-based modeling. We review criteria for selecting the most suitable method depending on 1) the purpose-type of problem and research questions being investigated, 2) the object-scope of the model, and 3) the method to model the object to achieve the purpose. Finally, we provide guidance for emerging good practices for dynamic simulation modeling in the health sector, covering all aspects, from the engagement of decision makers in the model design through model maintenance and upkeep. We conclude by providing some recommendations about the application of these methods to add value to informed decision making, with an emphasis on stakeholder engagement, starting with the problem definition. Finally, we identify areas in which further methodological development will likely occur given the growing "volume, velocity and variety" and availability of "big data" to provide empirical evidence and techniques such as machine learning for parameter estimation in dynamic simulation models. Upon reviewing this report in addition to using the SIMULATE checklist, the readers should be able to identify whether dynamic simulation modeling methods are appropriate to address the problem at hand and to recognize the differences of these methods from those of other, more traditional modeling approaches such as Markov models and decision trees. This report provides an overview of these modeling methods and examples of health care system problems in which such methods have been useful. The primary aim of the report was to aid decisions as to whether these simulation methods are appropriate to address specific health systems problems. The report directs readers to other resources for further education on these individual modeling methods for system interventions in the emerging field of health care delivery science and implementation. Copyright © 2015. Published by Elsevier Inc.

A multicriteria decision making approach applied to improving maintenance policies in healthcare organizations.

PubMed

Carnero, María Carmen; Gómez, Andrés

2016-04-23

Healthcare organizations have far greater maintenance needs for their medical equipment than other organization, as many are used directly with patients. However, the literature on asset management in healthcare organizations is very limited. The aim of this research is to provide more rational application of maintenance policies, leading to an increase in quality of care. This article describes a multicriteria decision-making approach which integrates Markov chains with the multicriteria Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH), to facilitate the best choice of combination of maintenance policies by using the judgements of a multi-disciplinary decision group. The proposed approach takes into account the level of acceptance that a given alternative would have among professionals. It also takes into account criteria related to cost, quality of care and impact of care cover. This multicriteria approach is applied to four dialysis subsystems: patients infected with hepatitis C, infected with hepatitis B, acute and chronic; in all cases, the maintenance strategy obtained consists of applying corrective and preventive maintenance plus two reserve machines. The added value in decision-making practices from this research comes from: (i) integrating the use of Markov chains to obtain the alternatives to be assessed by a multicriteria methodology; (ii) proposing the use of MACBETH to make rational decisions on asset management in healthcare organizations; (iii) applying the multicriteria approach to select a set or combination of maintenance policies in four dialysis subsystems of a health care organization. In the multicriteria decision making approach proposed, economic criteria have been used, related to the quality of care which is desired for patients (availability), and the acceptance that each alternative would have considering the maintenance and healthcare resources which exist in the organization, with the inclusion of a decision-making group. This approach is better suited to actual health care organization practice and depending on the subsystem analysed, improvements are introduced that are not included in normal maintenance policies; in this way, not only have different maintenance policies been suggested, but also alternatives that, in each case and according to viability, provide a more complete decision tool for the maintenance manager.

Towards automatic Markov reliability modeling of computer architectures

NASA Technical Reports Server (NTRS)

Liceaga, C. A.; Siewiorek, D. P.

1986-01-01

The analysis and evaluation of reliability measures using time-varying Markov models is required for Processor-Memory-Switch (PMS) structures that have competing processes such as standby redundancy and repair, or renewal processes such as transient or intermittent faults. The task of generating these models is tedious and prone to human error due to the large number of states and transitions involved in any reasonable system. Therefore model formulation is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model formulation. This paper presents an overview of the Automated Reliability Modeling (ARM) program, under development at NASA Langley Research Center. ARM will accept as input a description of the PMS interconnection graph, the behavior of the PMS components, the fault-tolerant strategies, and the operational requirements. The output of ARM will be the reliability of availability Markov model formulated for direct use by evaluation programs. The advantages of such an approach are (a) utility to a large class of users, not necessarily expert in reliability analysis, and (b) a lower probability of human error in the computation.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

A proactive transfer policy for critical patient flow management.

PubMed

González, Jaime; Ferrer, Juan-Carlos; Cataldo, Alejandro; Rojas, Luis

2018-02-17

Hospital emergency departments are often overcrowded, resulting in long wait times and a public perception of poor attention. Delays in transferring patients needing further treatment increases emergency department congestion, has negative impacts on their health and may increase their mortality rates. A model built around a Markov decision process is proposed to improve the efficiency of patient flows between the emergency department and other hospital units. With each day divided into time periods, the formulation estimates bed demand for the next period as the basis for determining a proactive rather than reactive transfer decision policy. Due to the high dimensionality of the optimization problem involved, an approximate dynamic programming approach is used to derive an approximation of the optimal decision policy, which indicates that a certain number of beds should be kept free in the different units as a function of the next period demand estimate. Testing the model on two instances of different sizes demonstrates that the optimal number of patient transfers between units changes when the emergency patient arrival rate for transfer to other units changes at a single unit, but remains stable if the change is proportionally the same for all units. In a simulation using real data for a hospital in Chile, significant improvements are achieved by the model in key emergency department performance indicators such as patient wait times (reduction higher than 50%), patient capacity (21% increase) and queue abandonment (from 7% down to less than 1%).

Application of the intelligent techniques in transplantation databases: a review of articles published in 2009 and 2010.

PubMed

Sousa, F S; Hummel, A D; Maciel, R F; Cohrs, F M; Falcão, A E J; Teixeira, F; Baptista, R; Mancini, F; da Costa, T M; Alves, D; Pisa, I T

2011-05-01

The replacement of defective organs with healthy ones is an old problem, but only a few years ago was this issue put into practice. Improvements in the whole transplantation process have been increasingly important in clinical practice. In this context are clinical decision support systems (CDSSs), which have reflected a significant amount of work to use mathematical and intelligent techniques. The aim of this article was to present consideration of intelligent techniques used in recent years (2009 and 2010) to analyze organ transplant databases. To this end, we performed a search of the PubMed and Institute for Scientific Information (ISI) Web of Knowledge databases to find articles published in 2009 and 2010 about intelligent techniques applied to transplantation databases. Among 69 retrieved articles, we chose according to inclusion and exclusion criteria. The main techniques were: Artificial Neural Networks (ANN), Logistic Regression (LR), Decision Trees (DT), Markov Models (MM), and Bayesian Networks (BN). Most articles used ANN. Some publications described comparisons between techniques or the use of various techniques together. The use of intelligent techniques to extract knowledge from databases of healthcare is increasingly common. Although authors preferred to use ANN, statistical techniques were equally effective for this enterprise. Copyright © 2011 Elsevier Inc. All rights reserved.

Reciprocal Markov Modeling of Feedback Mechanisms Between Emotion and Dietary Choice Using Experience-Sampling Data.

PubMed

Lu, Ji; Pan, Junhao; Zhang, Qiang; Dubé, Laurette; Ip, Edward H

2015-01-01

With intensively collected longitudinal data, recent advances in the experience-sampling method (ESM) benefit social science empirical research, but also pose important methodological challenges. As traditional statistical models are not generally well equipped to analyze a system of variables that contain feedback loops, this paper proposes the utility of an extended hidden Markov model to model reciprocal the relationship between momentary emotion and eating behavior. This paper revisited an ESM data set (Lu, Huet, & Dube, 2011) that observed 160 participants' food consumption and momentary emotions 6 times per day in 10 days. Focusing on the analyses on feedback loop between mood and meal-healthiness decision, the proposed reciprocal Markov model (RMM) can accommodate both hidden ("general" emotional states: positive vs. negative state) and observed states (meal: healthier, same or less healthy than usual) without presuming independence between observations and smooth trajectories of mood or behavior changes. The results of RMM analyses illustrated the reciprocal chains of meal consumption and mood as well as the effect of contextual factors that moderate the interrelationship between eating and emotion. A simulation experiment that generated data consistent with the empirical study further demonstrated that the procedure is promising in terms of recovering the parameters.

Meta-heuristic ant colony optimization technique to forecast the amount of summer monsoon rainfall: skill comparison with Markov chain model

NASA Astrophysics Data System (ADS)

Chaudhuri, Sutapa; Goswami, Sayantika; Das, Debanjana; Middey, Anirban

2014-05-01

Forecasting summer monsoon rainfall with precision becomes crucial for the farmers to plan for harvesting in a country like India where the national economy is mostly based on regional agriculture. The forecast of monsoon rainfall based on artificial neural network is a well-researched problem. In the present study, the meta-heuristic ant colony optimization (ACO) technique is implemented to forecast the amount of summer monsoon rainfall for the next day over Kolkata (22.6°N, 88.4°E), India. The ACO technique belongs to swarm intelligence and simulates the decision-making processes of ant colony similar to other adaptive learning techniques. ACO technique takes inspiration from the foraging behaviour of some ant species. The ants deposit pheromone on the ground in order to mark a favourable path that should be followed by other members of the colony. A range of rainfall amount replicating the pheromone concentration is evaluated during the summer monsoon season. The maximum amount of rainfall during summer monsoon season (June—September) is observed to be within the range of 7.5-35 mm during the period from 1998 to 2007, which is in the range 4 category set by the India Meteorological Department (IMD). The result reveals that the accuracy in forecasting the amount of rainfall for the next day during the summer monsoon season using ACO technique is 95 % where as the forecast accuracy is 83 % with Markov chain model (MCM). The forecast through ACO and MCM are compared with other existing models and validated with IMD observations from 2008 to 2012.

(n, N) type maintenance policy for multi-component systems with failure interactions

NASA Astrophysics Data System (ADS)

Zhang, Zhuoqi; Wu, Su; Li, Binfeng; Lee, Seungchul

2015-04-01

This paper studies maintenance policies for multi-component systems in which failure interactions and opportunistic maintenance (OM) involve. This maintenance problem can be formulated as a Markov decision process (MDP). However, since an action set and state space in MDP exponentially expand as the number of components increase, traditional approaches are computationally intractable. To deal with curse of dimensionality, we decompose such a multi-component system into mutually influential single-component systems. Each single-component system is formulated as an MDP with the objective of minimising its long-run average maintenance cost. Under some reasonable assumptions, we prove the existence of the optimal (n, N) type policy for a single-component system. An algorithm to obtain the optimal (n, N) type policy is also proposed. Based on the proposed algorithm, we develop an iterative approximation algorithm to obtain an acceptable maintenance policy for a multi-component system. Numerical examples find that failure interactions and OM pose significant effects on a maintenance policy.

Microgrid energy dispatching for industrial zones with renewable generations and electric vehicles via stochastic optimization and learning

NASA Astrophysics Data System (ADS)

Zhang, Kai; Li, Jingzhi; He, Zhubin; Yan, Wanfeng

2018-07-01

In this paper, a stochastic optimization framework is proposed to address the microgrid energy dispatching problem with random renewable generation and vehicle activity pattern, which is closer to the practical applications. The patterns of energy generation, consumption and storage availability are all random and unknown at the beginning, and the microgrid controller design (MCD) is formulated as a Markov decision process (MDP). Hence, an online learning-based control algorithm is proposed for the microgrid, which could adapt the control policy with increasing knowledge of the system dynamics and converges to the optimal algorithm. We adopt the linear approximation idea to decompose the original value functions as the summation of each per-battery value function. As a consequence, the computational complexity is significantly reduced from exponential growth to linear growth with respect to the size of battery states. Monte Carlo simulation of different scenarios demonstrates the effectiveness and efficiency of our algorithm.

Markov Chain Monte Carlo Methods for Bayesian Data Analysis in Astronomy

NASA Astrophysics Data System (ADS)

Sharma, Sanjib

2017-08-01

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis. Finally, we discuss advanced ideas that enable us to tackle complex problems and thus hold great promise for the future. We also distribute downloadable computer software (available at https://github.com/sanjibs/bmcmc/ ) that implements some of the algorithms and examples discussed here.

From empirical data to time-inhomogeneous continuous Markov processes.

PubMed

Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G

2016-03-01

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

Multiscale Modelling and Analysis of Collective Decision Making in Swarm Robotics

PubMed Central

Vigelius, Matthias; Meyer, Bernd; Pascoe, Geoffrey

2014-01-01

We present a unified approach to describing certain types of collective decision making in swarm robotics that bridges from a microscopic individual-based description to aggregate properties. Our approach encompasses robot swarm experiments, microscopic and probabilistic macroscopic-discrete simulations as well as an analytic mathematical model. Following up on previous work, we identify the symmetry parameter, a measure of the progress of the swarm towards a decision, as a fundamental integrated swarm property and formulate its time evolution as a continuous-time Markov process. Contrary to previous work, which justified this approach only empirically and a posteriori, we justify it from first principles and derive hard limits on the parameter regime in which it is applicable. PMID:25369026

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1995-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) (vertical bar)/x), 1 less than or equal to i isless than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Hidden Markov models for fault detection in dynamic systems

NASA Technical Reports Server (NTRS)

Smyth, Padhraic J. (Inventor)

1993-01-01

The invention is a system failure monitoring method and apparatus which learns the symptom-fault mapping directly from training data. The invention first estimates the state of the system at discrete intervals in time. A feature vector x of dimension k is estimated from sets of successive windows of sensor data. A pattern recognition component then models the instantaneous estimate of the posterior class probability given the features, p(w(sub i) perpendicular to x), 1 less than or equal to i is less than or equal to m. Finally, a hidden Markov model is used to take advantage of temporal context and estimate class probabilities conditioned on recent past history. In this hierarchical pattern of information flow, the time series data is transformed and mapped into a categorical representation (the fault classes) and integrated over time to enable robust decision-making.

Predicting Loss-of-Control Boundaries Toward a Piloting Aid

NASA Technical Reports Server (NTRS)

Barlow, Jonathan; Stepanyan, Vahram; Krishnakumar, Kalmanje

2012-01-01

This work presents an approach to predicting loss-of-control with the goal of providing the pilot a decision aid focused on maintaining the pilot's control action within predicted loss-of-control boundaries. The predictive architecture combines quantitative loss-of-control boundaries, a data-based predictive control boundary estimation algorithm and an adaptive prediction method to estimate Markov model parameters in real-time. The data-based loss-of-control boundary estimation algorithm estimates the boundary of a safe set of control inputs that will keep the aircraft within the loss-of-control boundaries for a specified time horizon. The adaptive prediction model generates estimates of the system Markov Parameters, which are used by the data-based loss-of-control boundary estimation algorithm. The combined algorithm is applied to a nonlinear generic transport aircraft to illustrate the features of the architecture.

HIPPI: highly accurate protein family classification with ensembles of HMMs.

PubMed

Nguyen, Nam-Phuong; Nute, Michael; Mirarab, Siavash; Warnow, Tandy

2016-11-11

Given a new biological sequence, detecting membership in a known family is a basic step in many bioinformatics analyses, with applications to protein structure and function prediction and metagenomic taxon identification and abundance profiling, among others. Yet family identification of sequences that are distantly related to sequences in public databases or that are fragmentary remains one of the more difficult analytical problems in bioinformatics. We present a new technique for family identification called HIPPI (Hierarchical Profile Hidden Markov Models for Protein family Identification). HIPPI uses a novel technique to represent a multiple sequence alignment for a given protein family or superfamily by an ensemble of profile hidden Markov models computed using HMMER. An evaluation of HIPPI on the Pfam database shows that HIPPI has better overall precision and recall than blastp, HMMER, and pipelines based on HHsearch, and maintains good accuracy even for fragmentary query sequences and for protein families with low average pairwise sequence identity, both conditions where other methods degrade in accuracy. HIPPI provides accurate protein family identification and is robust to difficult model conditions. Our results, combined with observations from previous studies, show that ensembles of profile Hidden Markov models can better represent multiple sequence alignments than a single profile Hidden Markov model, and thus can improve downstream analyses for various bioinformatic tasks. Further research is needed to determine the best practices for building the ensemble of profile Hidden Markov models. HIPPI is available on GitHub at https://github.com/smirarab/sepp .

Using Partially Observed Markov Decision Processes (POMDPs) to Implement a Response to Intervention (RTI) Framework for Early Reading

ERIC Educational Resources Information Center

Tokac, Umit

2016-01-01

The dissertation explored the efficacy of using a POMDP to select and apply appropriate instruction. POMDPs are a tool for planning: selecting a sequence of actions that will lead to an optimal outcome. RTI is an approach to instruction, where teachers craft individual plans for students based on the results of screening test. The goal is to…

Bootstrap simulation, Markov decision process models, and role of discounting in the valuation of ecological criteria in uneven-aged forest management

Treesearch

Mo Zhou; Joseph Buongiorno; Jingjing Liang

2012-01-01

Besides the market value of timber, forests provide substantial nonmarket benefits, especially with continuous-cover silviculture, which have long been acknowledged by forest managers. They include wildlife habitat (e.g. Bevers and Hof 1999), carbon sequestration (e.g. Dewar and Cannell 1992), biodiversity (e.g. Kangas and Kuusipalo 1993; Austin and Meyers 1999),...

Blended near-optimal alternative generation, visualization, and interaction for water resources decision making

NASA Astrophysics Data System (ADS)

Rosenberg, David E.

2015-04-01

State-of-the-art systems analysis techniques focus on efficiently finding optimal solutions. Yet an optimal solution is optimal only for the modeled issues and managers often seek near-optimal alternatives that address unmodeled objectives, preferences, limits, uncertainties, and other issues. Early on, Modeling to Generate Alternatives (MGA) formalized near-optimal as performance within a tolerable deviation from the optimal objective function value and identified a few maximally different alternatives that addressed some unmodeled issues. This paper presents new stratified, Monte-Carlo Markov Chain sampling and parallel coordinate plotting tools that generate and communicate the structure and extent of the near-optimal region to an optimization problem. Interactive plot controls allow users to explore region features of most interest. Controls also streamline the process to elicit unmodeled issues and update the model formulation in response to elicited issues. Use for an example, single-objective, linear water quality management problem at Echo Reservoir, Utah, identifies numerous and flexible practices to reduce the phosphorus load to the reservoir and maintain close-to-optimal performance. Flexibility is upheld by further interactive alternative generation, transforming the formulation into a multiobjective problem, and relaxing the tolerance parameter to expand the near-optimal region. Compared to MGA, the new blended tools generate more numerous alternatives faster, more fully show the near-optimal region, and help elicit a larger set of unmodeled issues.

A multi-level solution algorithm for steady-state Markov chains

NASA Technical Reports Server (NTRS)

Horton, Graham; Leutenegger, Scott T.

1993-01-01

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Tropical geometry of statistical models.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

Optimal firm growth under the threat of entry

PubMed Central

Kort, Peter M.; Wrzaczek, Stefan

2015-01-01

The paper studies the incumbent-entrant problem in a fully dynamic setting. We find that under an open-loop information structure the incumbent anticipates entry by overinvesting, whereas in the Markov perfect equilibrium the incumbent slightly underinvests in the period before the entry. The entry cost level where entry accommodation passes into entry deterrence is lower in the Markov perfect equilibrium. Further we find that the incumbent’s capital stock level needed to deter entry is hump shaped as a function of the entry time, whereas the corresponding entry cost, where the entrant is indifferent between entry and non-entry, is U-shaped. PMID:26435573

Hypovigilance Detection for UCAV Operators Based on a Hidden Markov Model

PubMed Central

Kwon, Namyeon; Shin, Yongwook; Ryo, Chuh Yeop; Park, Jonghun

2014-01-01

With the advance of military technology, the number of unmanned combat aerial vehicles (UCAVs) has rapidly increased. However, it has been reported that the accident rate of UCAVs is much higher than that of manned combat aerial vehicles. One of the main reasons for the high accident rate of UCAVs is the hypovigilance problem which refers to the decrease in vigilance levels of UCAV operators while maneuvering. In this paper, we propose hypovigilance detection models for UCAV operators based on EEG signal to minimize the number of occurrences of hypovigilance. To enable detection, we have applied hidden Markov models (HMMs), two of which are used to indicate the operators' dual states, normal vigilance and hypovigilance, and, for each operator, the HMMs are trained as a detection model. To evaluate the efficacy and effectiveness of the proposed models, we conducted two experiments on the real-world data obtained by using EEG-signal acquisition devices, and they yielded satisfactory results. By utilizing the proposed detection models, the problem of hypovigilance of UCAV operators and the problem of high accident rate of UCAVs can be addressed. PMID:24963338

Set-free Markov state model building

NASA Astrophysics Data System (ADS)

Weber, Marcus; Fackeldey, Konstantin; Schütte, Christof

2017-03-01

Molecular dynamics (MD) simulations face challenging problems since the time scales of interest often are much longer than what is possible to simulate; and even if sufficiently long simulations are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant time scales accessible via coarse grained representations that also allow for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows us to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.

INDEXABILITY AND OPTIMAL INDEX POLICIES FOR A CLASS OF REINITIALISING RESTLESS BANDITS.

PubMed

Villar, Sofía S

2016-01-01

Motivated by a class of Partially Observable Markov Decision Processes with application in surveillance systems in which a set of imperfectly observed state processes is to be inferred from a subset of available observations through a Bayesian approach, we formulate and analyze a special family of multi-armed restless bandit problems. We consider the problem of finding an optimal policy for observing the processes that maximizes the total expected net rewards over an infinite time horizon subject to the resource availability. From the Lagrangian relaxation of the original problem, an index policy can be derived, as long as the existence of the Whittle index is ensured. We demonstrate that such a class of reinitializing bandits in which the projects' state deteriorates while active and resets to its initial state when passive until its completion possesses the structural property of indexability and we further show how to compute the index in closed form. In general, the Whittle index rule for restless bandit problems does not achieve optimality. However, we show that the proposed Whittle index rule is optimal for the problem under study in the case of stochastically heterogenous arms under the expected total criterion, and it is further recovered by a simple tractable rule referred to as the 1-limited Round Robin rule. Moreover, we illustrate the significant suboptimality of other widely used heuristic: the Myopic index rule, by computing in closed form its suboptimality gap. We present numerical studies which illustrate for the more general instances the performance advantages of the Whittle index rule over other simple heuristics.

INDEXABILITY AND OPTIMAL INDEX POLICIES FOR A CLASS OF REINITIALISING RESTLESS BANDITS

PubMed Central

Villar, Sofía S.

2016-01-01

Motivated by a class of Partially Observable Markov Decision Processes with application in surveillance systems in which a set of imperfectly observed state processes is to be inferred from a subset of available observations through a Bayesian approach, we formulate and analyze a special family of multi-armed restless bandit problems. We consider the problem of finding an optimal policy for observing the processes that maximizes the total expected net rewards over an infinite time horizon subject to the resource availability. From the Lagrangian relaxation of the original problem, an index policy can be derived, as long as the existence of the Whittle index is ensured. We demonstrate that such a class of reinitializing bandits in which the projects’ state deteriorates while active and resets to its initial state when passive until its completion possesses the structural property of indexability and we further show how to compute the index in closed form. In general, the Whittle index rule for restless bandit problems does not achieve optimality. However, we show that the proposed Whittle index rule is optimal for the problem under study in the case of stochastically heterogenous arms under the expected total criterion, and it is further recovered by a simple tractable rule referred to as the 1-limited Round Robin rule. Moreover, we illustrate the significant suboptimality of other widely used heuristic: the Myopic index rule, by computing in closed form its suboptimality gap. We present numerical studies which illustrate for the more general instances the performance advantages of the Whittle index rule over other simple heuristics. PMID:27212781

Network switching strategy for energy conservation in heterogeneous networks.

PubMed

Song, Yujae; Choi, Wooyeol; Baek, Seungjae

2017-01-01

In heterogeneous networks (HetNets), the large-scale deployment of small base stations (BSs) together with traditional macro BSs is an economical and efficient solution that is employed to address the exponential growth in mobile data traffic. In dense HetNets, network switching, i.e., handovers, plays a critical role in connecting a mobile terminal (MT) to the best of all accessible networks. In the existing literature, a handover decision is made using various handover metrics such as the signal-to-noise ratio, data rate, and movement speed. However, there are few studies on handovers that focus on energy efficiency in HetNets. In this paper, we propose a handover strategy that helps to minimize energy consumption at BSs in HetNets without compromising the quality of service (QoS) of each MT. The proposed handover strategy aims to capture the effect of the stochastic behavior of handover parameters and the expected energy consumption due to handover execution when making a handover decision. To identify the validity of the proposed handover strategy, we formulate a handover problem as a constrained Markov decision process (CMDP), by which the effects of the stochastic behaviors of handover parameters and consequential handover energy consumption can be accurately reflected when making a handover decision. In the CMDP, the aim is to minimize the energy consumption to service an MT over the lifetime of its connection, and the constraint is to guarantee the QoS requirements of the MT given in terms of the transmission delay and call-dropping probability. We find an optimal policy for the CMDP using a combination of the Lagrangian method and value iteration. Simulation results verify the validity of the proposed handover strategy.

High-Resolution Remote Sensing Image Building Extraction Based on Markov Model

NASA Astrophysics Data System (ADS)

Zhao, W.; Yan, L.; Chang, Y.; Gong, L.

2018-04-01

With the increase of resolution, remote sensing images have the characteristics of increased information load, increased noise, more complex feature geometry and texture information, which makes the extraction of building information more difficult. To solve this problem, this paper designs a high resolution remote sensing image building extraction method based on Markov model. This method introduces Contourlet domain map clustering and Markov model, captures and enhances the contour and texture information of high-resolution remote sensing image features in multiple directions, and further designs the spectral feature index that can characterize "pseudo-buildings" in the building area. Through the multi-scale segmentation and extraction of image features, the fine extraction from the building area to the building is realized. Experiments show that this method can restrain the noise of high-resolution remote sensing images, reduce the interference of non-target ground texture information, and remove the shadow, vegetation and other pseudo-building information, compared with the traditional pixel-level image information extraction, better performance in building extraction precision, accuracy and completeness.

Large deviations and mixing for dissipative PDEs with unbounded random kicks

NASA Astrophysics Data System (ADS)

Jakšić, V.; Nersesyan, V.; Pillet, C.-A.; Shirikyan, A.

2018-02-01

We study the problem of exponential mixing and large deviations for discrete-time Markov processes associated with a class of random dynamical systems. Under some dissipativity and regularisation hypotheses for the underlying deterministic dynamics and a non-degeneracy condition for the driving random force, we discuss the existence and uniqueness of a stationary measure and its exponential stability in the Kantorovich-Wasserstein metric. We next turn to the large deviations principle (LDP) and establish its validity for the occupation measures of the Markov processes in question. The proof is based on Kifer’s criterion for non-compact spaces, a result on large-time asymptotics for generalised Markov semigroup, and a coupling argument. These tools combined together constitute a new approach to LDP for infinite-dimensional processes without strong Feller property in a non-compact space. The results obtained can be applied to the two-dimensional Navier-Stokes system in a bounded domain and to the complex Ginzburg-Landau equation.

Stochastic Adaptive Estimation and Control.

DTIC Science & Technology

1994-10-26

Marcus, "Language Stability and Stabilizability of Discrete Event Dynamical Systems ," SIAM Journal on Control and Optimization, 31, September 1993...in the hierarchical control of flexible manufacturing systems ; in this problem, the model involves a hybrid process in continuous time whose state is...of the average cost control problem for discrete- time Markov processes. Our exposition covers from finite to Borel state and action spaces and

The Embedding Problem for Markov Models of Nucleotide Substitution

PubMed Central

Verbyla, Klara L.; Yap, Von Bing; Pahwa, Anuj; Shao, Yunli; Huttley, Gavin A.

2013-01-01

Continuous-time Markov processes are often used to model the complex natural phenomenon of sequence evolution. To make the process of sequence evolution tractable, simplifying assumptions are often made about the sequence properties and the underlying process. The validity of one such assumption, time-homogeneity, has never been explored. Violations of this assumption can be found by identifying non-embeddability. A process is non-embeddable if it can not be embedded in a continuous time-homogeneous Markov process. In this study, non-embeddability was demonstrated to exist when modelling sequence evolution with Markov models. Evidence of non-embeddability was found primarily at the third codon position, possibly resulting from changes in mutation rate over time. Outgroup edges and those with a deeper time depth were found to have an increased probability of the underlying process being non-embeddable. Overall, low levels of non-embeddability were detected when examining individual edges of triads across a diverse set of alignments. Subsequent phylogenetic reconstruction analyses demonstrated that non-embeddability could impact on the correct prediction of phylogenies, but at extremely low levels. Despite the existence of non-embeddability, there is minimal evidence of violations of the local time homogeneity assumption and consequently the impact is likely to be minor. PMID:23935949

Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures

NASA Astrophysics Data System (ADS)

Larmier, Coline; Zoia, Andrea; Malvagi, Fausto; Dumonteil, Eric; Mazzolo, Alain

2018-02-01

Particle transport in Markov mixtures can be addressed by the so-called Chord Length Sampling (CLS) methods, a family of Monte Carlo algorithms taking into account the effects of stochastic media on particle propagation by generating on-the-fly the material interfaces crossed by the random walkers during their trajectories. Such methods enable a significant reduction of computational resources as opposed to reference solutions obtained by solving the Boltzmann equation for a large number of realizations of random media. CLS solutions, which neglect correlations induced by the spatial disorder, are faster albeit approximate, and might thus show discrepancies with respect to reference solutions. In this work we propose a new family of algorithms (called 'Poisson Box Sampling', PBS) aimed at improving the accuracy of the CLS approach for transport in d-dimensional binary Markov mixtures. In order to probe the features of PBS methods, we will focus on three-dimensional Markov media and revisit the benchmark problem originally proposed by Adams, Larsen and Pomraning [1] and extended by Brantley [2]: for these configurations we will compare reference solutions, standard CLS solutions and the new PBS solutions for scalar particle flux, transmission and reflection coefficients. PBS will be shown to perform better than CLS at the expense of a reasonable increase in computational time.

Markov blanket-based approach for learning multi-dimensional Bayesian network classifiers: an application to predict the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39).

PubMed

Borchani, Hanen; Bielza, Concha; Martı Nez-Martı N, Pablo; Larrañaga, Pedro

2012-12-01

Multi-dimensional Bayesian network classifiers (MBCs) are probabilistic graphical models recently proposed to deal with multi-dimensional classification problems, where each instance in the data set has to be assigned to more than one class variable. In this paper, we propose a Markov blanket-based approach for learning MBCs from data. Basically, it consists of determining the Markov blanket around each class variable using the HITON algorithm, then specifying the directionality over the MBC subgraphs. Our approach is applied to the prediction problem of the European Quality of Life-5 Dimensions (EQ-5D) from the 39-item Parkinson's Disease Questionnaire (PDQ-39) in order to estimate the health-related quality of life of Parkinson's patients. Fivefold cross-validation experiments were carried out on randomly generated synthetic data sets, Yeast data set, as well as on a real-world Parkinson's disease data set containing 488 patients. The experimental study, including comparison with additional Bayesian network-based approaches, back propagation for multi-label learning, multi-label k-nearest neighbor, multinomial logistic regression, ordinary least squares, and censored least absolute deviations, shows encouraging results in terms of predictive accuracy as well as the identification of dependence relationships among class and feature variables. Copyright © 2012 Elsevier Inc. All rights reserved.

[Modeling in value-based medicine].

PubMed

Neubauer, A S; Hirneiss, C; Kampik, A

2010-03-01

Modeling plays an important role in value-based medicine (VBM). It allows decision support by predicting potential clinical and economic consequences, frequently combining different sources of evidence. Based on relevant publications and examples focusing on ophthalmology the key economic modeling methods are explained and definitions are given. The most frequently applied model types are decision trees, Markov models, and discrete event simulation (DES) models. Model validation includes besides verifying internal validity comparison with other models (external validity) and ideally validation of its predictive properties. The existing uncertainty with any modeling should be clearly stated. This is true for economic modeling in VBM as well as when using disease risk models to support clinical decisions. In economic modeling uni- and multivariate sensitivity analyses are usually applied; the key concepts here are tornado plots and cost-effectiveness acceptability curves. Given the existing uncertainty, modeling helps to make better informed decisions than without this additional information.

Availability analysis of mechanical systems with condition-based maintenance using semi-Markov and evaluation of optimal condition monitoring interval

NASA Astrophysics Data System (ADS)

Kumar, Girish; Jain, Vipul; Gandhi, O. P.

2018-03-01

Maintenance helps to extend equipment life by improving its condition and avoiding catastrophic failures. Appropriate model or mechanism is, thus, needed to quantify system availability vis-a-vis a given maintenance strategy, which will assist in decision-making for optimal utilization of maintenance resources. This paper deals with semi-Markov process (SMP) modeling for steady state availability analysis of mechanical systems that follow condition-based maintenance (CBM) and evaluation of optimal condition monitoring interval. The developed SMP model is solved using two-stage analytical approach for steady-state availability analysis of the system. Also, CBM interval is decided for maximizing system availability using Genetic Algorithm approach. The main contribution of the paper is in the form of a predictive tool for system availability that will help in deciding the optimum CBM policy. The proposed methodology is demonstrated for a centrifugal pump.

Learning Instance-Specific Predictive Models

PubMed Central

Visweswaran, Shyam; Cooper, Gregory F.

2013-01-01

This paper introduces a Bayesian algorithm for constructing predictive models from data that are optimized to predict a target variable well for a particular instance. This algorithm learns Markov blanket models, carries out Bayesian model averaging over a set of models to predict a target variable of the instance at hand, and employs an instance-specific heuristic to locate a set of suitable models to average over. We call this method the instance-specific Markov blanket (ISMB) algorithm. The ISMB algorithm was evaluated on 21 UCI data sets using five different performance measures and its performance was compared to that of several commonly used predictive algorithms, including nave Bayes, C4.5 decision tree, logistic regression, neural networks, k-Nearest Neighbor, Lazy Bayesian Rules, and AdaBoost. Over all the data sets, the ISMB algorithm performed better on average on all performance measures against all the comparison algorithms. PMID:25045325

A Holistic Approach to Networked Information Systems Design and Analysis

DTIC Science & Technology

2016-04-15

attain quite substantial savings. 11. Optimal algorithms for energy harvesting in wireless networks. We use a Markov- decision-process (MDP) based...approach to obtain optimal policies for transmissions . The key advantage of our approach is that it holistically considers information and energy in a...Coding technique to minimize delays and the number of transmissions in Wireless Systems. As we approach an era of ubiquitous computing with information

Prosthetic Cost Projections for Servicemembers with Major Limb Loss from Vietnam and OIF/OEF

DTIC Science & Technology

2010-01-01

death rates ), DOD = Department of Defense, DSS = Decision Support Sys- tem, MFCL = Medicare Functional Classification Level, OEF = Operation...age-sex-race-adjusted death rates . Figure 3. Markov model for unilateral upper limb and bilateral upper limbs for Operation Iraqi Freedom...Operation Enduring Freedom (OIF/OEF) group. ASR = age-sex-race-adjusted death rates . 394 JRRD, Volume 47, Number 4, 2010 higher, one level lower, or

Decision-Tree Program

NASA Technical Reports Server (NTRS)

Buntine, Wray

1994-01-01

IND computer program introduces Bayesian and Markov/maximum-likelihood (MML) methods and more-sophisticated methods of searching in growing trees. Produces more-accurate class-probability estimates important in applications like diagnosis. Provides range of features and styles with convenience for casual user, fine-tuning for advanced user or for those interested in research. Consists of four basic kinds of routines: data-manipulation, tree-generation, tree-testing, and tree-display. Written in C language.

Cost utility analysis of endoscopic biliary stent in unresectable hilar cholangiocarcinoma: decision analytic modeling approach.

PubMed

Sangchan, Apichat; Chaiyakunapruk, Nathorn; Supakankunti, Siripen; Pugkhem, Ake; Mairiang, Pisaln

2014-01-01

Endoscopic biliary drainage using metal and plastic stent in unresectable hilar cholangiocarcinoma (HCA) is widely used but little is known about their cost-effectiveness. This study evaluated the cost-utility of endoscopic metal and plastic stent drainage in unresectable complex, Bismuth type II-IV, HCA patients. Decision analytic model, Markov model, was used to evaluate cost and quality-adjusted life year (QALY) of endoscopic biliary drainage in unresectable HCA. Costs of treatment and utilities of each Markov state were retrieved from hospital charges and unresectable HCA patients from tertiary care hospital in Thailand, respectively. Transition probabilities were derived from international literature. Base case analyses and sensitivity analyses were performed. Under the base-case analysis, metal stent is more effective but more expensive than plastic stent. An incremental cost per additional QALY gained is 192,650 baht (US$ 6,318). From probabilistic sensitivity analysis, at the willingness to pay threshold of one and three times GDP per capita or 158,000 baht (US$ 5,182) and 474,000 baht (US$ 15,546), the probability of metal stent being cost-effective is 26.4% and 99.8%, respectively. Based on the WHO recommendation regarding the cost-effectiveness threshold criteria, endoscopic metal stent drainage is cost-effective compared to plastic stent in unresectable complex HCA.

Decision-analytic modeling studies: An overview for clinicians using multiple myeloma as an example.

PubMed

Rochau, U; Jahn, B; Qerimi, V; Burger, E A; Kurzthaler, C; Kluibenschaedl, M; Willenbacher, E; Gastl, G; Willenbacher, W; Siebert, U

2015-05-01

The purpose of this study was to provide a clinician-friendly overview of decision-analytic models evaluating different treatment strategies for multiple myeloma (MM). We performed a systematic literature search to identify studies evaluating MM treatment strategies using mathematical decision-analytic models. We included studies that were published as full-text articles in English, and assessed relevant clinical endpoints, and summarized methodological characteristics (e.g., modeling approaches, simulation techniques, health outcomes, perspectives). Eleven decision-analytic modeling studies met our inclusion criteria. Five different modeling approaches were adopted: decision-tree modeling, Markov state-transition modeling, discrete event simulation, partitioned-survival analysis and area-under-the-curve modeling. Health outcomes included survival, number-needed-to-treat, life expectancy, and quality-adjusted life years. Evaluated treatment strategies included novel agent-based combination therapies, stem cell transplantation and supportive measures. Overall, our review provides a comprehensive summary of modeling studies assessing treatment of MM and highlights decision-analytic modeling as an important tool for health policy decision making. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

A new compound arithmetic crossover-based genetic algorithm for constrained optimisation in enterprise systems

NASA Astrophysics Data System (ADS)

Jin, Chenxia; Li, Fachao; Tsang, Eric C. C.; Bulysheva, Larissa; Kataev, Mikhail Yu

2017-01-01

In many real industrial applications, the integration of raw data with a methodology can support economically sound decision-making. Furthermore, most of these tasks involve complex optimisation problems. Seeking better solutions is critical. As an intelligent search optimisation algorithm, genetic algorithm (GA) is an important technique for complex system optimisation, but it has internal drawbacks such as low computation efficiency and prematurity. Improving the performance of GA is a vital topic in academic and applications research. In this paper, a new real-coded crossover operator, called compound arithmetic crossover operator (CAC), is proposed. CAC is used in conjunction with a uniform mutation operator to define a new genetic algorithm CAC10-GA. This GA is compared with an existing genetic algorithm (AC10-GA) that comprises an arithmetic crossover operator and a uniform mutation operator. To judge the performance of CAC10-GA, two kinds of analysis are performed. First the analysis of the convergence of CAC10-GA is performed by the Markov chain theory; second, a pair-wise comparison is carried out between CAC10-GA and AC10-GA through two test problems available in the global optimisation literature. The overall comparative study shows that the CAC performs quite well and the CAC10-GA defined outperforms the AC10-GA.

Blended near-optimal tools for flexible water resources decision making

NASA Astrophysics Data System (ADS)

Rosenberg, David

2015-04-01

State-of-the-art systems analysis techniques focus on efficiently finding optimal solutions. Yet an optimal solution is optimal only for the static modelled issues and managers often seek near-optimal alternatives that address un-modelled or changing objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as performance within a tolerable deviation from the optimal objective function value and identified a few maximally-different alternatives that addressed select un-modelled issues. This paper presents new stratified, Monte Carlo Markov Chain sampling and parallel coordinate plotting tools that generate and communicate the structure and full extent of the near-optimal region to an optimization problem. Plot controls allow users to interactively explore region features of most interest. Controls also streamline the process to elicit un-modelled issues and update the model formulation in response to elicited issues. Use for a single-objective water quality management problem at Echo Reservoir, Utah identifies numerous and flexible practices to reduce the phosphorus load to the reservoir and maintain close-to-optimal performance. Compared to MGA, the new blended tools generate more numerous alternatives faster, more fully show the near-optimal region, help elicit a larger set of un-modelled issues, and offer managers greater flexibility to cope in a changing world.

Virtual Network Embedding via Monte Carlo Tree Search.

PubMed

Haeri, Soroush; Trajkovic, Ljiljana

2018-02-01

Network virtualization helps overcome shortcomings of the current Internet architecture. The virtualized network architecture enables coexistence of multiple virtual networks (VNs) on an existing physical infrastructure. VN embedding (VNE) problem, which deals with the embedding of VN components onto a physical network, is known to be -hard. In this paper, we propose two VNE algorithms: MaVEn-M and MaVEn-S. MaVEn-M employs the multicommodity flow algorithm for virtual link mapping while MaVEn-S uses the shortest-path algorithm. They formalize the virtual node mapping problem by using the Markov decision process (MDP) framework and devise action policies (node mappings) for the proposed MDP using the Monte Carlo tree search algorithm. Service providers may adjust the execution time of the MaVEn algorithms based on the traffic load of VN requests. The objective of the algorithms is to maximize the profit of infrastructure providers. We develop a discrete event VNE simulator to implement and evaluate performance of MaVEn-M, MaVEn-S, and several recently proposed VNE algorithms. We introduce profitability as a new performance metric that captures both acceptance and revenue to cost ratios. Simulation results show that the proposed algorithms find more profitable solutions than the existing algorithms. Given additional computation time, they further improve embedding solutions.

Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo

NASA Astrophysics Data System (ADS)

Schön, Thomas B.; Svensson, Andreas; Murray, Lawrence; Lindsten, Fredrik

2018-05-01

Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods-the particle Metropolis-Hastings algorithm-which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis-Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods-including particle Metropolis-Hastings-to a large group of users without requiring them to know all the underlying mathematical details.

Reciprocal Markov modeling of feedback mechanisms between emotion and dietary choice using experience sampling data

PubMed Central

Lu, Ji; Pan, Junhao; Zhang, Qiang; Dubé, Laurette; Ip, Edward H.

2015-01-01

With intensively collected longitudinal data, recent advances in Experience Sampling Method (ESM) benefit social science empirical research, but also pose important methodological challenges. As traditional statistical models are not generally well-equipped to analyze a system of variables that contain feedback loops, this paper proposes the utility of an extended hidden Markov model to model reciprocal relationship between momentary emotion and eating behavior. This paper revisited an ESM data set (Lu, Huet & Dube, 2011) that observed 160 participants’ food consumption and momentary emotions six times per day in 10 days. Focusing on the analyses on feedback loop between mood and meal healthiness decision, the proposed Reciprocal Markov Model (RMM) can accommodate both hidden (“general” emotional states: positive vs. negative state) and observed states (meal: healthier, same or less healthy than usual) without presuming independence between observations and smooth trajectories of mood or behavior changes. The results of RMM analyses illustrated the reciprocal chains of meal consumption and mood as well as the effect of contextual factors that moderate the interrelationship between eating and emotion. A simulation experiment that generated data consistent to the empirical study further demonstrated that the procedure is promising in terms of recovering the parameters. PMID:26717120

Annealed Importance Sampling Reversible Jump MCMC algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karagiannis, Georgios; Andrieu, Christophe

2013-03-20

It will soon be 20 years since reversible jump Markov chain Monte Carlo (RJ-MCMC) algorithms have been proposed. They have significantly extended the scope of Markov chain Monte Carlo simulation methods, offering the promise to be able to routinely tackle transdimensional sampling problems, as encountered in Bayesian model selection problems for example, in a principled and flexible fashion. Their practical efficient implementation, however, still remains a challenge. A particular difficulty encountered in practice is in the choice of the dimension matching variables (both their nature and their distribution) and the reversible transformations which allow one to define the one-to-one mappingsmore » underpinning the design of these algorithms. Indeed, even seemingly sensible choices can lead to algorithms with very poor performance. The focus of this paper is the development and performance evaluation of a method, annealed importance sampling RJ-MCMC (aisRJ), which addresses this problem by mitigating the sensitivity of RJ-MCMC algorithms to the aforementioned poor design. As we shall see the algorithm can be understood as being an “exact approximation” of an idealized MCMC algorithm that would sample from the model probabilities directly in a model selection set-up. Such an idealized algorithm may have good theoretical convergence properties, but typically cannot be implemented, and our algorithms can approximate the performance of such idealized algorithms to an arbitrary degree while not introducing any bias for any degree of approximation. Our approach combines the dimension matching ideas of RJ-MCMC with annealed importance sampling and its Markov chain Monte Carlo implementation. We illustrate the performance of the algorithm with numerical simulations which indicate that, although the approach may at first appear computationally involved, it is in fact competitive.« less

Bayesian tomography by interacting Markov chains

NASA Astrophysics Data System (ADS)

Romary, T.

2017-12-01

In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.

Application of Markov chain theory to ASTP natural environment launch criteria at Kennedy Space Center

NASA Technical Reports Server (NTRS)

Graves, M. E.; Perlmutter, M.

1974-01-01

To aid the planning of the Apollo Soyuz Test Program (ASTP), certain natural environment statistical relationships are presented, based on Markov theory and empirical counts. The practical results are in terms of conditional probability of favorable and unfavorable launch conditions at Kennedy Space Center (KSC). They are based upon 15 years of recorded weather data which are analyzed under a set of natural environmental launch constraints. Three specific forecasting problems were treated: (1) the length of record of past weather which is useful to a prediction; (2) the effect of persistence in runs of favorable and unfavorable conditions; and (3) the forecasting of future weather in probabilistic terms.

The Communication Link and Error ANalysis (CLEAN) simulator

NASA Technical Reports Server (NTRS)

Ebel, William J.; Ingels, Frank M.; Crowe, Shane

1993-01-01

During the period July 1, 1993 through December 30, 1993, significant developments to the Communication Link and Error ANalysis (CLEAN) simulator were completed and include: (1) Soft decision Viterbi decoding; (2) node synchronization for the Soft decision Viterbi decoder; (3) insertion/deletion error programs; (4) convolutional encoder; (5) programs to investigate new convolutional codes; (6) pseudo-noise sequence generator; (7) soft decision data generator; (8) RICE compression/decompression (integration of RICE code generated by Pen-Shu Yeh at Goddard Space Flight Center); (9) Markov Chain channel modeling; (10) percent complete indicator when a program is executed; (11) header documentation; and (12) help utility. The CLEAN simulation tool is now capable of simulating a very wide variety of satellite communication links including the TDRSS downlink with RFI. The RICE compression/decompression schemes allow studies to be performed on error effects on RICE decompressed data. The Markov Chain modeling programs allow channels with memory to be simulated. Memory results from filtering, forward error correction encoding/decoding, differential encoding/decoding, channel RFI, nonlinear transponders and from many other satellite system processes. Besides the development of the simulation, a study was performed to determine whether the PCI provides a performance improvement for the TDRSS downlink. There exist RFI with several duty cycles for the TDRSS downlink. We conclude that the PCI does not improve performance for any of these interferers except possibly one which occurs for the TDRS East. Therefore, the usefulness of the PCI is a function of the time spent transmitting data to the WSGT through the TDRS East transponder.

Cost-effectiveness of antibiotic prophylaxis for dental patients with prosthetic joints: Comparisons of antibiotic regimens for patients with total hip arthroplasty.

PubMed

Skaar, Daniel D; Park, Taehwan; Swiontkowski, Marc F; Kuntz, Karen M

2015-11-01

Clinician uncertainty concerning the need for antibiotic prophylaxis to prevent prosthetic joint infection (PJI) after undergoing dental procedures persists. Improved understanding of the potential clinical and economic risks and benefits of antibiotic prophylaxis will help inform the debate and facilitate the continuing evolution of clinical management guidelines for dental patients with prosthetic joints. The authors developed a Markov decision model to compare the lifetime cost-effectiveness of alternative antibiotic prophylaxis strategies for dental patients aged 65 years who had undergone total hip arthroplasty (THA). On the basis of the authors' interpretation of previous recommendations from the American Dental Association and American Academy of Orthopaedic Surgeons, they compared the following strategies: no prophylaxis, prophylaxis for the first 2 years after arthroplasty, and lifetime prophylaxis. A strategy of foregoing antibiotic prophylaxis before dental visits was cost-effective and resulted in lower lifetime accumulated costs ($11,909) and higher accumulated quality-adjusted life years (QALYs) (12.375) when compared with alternative prophylaxis strategies. The results of Markov decision modeling indicated that a no-antibiotic prophylaxis strategy was cost-effective for dental patients who had undergone THA. These results support the findings of case-control studies and the conclusions of an American Dental Association Council on Scientific Affairs report that questioned general recommendations for antibiotic prophylaxis before dental procedures. The results of cost-effectiveness decision modeling support the contention that routine antibiotic prophylaxis for dental patients with total joint arthroplasty should be reconsidered. Copyright © 2015 American Dental Association. Published by Elsevier Inc. All rights reserved.

Markov modeling and discrete event simulation in health care: a systematic comparison.

PubMed

Standfield, Lachlan; Comans, Tracy; Scuffham, Paul

2014-04-01

The aim of this study was to assess if the use of Markov modeling (MM) or discrete event simulation (DES) for cost-effectiveness analysis (CEA) may alter healthcare resource allocation decisions. A systematic literature search and review of empirical and non-empirical studies comparing MM and DES techniques used in the CEA of healthcare technologies was conducted. Twenty-two pertinent publications were identified. Two publications compared MM and DES models empirically, one presented a conceptual DES and MM, two described a DES consensus guideline, and seventeen drew comparisons between MM and DES through the authors' experience. The primary advantages described for DES over MM were the ability to model queuing for limited resources, capture individual patient histories, accommodate complexity and uncertainty, represent time flexibly, model competing risks, and accommodate multiple events simultaneously. The disadvantages of DES over MM were the potential for model overspecification, increased data requirements, specialized expensive software, and increased model development, validation, and computational time. Where individual patient history is an important driver of future events an individual patient simulation technique like DES may be preferred over MM. Where supply shortages, subsequent queuing, and diversion of patients through other pathways in the healthcare system are likely to be drivers of cost-effectiveness, DES modeling methods may provide decision makers with more accurate information on which to base resource allocation decisions. Where these are not major features of the cost-effectiveness question, MM remains an efficient, easily validated, parsimonious, and accurate method of determining the cost-effectiveness of new healthcare interventions.

Indexed semi-Markov process for wind speed modeling.

NASA Astrophysics Data System (ADS)

Petroni, F.; D'Amico, G.; Prattico, F.

2012-04-01

The increasing interest in renewable energy leads scientific research to find a better way to recover most of the available energy. Particularly, the maximum energy recoverable from wind is equal to 59.3% of that available (Betz law) at a specific pitch angle and when the ratio between the wind speed in output and in input is equal to 1/3. The pitch angle is the angle formed between the airfoil of the blade of the wind turbine and the wind direction. Old turbine and a lot of that actually marketed, in fact, have always the same invariant geometry of the airfoil. This causes that wind turbines will work with an efficiency that is lower than 59.3%. New generation wind turbines, instead, have a system to variate the pitch angle by rotating the blades. This system able the wind turbines to recover, at different wind speed, always the maximum energy, working in Betz limit at different speed ratios. A powerful system control of the pitch angle allows the wind turbine to recover better the energy in transient regime. A good stochastic model for wind speed is then needed to help both the optimization of turbine design and to assist the system control to predict the value of the wind speed to positioning the blades quickly and correctly. The possibility to have synthetic data of wind speed is a powerful instrument to assist designer to verify the structures of the wind turbines or to estimate the energy recoverable from a specific site. To generate synthetic data, Markov chains of first or higher order are often used [1,2,3]. In particular in [1] is presented a comparison between a first-order Markov chain and a second-order Markov chain. A similar work, but only for the first-order Markov chain, is conduced by [2], presenting the probability transition matrix and comparing the energy spectral density and autocorrelation of real and synthetic wind speed data. A tentative to modeling and to join speed and direction of wind is presented in [3], by using two models, first-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Renewable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribution, Renewable Energy 28 (2003) 1787-1802.

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goreac, Dan, E-mail: Dan.Goreac@u-pem.fr; Kobylanski, Magdalena, E-mail: Magdalena.Kobylanski@u-pem.fr; Martinez, Miguel, E-mail: Miguel.Martinez@u-pem.fr

2016-10-15

We study optimal control problems in infinite horizon whxen the dynamics belong to a specific class of piecewise deterministic Markov processes constrained to star-shaped networks (corresponding to a toy traffic model). We adapt the results in Soner (SIAM J Control Optim 24(6):1110–1122, 1986) to prove the regularity of the value function and the dynamic programming principle. Extending the networks and Krylov’s “shaking the coefficients” method, we prove that the value function can be seen as the solution to a linearized optimization problem set on a convenient set of probability measures. The approach relies entirely on viscosity arguments. As a by-product,more » the dual formulation guarantees that the value function is the pointwise supremum over regular subsolutions of the associated Hamilton–Jacobi integrodifferential system. This ensures that the value function satisfies Perron’s preconization for the (unique) candidate to viscosity solution.« less

Invariant graphs of a family of non-uniformly expanding skew products over Markov maps

NASA Astrophysics Data System (ADS)

Walkden, C. P.; Withers, T.

2018-06-01

We consider a family of skew-products of the form where T is a continuous, expanding, locally eventually onto Markov map and is a family of homeomorphisms of . A function is said to be an invariant graph if is an invariant set for the skew-product; equivalently, u(T(x))  =  g x (u(x)). A well-studied problem is to consider the existence, regularity and dimension-theoretic properties of such functions, usually under strong contraction or expansion conditions (in terms of Lyapunov exponents or partial hyperbolicity) in the fibre direction. Here we consider such problems in a setting where the Lyapunov exponent in the fibre direction is zero on a set of periodic orbits but expands except on a neighbourhood of these periodic orbits. We prove that u either has the structure of a ‘quasi-graph’ (or ‘bony graph’) or is as smooth as the dynamics, and we give a criteria for this to happen.

Optimal rotation sequences for active perception

NASA Astrophysics Data System (ADS)

Nakath, David; Rachuy, Carsten; Clemens, Joachim; Schill, Kerstin

2016-05-01

One major objective of autonomous systems navigating in dynamic environments is gathering information needed for self localization, decision making, and path planning. To account for this, such systems are usually equipped with multiple types of sensors. As these sensors often have a limited field of view and a fixed orientation, the task of active perception breaks down to the problem of calculating alignment sequences which maximize the information gain regarding expected measurements. Action sequences that rotate the system according to the calculated optimal patterns then have to be generated. In this paper we present an approach for calculating these sequences for an autonomous system equipped with multiple sensors. We use a particle filter for multi- sensor fusion and state estimation. The planning task is modeled as a Markov decision process (MDP), where the system decides in each step, what actions to perform next. The optimal control policy, which provides the best action depending on the current estimated state, maximizes the expected cumulative reward. The latter is computed from the expected information gain of all sensors over time using value iteration. The algorithm is applied to a manifold representation of the joint space of rotation and time. We show the performance of the approach in a spacecraft navigation scenario where the information gain is changing over time, caused by the dynamic environment and the continuous movement of the spacecraft

Optimal strategies for electric energy contract decision making

NASA Astrophysics Data System (ADS)

Song, Haili

2000-10-01

The power industry restructuring in various countries in recent years has created an environment where trading of electric energy is conducted in a market environment. In such an environment, electric power companies compete for the market share through spot and bilateral markets. Being profit driven, electric power companies need to make decisions on spot market bidding, contract evaluation, and risk management. New methods and software tools are required to meet these upcoming needs. In this research, bidding strategy and contract pricing are studied from a market participant's viewpoint; new methods are developed to guide a market participant in spot and bilateral market operation. A supplier's spot market bidding decision is studied. Stochastic optimization is formulated to calculate a supplier's optimal bids in a single time period. This decision making problem is also formulated as a Markov Decision Process. All the competitors are represented by their bidding parameters with corresponding probabilities. A systematic method is developed to calculate transition probabilities and rewards. The optimal strategy is calculated to maximize the expected reward over a planning horizon. Besides the spot market, a power producer can also trade in the bilateral markets. Bidding strategies in a bilateral market are studied with game theory techniques. Necessary and sufficient conditions of Nash Equilibrium (NE) bidding strategy are derived based on the generators' cost and the loads' willingness to pay. The study shows that in any NE, market efficiency is achieved. Furthermore, all Nash equilibria are revenue equivalent for the generators. The pricing of "Flexible" contracts, which allow delivery flexibility over a period of time with a fixed total amount of electricity to be delivered, is analyzed based on the no-arbitrage pricing principle. The proposed algorithm calculates the price based on the optimality condition of the stochastic optimization formulation. Simulation examples illustrate the tradeoffs between prices and scheduling flexibility. Spot bidding and contract pricing are not independent decision processes. The interaction between spot bidding and contract evaluation is demonstrated with game theory equilibrium model and market simulation results. It leads to the conclusion that a market participant's contract decision making needs to be further investigated as an integrated optimization formulation.

Exact Test of Independence Using Mutual Information

DTIC Science & Technology

2014-05-23

1000 × 0.05 = 50. Entropy 2014, 16 2844 Importantly, the permutation test, which does not preserve Markov order, resulted in 489 Type I errors! Using...Block 13 ARO Report Number Block 13: Supplementary Note © 2014 . Published in Entropy , Vol. Ed. 0 16, (7) (2014), (, (7). DoD Components reserve a...official Department of the Army position, policy or decision, unless so designated by other documentation. ... Entropy 2014, 16, 2839-2849; doi:10.3390

Learning Representation and Control in Markov Decision Processes

DTIC Science & Technology

2013-10-21

π. Figure 3 shows that Drazin bases outperforms the other bases on a two-room MDP. However, a drawback of Drazin bases is that they are...stochastic matrices. One drawback of diffusion wavelets is that it can gen- erate a large number of overcomplete bases, which needs to be effectively...proposed in [52], overcoming some of the drawbacks of LARS-TD. An approximate linear programming for finding l1 regularized solutions of the Bellman

Combining Offline and Online Computation for Solving Partially Observable Markov Decision Process

DTIC Science & Technology

2015-03-06

David Hsu and Wee Sun Lee, Monte Carlo Bayesian Reinforcement Learning, International Conference on Machine Learning (ICML), 2012. • Haoyu Bai, David...and Automation (ICRA), 2015. • Zhan Wei Lim, David Hsu, and Wee Sun Lee, Adaptive Informative Path Planning in Metric Spaces. Submitted to Int. J... Automation (ICRA), 2015. 2. Bai, H., Hsu, D., Kochenderfer, M. J., and Lee, W. S., Unmanned aircraft collision avoidance using continuous state POMDPs

Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

NASA Astrophysics Data System (ADS)

Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji

2015-12-01

Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.

Hidden Markov random field model and Broyden-Fletcher-Goldfarb-Shanno algorithm for brain image segmentation

NASA Astrophysics Data System (ADS)

Guerrout, EL-Hachemi; Ait-Aoudia, Samy; Michelucci, Dominique; Mahiou, Ramdane

2018-05-01

Many routine medical examinations produce images of patients suffering from various pathologies. With the huge number of medical images, the manual analysis and interpretation became a tedious task. Thus, automatic image segmentation became essential for diagnosis assistance. Segmentation consists in dividing the image into homogeneous and significant regions. We focus on hidden Markov random fields referred to as HMRF to model the problem of segmentation. This modelisation leads to a classical function minimisation problem. Broyden-Fletcher-Goldfarb-Shanno algorithm referred to as BFGS is one of the most powerful methods to solve unconstrained optimisation problem. In this paper, we investigate the combination of HMRF and BFGS algorithm to perform the segmentation operation. The proposed method shows very good segmentation results comparing with well-known approaches. The tests are conducted on brain magnetic resonance image databases (BrainWeb and IBSR) largely used to objectively confront the results obtained. The well-known Dice coefficient (DC) was used as similarity metric. The experimental results show that, in many cases, our proposed method approaches the perfect segmentation with a Dice Coefficient above .9. Moreover, it generally outperforms other methods in the tests conducted.

Two fundamental questions about protein evolution.

PubMed

Penny, David; Zhong, Bojian

2015-12-01

Two basic questions are considered that approach protein evolution from different directions; the problems arising from using Markov models for the deeper divergences, and then the origin of proteins themselves. The real problem for the first question (going backwards in time) is that at deeper phylogenies the Markov models of sequence evolution must lose information exponentially at deeper divergences, and several testable methods are suggested that should help resolve these deeper divergences. For the second question (coming forwards in time) a problem is that most models for the origin of protein synthesis do not give a role for the very earliest stages of the process. From our knowledge of the importance of replication accuracy in limiting the length of a coding molecule, a testable hypothesis is proposed. The length of the code, the code itself, and tRNAs would all have prior roles in increasing the accuracy of RNA replication; thus proteins would have been formed only after the tRNAs and the length of the triplet code are already formed. Both questions lead to testable predictions. Copyright © 2014 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

Generalization bounds of ERM-based learning processes for continuous-time Markov chains.

PubMed

Zhang, Chao; Tao, Dacheng

2012-12-01

Many existing results on statistical learning theory are based on the assumption that samples are independently and identically distributed (i.i.d.). However, the assumption of i.i.d. samples is not suitable for practical application to problems in which samples are time dependent. In this paper, we are mainly concerned with the empirical risk minimization (ERM) based learning process for time-dependent samples drawn from a continuous-time Markov chain. This learning process covers many kinds of practical applications, e.g., the prediction for a time series and the estimation of channel state information. Thus, it is significant to study its theoretical properties including the generalization bound, the asymptotic convergence, and the rate of convergence. It is noteworthy that, since samples are time dependent in this learning process, the concerns of this paper cannot (at least straightforwardly) be addressed by existing methods developed under the sample i.i.d. assumption. We first develop a deviation inequality for a sequence of time-dependent samples drawn from a continuous-time Markov chain and present a symmetrization inequality for such a sequence. By using the resultant deviation inequality and symmetrization inequality, we then obtain the generalization bounds of the ERM-based learning process for time-dependent samples drawn from a continuous-time Markov chain. Finally, based on the resultant generalization bounds, we analyze the asymptotic convergence and the rate of convergence of the learning process.

Teaching Probability in Intermediate Grades

ERIC Educational Resources Information Center

Engel, Arthur

1971-01-01

A discussion of the importance and procedures for including probability in the elementary through secondary mathematics curriculum is presented. Many examples and problems are presented which the author feels students can understand and will be motivated to do. Random digits, Monte Carlo methods, combinatorial theory, and Markov chains are…

Cough event classification by pretrained deep neural network.

PubMed

Liu, Jia-Ming; You, Mingyu; Wang, Zheng; Li, Guo-Zheng; Xu, Xianghuai; Qiu, Zhongmin

2015-01-01

Cough is an essential symptom in respiratory diseases. In the measurement of cough severity, an accurate and objective cough monitor is expected by respiratory disease society. This paper aims to introduce a better performed algorithm, pretrained deep neural network (DNN), to the cough classification problem, which is a key step in the cough monitor. The deep neural network models are built from two steps, pretrain and fine-tuning, followed by a Hidden Markov Model (HMM) decoder to capture tamporal information of the audio signals. By unsupervised pretraining a deep belief network, a good initialization for a deep neural network is learned. Then the fine-tuning step is a back propogation tuning the neural network so that it can predict the observation probability associated with each HMM states, where the HMM states are originally achieved by force-alignment with a Gaussian Mixture Model Hidden Markov Model (GMM-HMM) on the training samples. Three cough HMMs and one noncough HMM are employed to model coughs and noncoughs respectively. The final decision is made based on viterbi decoding algorihtm that generates the most likely HMM sequence for each sample. A sample is labeled as cough if a cough HMM is found in the sequence. The experiments were conducted on a dataset that was collected from 22 patients with respiratory diseases. Patient dependent (PD) and patient independent (PI) experimental settings were used to evaluate the models. Five criteria, sensitivity, specificity, F1, macro average and micro average are shown to depict different aspects of the models. From overall evaluation criteria, the DNN based methods are superior to traditional GMM-HMM based method on F1 and micro average with maximal 14% and 11% error reduction in PD and 7% and 10% in PI, meanwhile keep similar performances on macro average. They also surpass GMM-HMM model on specificity with maximal 14% error reduction on both PD and PI. In this paper, we tried pretrained deep neural network in cough classification problem. Our results showed that comparing with the conventional GMM-HMM framework, the HMM-DNN could get better overall performance on cough classification task.

Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit

NASA Astrophysics Data System (ADS)

Izvekov, Sergei

2017-01-01

We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.

Automatic specification of reliability models for fault-tolerant computers

NASA Technical Reports Server (NTRS)

Liceaga, Carlos A.; Siewiorek, Daniel P.

1993-01-01

The calculation of reliability measures using Markov models is required for life-critical processor-memory-switch structures that have standby redundancy or that are subject to transient or intermittent faults or repair. The task of specifying these models is tedious and prone to human error because of the large number of states and transitions required in any reasonable system. Therefore, model specification is a major analysis bottleneck, and model verification is a major validation problem. The general unfamiliarity of computer architects with Markov modeling techniques further increases the necessity of automating the model specification. Automation requires a general system description language (SDL). For practicality, this SDL should also provide a high level of abstraction and be easy to learn and use. The first attempt to define and implement an SDL with those characteristics is presented. A program named Automated Reliability Modeling (ARM) was constructed as a research vehicle. The ARM program uses a graphical interface as its SDL, and it outputs a Markov reliability model specification formulated for direct use by programs that generate and evaluate the model.

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

NASA Astrophysics Data System (ADS)

Tian, Yu-Kun; Zhou, Hui; Chen, Han-Ming; Zou, Ya-Ming; Guan, Shou-Jun

2013-12-01

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber-Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

Integrated testing strategies can be optimal for chemical risk classification.

PubMed

Raseta, Marko; Pitchford, Jon; Cussens, James; Doe, John

2017-08-01

There is an urgent need to refine strategies for testing the safety of chemical compounds. This need arises both from the financial and ethical costs of animal tests, but also from the opportunities presented by new in-vitro and in-silico alternatives. Here we explore the mathematical theory underpinning the formulation of optimal testing strategies in toxicology. We show how the costs and imprecisions of the various tests, and the variability in exposures and responses of individuals, can be assembled rationally to form a Markov Decision Problem. We compute the corresponding optimal policies using well developed theory based on Dynamic Programming, thereby identifying and overcoming some methodological and logical inconsistencies which may exist in the current toxicological testing. By illustrating our methods for two simple but readily generalisable examples we show how so-called integrated testing strategies, where information of different precisions from different sources is combined and where different initial test outcomes lead to different sets of future tests, can arise naturally as optimal policies. Copyright © 2017 Elsevier Inc. All rights reserved.

Distributed Algorithms for Probabilistic Solution of Computational Vision Problems.

DTIC Science & Technology

1988-03-01

34 targets. Legters and Young (1982) developed an operator-based approach r% using foreground and background models and solved a least-squares minimiza...1960), "Finite Markov Chains", Van Nostrand, , - New York. Legters , G.R., and Young, T.Y. (1982), "A Mathematical Model for Computer Image Tracking

Overeducation Dynamics and Personality

ERIC Educational Resources Information Center

Blazquez, Maite; Budria, Santiago

2012-01-01

In this paper, we use the 2000-2008 waves of the German Socioeconomic Panel to examine overeducation transitions. The results are based on a first-order Markov model that allows us to account for both the initial conditions problem and potential endogeneity in attrition. We found that overeducation dynamics, especially the probability of entering…

Analysis of single ion channel data incorporating time-interval omission and sampling

PubMed Central

The, Yu-Kai; Timmer, Jens

2005-01-01

Hidden Markov models are widely used to describe single channel currents from patch-clamp experiments. The inevitable anti-aliasing filter limits the time resolution of the measurements and therefore the standard hidden Markov model is not adequate anymore. The notion of time-interval omission has been introduced where brief events are not detected. The developed, exact solutions to this problem do not take into account that the measured intervals are limited by the sampling time. In this case the dead-time that specifies the minimal detectable interval length is not defined unambiguously. We show that a wrong choice of the dead-time leads to considerably biased estimates and present the appropriate equations to describe sampled data. PMID:16849220

Model-Averaged ℓ1 Regularization using Markov Chain Monte Carlo Model Composition

PubMed Central

Fraley, Chris; Percival, Daniel

2014-01-01

Bayesian Model Averaging (BMA) is an effective technique for addressing model uncertainty in variable selection problems. However, current BMA approaches have computational difficulty dealing with data in which there are many more measurements (variables) than samples. This paper presents a method for combining ℓ1 regularization and Markov chain Monte Carlo model composition techniques for BMA. By treating the ℓ1 regularization path as a model space, we propose a method to resolve the model uncertainty issues arising in model averaging from solution path point selection. We show that this method is computationally and empirically effective for regression and classification in high-dimensional datasets. We apply our technique in simulations, as well as to some applications that arise in genomics. PMID:25642001

Detection of digital FSK using a phase-locked loop

NASA Technical Reports Server (NTRS)

Lindsey, W. C.; Simon, M. K.

1975-01-01

A theory is presented for the design of a digital FSK receiver which employs a phase-locked loop to set up the desired matched filter as the arriving signal frequency switches. The developed mathematical model makes it possible to establish the error probability performance of systems which employ a class of digital FM modulations. The noise mechanism which accounts for decision errors is modeled on the basis of the Meyr distribution and renewal Markov process theory.

Multi-level Operational C2 Holonic Reference Architecture Modeling for MHQ with MOC

DTIC Science & Technology

2009-06-01

x), x(k), uj(k)) is defined as the task success probability, based on the asset allocation and task execution activities at the tactical level...on outcomes of asset- task allocation at the tactical level. We employ semi-Markov decision process (SMDP) approach to decide on missions to be...AGA) graph for addressing the mission monitoring/ planning issues related to task sequencing and asset allocation at the OLC-TLC layer (coordination

Naval Research Logistics Quarterly. Volume 28, Number 4,

DTIC Science & Technology

1981-12-01

Fan [31 and an observation by Meijerink and van der Vorst [181 guarantee that after pivoting on any diagonal element of a diagonally dominant M- matrix...Science, 3, 255-269 (1957). 1181 Meijerink, J. and H. Van der Vorst, "An Iterative Solution Method for Linear Systems of which the Coefficient Matrix Is a...Hee, K., A. Hordijk and J. Van der Wal, "Successive Approximations for Convergent Dynamic Programming," in Markov Decision Theory, H. Tijms and J

Comparing efficacy of reduced-toxicity allogeneic hematopoietic cell transplantation with conventional chemo-(immuno) therapy in patients with relapsed or refractory CLL: a Markov decision analysis.

PubMed

Kharfan-Dabaja, M A; Pidala, J; Kumar, A; Terasawa, T; Djulbegovic, B

2012-09-01

Despite therapeutic advances, relapsed/refractory CLL, particularly after fludarabine-based regimens, remains a major challenge for which optimal therapy is undefined. No randomized comparative data exist to suggest the superiority of reduced-toxicity allogeneic hematopoietic cell transplantation (RT-allo-HCT) over conventional chemo-(immuno) therapy (CCIT). By using estimates from a systematic review and by meta-analysis of available published evidence, we constructed a Markov decision model to examine these competing modalities. Cohort analysis demonstrated superior outcome for RT-allo-HCT, with a 10-month overall life expectancy (and 6-month quality-adjusted life expectancy (QALE)) advantage over CCIT. Although the model was sensitive to changes in base-case assumptions and transition probabilities, RT-allo-HCT provided superior overall life expectancy through a range of values supported by the meta-analysis. QALE was superior for RT-allo-HCT compared with CCIT. This conclusion was sensitive to change in the anticipated state utility associated with the post-allogeneic HCT state; however, RT-allo-HCT remained the optimal strategy for values supported by existing literature. This analysis provides a quantitative comparison of outcomes between RT-allo-HCT and CCIT for relapsed/refractory CLL in the absence of randomized comparative trials. Confirmation of these findings requires a prospective randomized trial, which compares the most effective RT-allo-HCT and CCIT regimens for relapsed/refractory CLL.

Model averaging in the presence of structural uncertainty about treatment effects: influence on treatment decision and expected value of information.

PubMed

Price, Malcolm J; Welton, Nicky J; Briggs, Andrew H; Ades, A E

2011-01-01

Standard approaches to estimation of Markov models with data from randomized controlled trials tend either to make a judgment about which transition(s) treatments act on, or they assume that treatment has a separate effect on every transition. An alternative is to fit a series of models that assume that treatment acts on specific transitions. Investigators can then choose among alternative models using goodness-of-fit statistics. However, structural uncertainty about any chosen parameterization will remain and this may have implications for the resulting decision and the need for further research. We describe a Bayesian approach to model estimation, and model selection. Structural uncertainty about which parameterization to use is accounted for using model averaging and we developed a formula for calculating the expected value of perfect information (EVPI) in averaged models. Marginal posterior distributions are generated for each of the cost-effectiveness parameters using Markov Chain Monte Carlo simulation in WinBUGS, or Monte-Carlo simulation in Excel (Microsoft Corp., Redmond, WA). We illustrate the approach with an example of treatments for asthma using aggregate-level data from a connected network of four treatments compared in three pair-wise randomized controlled trials. The standard errors of incremental net benefit using structured models is reduced by up to eight- or ninefold compared to the unstructured models, and the expected loss attaching to decision uncertainty by factors of several hundreds. Model averaging had considerable influence on the EVPI. Alternative structural assumptions can alter the treatment decision and have an overwhelming effect on model uncertainty and expected value of information. Structural uncertainty can be accounted for by model averaging, and the EVPI can be calculated for averaged models. Copyright © 2011 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

[Parameter of evidence-based medicine in health care economics].

PubMed

Wasem, J; Siebert, U

1999-08-01

In the view of scarcity of resources, economic evaluations in health care, in which not only effects but also costs related to a medical intervention are examined and a incremental cost-outcome-ratio is build, are an important supplement to the program of evidence based medicine. Outcomes of a medical intervention can be measured by clinical effectiveness, quality-adjusted life years, and monetary evaluation of benefits. As far as costs are concerned, direct medical costs, direct non-medical costs and indirect costs have to be considered in an economic evaluation. Data can be used from primary studies or secondary analysis; metaanalysis for synthesizing of data may be adequate. For calculation of incremental cost-benefit-ratios, models of decision analysis (decision tree models, Markov-models) often are necessary. Methodological and ethical limits for application of the results of economic evaluation in resource allocation decision in health care have to be regarded: Economic evaluations and the calculation of cost-outcome-rations should only support decision making but cannot replace it.

Message survival and decision dynamics in a class of reactive complex systems subject to external fields

NASA Astrophysics Data System (ADS)

Rodriguez Lucatero, C.; Schaum, A.; Alarcon Ramos, L.; Bernal-Jaquez, R.

2014-07-01

In this study, the dynamics of decisions in complex networks subject to external fields are studied within a Markov process framework using nonlinear dynamical systems theory. A mathematical discrete-time model is derived using a set of basic assumptions regarding the convincement mechanisms associated with two competing opinions. The model is analyzed with respect to the multiplicity of critical points and the stability of extinction states. Sufficient conditions for extinction are derived in terms of the convincement probabilities and the maximum eigenvalues of the associated connectivity matrices. The influences of exogenous (e.g., mass media-based) effects on decision behavior are analyzed qualitatively. The current analysis predicts: (i) the presence of fixed-point multiplicity (with a maximum number of four different fixed points), multi-stability, and sensitivity with respect to the process parameters; and (ii) the bounded but significant impact of exogenous perturbations on the decision behavior. These predictions were verified using a set of numerical simulations based on a scale-free network topology.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbachev, D V; Ivanov, V I

Gauss and Markov quadrature formulae with nodes at zeros of eigenfunctions of a Sturm-Liouville problem, which are exact for entire functions of exponential type, are established. They generalize quadrature formulae involving zeros of Bessel functions, which were first designed by Frappier and Olivier. Bessel quadratures correspond to the Fourier-Hankel integral transform. Some other examples, connected with the Jacobi integral transform, Fourier series in Jacobi orthogonal polynomials and the general Sturm-Liouville problem with regular weight are also given. Bibliography: 39 titles.

Personalized treatment planning with a model of radiation therapy outcomes for use in multiobjective optimization of IMRT plans for prostate cancer.

PubMed

Smith, Wade P; Kim, Minsun; Holdsworth, Clay; Liao, Jay; Phillips, Mark H

2016-03-11

To build a new treatment planning approach that extends beyond radiation transport and IMRT optimization by modeling the radiation therapy process and prognostic indicators for more outcome-focused decision making. An in-house treatment planning system was modified to include multiobjective inverse planning, a probabilistic outcome model, and a multi-attribute decision aid. A genetic algorithm generated a set of plans embodying trade-offs between the separate objectives. An influence diagram network modeled the radiation therapy process of prostate cancer using expert opinion, results of clinical trials, and published research. A Markov model calculated a quality adjusted life expectancy (QALE), which was the endpoint for ranking plans. The Multiobjective Evolutionary Algorithm (MOEA) was designed to produce an approximation of the Pareto Front representing optimal tradeoffs for IMRT plans. Prognostic information from the dosimetrics of the plans, and from patient-specific clinical variables were combined by the influence diagram. QALEs were calculated for each plan for each set of patient characteristics. Sensitivity analyses were conducted to explore changes in outcomes for variations in patient characteristics and dosimetric variables. The model calculated life expectancies that were in agreement with an independent clinical study. The radiation therapy model proposed has integrated a number of different physical, biological and clinical models into a more comprehensive model. It illustrates a number of the critical aspects of treatment planning that can be improved and represents a more detailed description of the therapy process. A Markov model was implemented to provide a stronger connection between dosimetric variables and clinical outcomes and could provide a practical, quantitative method for making difficult clinical decisions.

Cost effectiveness of ovarian reserve testing in in vitro fertilization: a Markov decision-analytic model.

PubMed

Moolenaar, Lobke M; Broekmans, Frank J M; van Disseldorp, Jeroen; Fauser, Bart C J M; Eijkemans, Marinus J C; Hompes, Peter G A; van der Veen, Fulco; Mol, Ben Willem J

2011-10-01

To compare the cost effectiveness of ovarian reserve testing in in vitro fertilization (IVF). A Markov decision model based on data from the literature and original patient data. Decision analytic framework. Computer-simulated cohort of subfertile women aged 20 to 45 years who are eligible for IVF. [1] No treatment, [2] up to three cycles of IVF limited to women under 41 years and no ovarian reserve testing, [3] up to three cycles of IVF with dose individualization of gonadotropins according to ovarian reserve, and [4] up to three cycles of IVF with ovarian reserve testing and exclusion of expected poor responders after the first cycle, with no treatment scenario as the reference scenario. Cumulative live birth over 1 year, total costs, and incremental cost-effectiveness ratios. The cumulative live birth was 9.0% in the no treatment scenario, 54.8% for scenario 2, 70.6% for scenario 3 and 51.9% for scenario 4. Absolute costs per woman for these scenarios were €0, €6,917, €6,678, and €5,892 for scenarios 1, 2, 3, and 4, respectively. Incremental cost-effectiveness ratios (ICER) for scenarios 2, 3, and 4 were €15,166, €10,837, and €13,743 per additional live birth. Sensitivity analysis showed the model to be robust over a wide range of values. Individualization of the follicle-stimulating hormone dose according to ovarian reserve is likely to be cost effective in women who are eligible for IVF, but this effectiveness needs to be confirmed in randomized clinical trials. Copyright © 2011 American Society for Reproductive Medicine. Published by Elsevier Inc. All rights reserved.

Theory of the decision/problem state

NASA Technical Reports Server (NTRS)

Dieterly, D. L.

1980-01-01

A theory of the decision-problem state was introduced and elaborated. Starting with the basic model of a decision-problem condition, an attempt was made to explain how a major decision-problem may consist of subsets of decision-problem conditions composing different condition sequences. In addition, the basic classical decision-tree model was modified to allow for the introduction of a series of characteristics that may be encountered in an analysis of a decision-problem state. The resulting hierarchical model reflects the unique attributes of the decision-problem state. The basic model of a decision-problem condition was used as a base to evolve a more complex model that is more representative of the decision-problem state and may be used to initiate research on decision-problem states.

SAR Image Change Detection Based on Fuzzy Markov Random Field Model

NASA Astrophysics Data System (ADS)

Zhao, J.; Huang, G.; Zhao, Z.

2018-04-01

Most existing SAR image change detection algorithms only consider single pixel information of different images, and not consider the spatial dependencies of image pixels. So the change detection results are susceptible to image noise, and the detection effect is not ideal. Markov Random Field (MRF) can make full use of the spatial dependence of image pixels and improve detection accuracy. When segmenting the difference image, different categories of regions have a high degree of similarity at the junction of them. It is difficult to clearly distinguish the labels of the pixels near the boundaries of the judgment area. In the traditional MRF method, each pixel is given a hard label during iteration. So MRF is a hard decision in the process, and it will cause loss of information. This paper applies the combination of fuzzy theory and MRF to the change detection of SAR images. The experimental results show that the proposed method has better detection effect than the traditional MRF method.

Markovian Search Games in Heterogeneous Spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

2009-01-01

We consider how to search for a mobile evader in a large heterogeneous region when sensors are used for detection. Sensors are modeled using probability of detection. Due to environmental effects, this probability will not be constant over the entire region. We map this problem to a graph search problem and, even though deterministic graph search is NP-complete, we derive a tractable, optimal, probabilistic search strategy. We do this by defining the problem as a differential game played on a Markov chain. We prove that this strategy is optimal in the sense of Nash. Simulations of an example problem illustratemore » our approach and verify our claims.« less

An Energy-Efficient Game-Theory-Based Spectrum Decision Scheme for Cognitive Radio Sensor Networks

PubMed Central

Salim, Shelly; Moh, Sangman

2016-01-01

A cognitive radio sensor network (CRSN) is a wireless sensor network in which sensor nodes are equipped with cognitive radio. In this paper, we propose an energy-efficient game-theory-based spectrum decision (EGSD) scheme for CRSNs to prolong the network lifetime. Note that energy efficiency is the most important design consideration in CRSNs because it determines the network lifetime. The central part of the EGSD scheme consists of two spectrum selection algorithms: random selection and game-theory-based selection. The EGSD scheme also includes a clustering algorithm, spectrum characterization with a Markov chain, and cluster member coordination. Our performance study shows that EGSD outperforms the existing popular framework in terms of network lifetime and coordination overhead. PMID:27376290

An Energy-Efficient Game-Theory-Based Spectrum Decision Scheme for Cognitive Radio Sensor Networks.

PubMed

Salim, Shelly; Moh, Sangman

2016-06-30

A cognitive radio sensor network (CRSN) is a wireless sensor network in which sensor nodes are equipped with cognitive radio. In this paper, we propose an energy-efficient game-theory-based spectrum decision (EGSD) scheme for CRSNs to prolong the network lifetime. Note that energy efficiency is the most important design consideration in CRSNs because it determines the network lifetime. The central part of the EGSD scheme consists of two spectrum selection algorithms: random selection and game-theory-based selection. The EGSD scheme also includes a clustering algorithm, spectrum characterization with a Markov chain, and cluster member coordination. Our performance study shows that EGSD outperforms the existing popular framework in terms of network lifetime and coordination overhead.

A Q-Learning Approach to Flocking With UAVs in a Stochastic Environment.

PubMed

Hung, Shao-Ming; Givigi, Sidney N

2017-01-01

In the past two decades, unmanned aerial vehicles (UAVs) have demonstrated their efficacy in supporting both military and civilian applications, where tasks can be dull, dirty, dangerous, or simply too costly with conventional methods. Many of the applications contain tasks that can be executed in parallel, hence the natural progression is to deploy multiple UAVs working together as a force multiplier. However, to do so requires autonomous coordination among the UAVs, similar to swarming behaviors seen in animals and insects. This paper looks at flocking with small fixed-wing UAVs in the context of a model-free reinforcement learning problem. In particular, Peng's Q(λ) with a variable learning rate is employed by the followers to learn a control policy that facilitates flocking in a leader-follower topology. The problem is structured as a Markov decision process, where the agents are modeled as small fixed-wing UAVs that experience stochasticity due to disturbances such as winds and control noises, as well as weight and balance issues. Learned policies are compared to ones solved using stochastic optimal control (i.e., dynamic programming) by evaluating the average cost incurred during flight according to a cost function. Simulation results demonstrate the feasibility of the proposed learning approach at enabling agents to learn how to flock in a leader-follower topology, while operating in a nonstationary stochastic environment.

Information distribution in distributed microprocessor based flight control systems

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1977-01-01

This paper presents an optimal control theory that accounts for variable time intervals in the information distribution to control effectors in a distributed microprocessor based flight control system. The theory is developed using a linear process model for the aircraft dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved that provides the control law that minimizes the expected value of a quadratic cost function. An example is presented where the theory is applied to the control of the longitudinal motions of the F8-DFBW aircraft. Theoretical and simulation results indicate that, for the example problem, the optimal cost obtained using a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained using a known uniform information update interval.

Tracking the visual focus of attention for a varying number of wandering people.

PubMed

Smith, Kevin; Ba, Sileye O; Odobez, Jean-Marc; Gatica-Perez, Daniel

2008-07-01

We define and address the problem of finding the visual focus of attention for a varying number of wandering people (VFOA-W), determining where the people's movement is unconstrained. VFOA-W estimation is a new and important problem with mplications for behavior understanding and cognitive science, as well as real-world applications. One such application, which we present in this article, monitors the attention passers-by pay to an outdoor advertisement. Our approach to the VFOA-W problem proposes a multi-person tracking solution based on a dynamic Bayesian network that simultaneously infers the (variable) number of people in a scene, their body locations, their head locations, and their head pose. For efficient inference in the resulting large variable-dimensional state-space we propose a Reversible Jump Markov Chain Monte Carlo (RJMCMC) sampling scheme, as well as a novel global observation model which determines the number of people in the scene and localizes them. We propose a Gaussian Mixture Model (GMM) and Hidden Markov Model (HMM)-based VFOA-W model which use head pose and location information to determine people's focus state. Our models are evaluated for tracking performance and ability to recognize people looking at an outdoor advertisement, with results indicating good performance on sequences where a moderate number of people pass in front of an advertisement.

Kernel-based least squares policy iteration for reinforcement learning.

PubMed

Xu, Xin; Hu, Dewen; Lu, Xicheng

2007-07-01

In this paper, we present a kernel-based least squares policy iteration (KLSPI) algorithm for reinforcement learning (RL) in large or continuous state spaces, which can be used to realize adaptive feedback control of uncertain dynamic systems. By using KLSPI, near-optimal control policies can be obtained without much a priori knowledge on dynamic models of control plants. In KLSPI, Mercer kernels are used in the policy evaluation of a policy iteration process, where a new kernel-based least squares temporal-difference algorithm called KLSTD-Q is proposed for efficient policy evaluation. To keep the sparsity and improve the generalization ability of KLSTD-Q solutions, a kernel sparsification procedure based on approximate linear dependency (ALD) is performed. Compared to the previous works on approximate RL methods, KLSPI makes two progresses to eliminate the main difficulties of existing results. One is the better convergence and (near) optimality guarantee by using the KLSTD-Q algorithm for policy evaluation with high precision. The other is the automatic feature selection using the ALD-based kernel sparsification. Therefore, the KLSPI algorithm provides a general RL method with generalization performance and convergence guarantee for large-scale Markov decision problems (MDPs). Experimental results on a typical RL task for a stochastic chain problem demonstrate that KLSPI can consistently achieve better learning efficiency and policy quality than the previous least squares policy iteration (LSPI) algorithm. Furthermore, the KLSPI method was also evaluated on two nonlinear feedback control problems, including a ship heading control problem and the swing up control of a double-link underactuated pendulum called acrobot. Simulation results illustrate that the proposed method can optimize controller performance using little a priori information of uncertain dynamic systems. It is also demonstrated that KLSPI can be applied to online learning control by incorporating an initial controller to ensure online performance.

Semantic segmentation of 3D textured meshes for urban scene analysis

NASA Astrophysics Data System (ADS)

Rouhani, Mohammad; Lafarge, Florent; Alliez, Pierre

2017-01-01

Classifying 3D measurement data has become a core problem in photogrammetry and 3D computer vision, since the rise of modern multiview geometry techniques, combined with affordable range sensors. We introduce a Markov Random Field-based approach for segmenting textured meshes generated via multi-view stereo into urban classes of interest. The input mesh is first partitioned into small clusters, referred to as superfacets, from which geometric and photometric features are computed. A random forest is then trained to predict the class of each superfacet as well as its similarity with the neighboring superfacets. Similarity is used to assign the weights of the Markov Random Field pairwise-potential and to account for contextual information between the classes. The experimental results illustrate the efficacy and accuracy of the proposed framework.

Quantum Markov semigroups constructed from quantum Bernoulli noises

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Caishi; Chen, Jinshu

2016-02-15

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combiningmore » the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.« less

SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.

PubMed

Thiede, Erik; VAN Koten, Brian; Weare, Jonathan

For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.

Observer-based sliding mode control of Markov jump systems with random sensor delays and partly unknown transition rates

NASA Astrophysics Data System (ADS)

Yao, Deyin; Lu, Renquan; Xu, Yong; Ren, Hongru

2017-10-01

In this paper, the sliding mode control problem of Markov jump systems (MJSs) with unmeasured state, partly unknown transition rates and random sensor delays is probed. In the practical engineering control, the exact information of transition rates is hard to obtain and the measurement channel is supposed to subject to random sensor delay. Design a Luenberger observer to estimate the unmeasured system state, and an integral sliding mode surface is constructed to ensure the exponential stability of MJSs. A sliding mode controller based on estimator is proposed to drive the system state onto the sliding mode surface and render the sliding mode dynamics exponentially mean-square stable with H∞ performance index. Finally, simulation results are provided to illustrate the effectiveness of the proposed results.

Robust model selection and the statistical classification of languages

NASA Astrophysics Data System (ADS)

García, J. E.; González-López, V. A.; Viola, M. L. L.

2012-10-01

In this paper we address the problem of model selection for the set of finite memory stochastic processes with finite alphabet, when the data is contaminated. We consider m independent samples, with more than half of them being realizations of the same stochastic process with law Q, which is the one we want to retrieve. We devise a model selection procedure such that for a sample size large enough, the selected process is the one with law Q. Our model selection strategy is based on estimating relative entropies to select a subset of samples that are realizations of the same law. Although the procedure is valid for any family of finite order Markov models, we will focus on the family of variable length Markov chain models, which include the fixed order Markov chain model family. We define the asymptotic breakdown point (ABDP) for a model selection procedure, and we show the ABDP for our procedure. This means that if the proportion of contaminated samples is smaller than the ABDP, then, as the sample size grows our procedure selects a model for the process with law Q. We also use our procedure in a setting where we have one sample conformed by the concatenation of sub-samples of two or more stochastic processes, with most of the subsamples having law Q. We conducted a simulation study. In the application section we address the question of the statistical classification of languages according to their rhythmic features using speech samples. This is an important open problem in phonology. A persistent difficulty on this problem is that the speech samples correspond to several sentences produced by diverse speakers, corresponding to a mixture of distributions. The usual procedure to deal with this problem has been to choose a subset of the original sample which seems to best represent each language. The selection is made by listening to the samples. In our application we use the full dataset without any preselection of samples. We apply our robust methodology estimating a model which represent the main law for each language. Our findings agree with the linguistic conjecture, related to the rhythm of the languages included on our dataset.

Reinforcement learning techniques for controlling resources in power networks

NASA Astrophysics Data System (ADS)

Kowli, Anupama Sunil

As power grids transition towards increased reliance on renewable generation, energy storage and demand response resources, an effective control architecture is required to harness the full functionalities of these resources. There is a critical need for control techniques that recognize the unique characteristics of the different resources and exploit the flexibility afforded by them to provide ancillary services to the grid. The work presented in this dissertation addresses these needs. Specifically, new algorithms are proposed, which allow control synthesis in settings wherein the precise distribution of the uncertainty and its temporal statistics are not known. These algorithms are based on recent developments in Markov decision theory, approximate dynamic programming and reinforcement learning. They impose minimal assumptions on the system model and allow the control to be "learned" based on the actual dynamics of the system. Furthermore, they can accommodate complex constraints such as capacity and ramping limits on generation resources, state-of-charge constraints on storage resources, comfort-related limitations on demand response resources and power flow limits on transmission lines. Numerical studies demonstrating applications of these algorithms to practical control problems in power systems are discussed. Results demonstrate how the proposed control algorithms can be used to improve the performance and reduce the computational complexity of the economic dispatch mechanism in a power network. We argue that the proposed algorithms are eminently suitable to develop operational decision-making tools for large power grids with many resources and many sources of uncertainty.

On Markov parameters in system identification

NASA Technical Reports Server (NTRS)

Phan, Minh; Juang, Jer-Nan; Longman, Richard W.

1991-01-01

A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.

Advanced techniques in reliability model representation and solution

NASA Technical Reports Server (NTRS)

Palumbo, Daniel L.; Nicol, David M.

1992-01-01

The current tendency of flight control system designs is towards increased integration of applications and increased distribution of computational elements. The reliability analysis of such systems is difficult because subsystem interactions are increasingly interdependent. Researchers at NASA Langley Research Center have been working for several years to extend the capability of Markov modeling techniques to address these problems. This effort has been focused in the areas of increased model abstraction and increased computational capability. The reliability model generator (RMG) is a software tool that uses as input a graphical object-oriented block diagram of the system. RMG uses a failure-effects algorithm to produce the reliability model from the graphical description. The ASSURE software tool is a parallel processing program that uses the semi-Markov unreliability range evaluator (SURE) solution technique and the abstract semi-Markov specification interface to the SURE tool (ASSIST) modeling language. A failure modes-effects simulation is used by ASSURE. These tools were used to analyze a significant portion of a complex flight control system. The successful combination of the power of graphical representation, automated model generation, and parallel computation leads to the conclusion that distributed fault-tolerant system architectures can now be analyzed.

Model-based Clustering of Categorical Time Series with Multinomial Logit Classification

NASA Astrophysics Data System (ADS)

Frühwirth-Schnatter, Sylvia; Pamminger, Christoph; Winter-Ebmer, Rudolf; Weber, Andrea

2010-09-01

A common problem in many areas of applied statistics is to identify groups of similar time series in a panel of time series. However, distance-based clustering methods cannot easily be extended to time series data, where an appropriate distance-measure is rather difficult to define, particularly for discrete-valued time series. Markov chain clustering, proposed by Pamminger and Frühwirth-Schnatter [6], is an approach for clustering discrete-valued time series obtained by observing a categorical variable with several states. This model-based clustering method is based on finite mixtures of first-order time-homogeneous Markov chain models. In order to further explain group membership we present an extension to the approach of Pamminger and Frühwirth-Schnatter [6] by formulating a probabilistic model for the latent group indicators within the Bayesian classification rule by using a multinomial logit model. The parameters are estimated for a fixed number of clusters within a Bayesian framework using an Markov chain Monte Carlo (MCMC) sampling scheme representing a (full) Gibbs-type sampler which involves only draws from standard distributions. Finally, an application to a panel of Austrian wage mobility data is presented which leads to an interesting segmentation of the Austrian labour market.

A hybrid degradation tendency measurement method for mechanical equipment based on moving window and Grey-Markov model

NASA Astrophysics Data System (ADS)

Jiang, Wei; Zhou, Jianzhong; Zheng, Yang; Liu, Han

2017-11-01

Accurate degradation tendency measurement is vital for the secure operation of mechanical equipment. However, the existing techniques and methodologies for degradation measurement still face challenges, such as lack of appropriate degradation indicator, insufficient accuracy, and poor capability to track the data fluctuation. To solve these problems, a hybrid degradation tendency measurement method for mechanical equipment based on a moving window and Grey-Markov model is proposed in this paper. In the proposed method, a 1D normalized degradation index based on multi-feature fusion is designed to assess the extent of degradation. Subsequently, the moving window algorithm is integrated with the Grey-Markov model for the dynamic update of the model. Two key parameters, namely the step size and the number of states, contribute to the adaptive modeling and multi-step prediction. Finally, three types of combination prediction models are established to measure the degradation trend of equipment. The effectiveness of the proposed method is validated with a case study on the health monitoring of turbine engines. Experimental results show that the proposed method has better performance, in terms of both measuring accuracy and data fluctuation tracing, in comparison with other conventional methods.

Nonlinear Markov Control Processes and Games

DTIC Science & Technology

2012-11-15

the analysis of a new class of stochastic games , nonlinear Markov games , as they arise as a ( competitive ) controlled version of nonlinear Markov... competitive interests) a nonlinear Markov game that we are investigating. I 0. :::tUt::JJt:.l.. I I t:t11VI;:, nonlinear Markov game , nonlinear Markov...corresponding stochastic game Γ+(T, h). In a slightly different setting one can assume that changes in a competitive control process occur as a

Zipf exponent of trajectory distribution in the hidden Markov model

NASA Astrophysics Data System (ADS)

Bochkarev, V. V.; Lerner, E. Yu

2014-03-01

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

Efficient Inference for Trees and Alignments: Modeling Monolingual and Bilingual Syntax with Hard and Soft Constraints and Latent Variables

ERIC Educational Resources Information Center

Smith, David Arthur

2010-01-01

Much recent work in natural language processing treats linguistic analysis as an inference problem over graphs. This development opens up useful connections between machine learning, graph theory, and linguistics. The first part of this dissertation formulates syntactic dependency parsing as a dynamic Markov random field with the novel…

An Efficient MCMC Algorithm to Sample Binary Matrices with Fixed Marginals

ERIC Educational Resources Information Center

Verhelst, Norman D.

2008-01-01

Uniform sampling of binary matrices with fixed margins is known as a difficult problem. Two classes of algorithms to sample from a distribution not too different from the uniform are studied in the literature: importance sampling and Markov chain Monte Carlo (MCMC). Existing MCMC algorithms converge slowly, require a long burn-in period and yield…

Forecasting client transitions in British Columbia's Long-Term Care Program.

PubMed Central

Lane, D; Uyeno, D; Stark, A; Gutman, G; McCashin, B

1987-01-01

This article presents a model for the annual transitions of clients through various home and facility placements in a long-term care program. The model, an application of Markov chain analysis, is developed, tested, and applied to over 9,000 clients (N = 9,483) in British Columbia's Long Term Care Program (LTC) over the period 1978-1983. Results show that the model gives accurate forecasts of the progress of groups of clients from state to state in the long-term care system from time of admission until eventual death. Statistical methods are used to test the modeling hypothesis that clients' year-over-year transitions occur in constant proportions from state to state within the long-term care system. Tests are carried out by examining actual year-over-year transitions of each year's new admission cohort (1978-1983). Various subsets of the available data are analyzed and, after accounting for clear differences among annual cohorts, the most acceptable model of the actual client transition data occurred when clients were separated into male and female groups, i.e., the transition behavior of each group is describable by a different Markov model. To validate the model, we develop model estimates for the numbers of existing clients in each state of the long-term care system for the period (1981-1983) for which actual data are available. When these estimates are compared with the actual data, total weighted absolute deviations do not exceed 10 percent of actuals. Finally, we use the properties of the Markov chain probability transition matrix and simulation methods to develop three-year forecasts with prediction intervals for the distribution of the existing total clients into each state of the system. The tests, forecasts, and Markov model supplemental information are contained in a mechanized procedure suitable for a microcomputer. The procedure provides a powerful, efficient tool for decision makers planning facilities and services in response to the needs of long-term care clients. PMID:3121537

Utilization of two web-based continuing education courses evaluated by Markov chain model.

PubMed

Tian, Hao; Lin, Jin-Mann S; Reeves, William C

2012-01-01

To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Markov chain models were built from 2008 web usage data to evaluate the courses' web structure and navigation patterns. The web site was then modified to resolve identified design issues and the improvement in user activity over the subsequent 12 months was quantitatively evaluated. Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. The continuing education courses' sequential structure design was clearly reflected in the resulting actual web usage models, and none of the skip transitions provided was heavily used. The web navigation patterns of the two different continuing education courses were similar. Two possible design flaws were identified and fixed in only one of the two courses. Over the following 12 months, the drop-out rate in the modified course significantly decreased from 41% to 35%, but remained unchanged in the unmodified course. The web improvement effects were further verified via a second-order Markov chain model. The results imply that differences in web content have less impact than web structure design on how learners navigate through continuing education courses. Evaluation of user navigation can help identify web design flaws and guide modifications. This study showed that Markov chain models provide a valuable tool to evaluate web-based education courses. Both the results and techniques in this study would be very useful for public health education and research specialists.

DNA motif alignment by evolving a population of Markov chains.

PubMed

Bi, Chengpeng

2009-01-30

Deciphering cis-regulatory elements or de novo motif-finding in genomes still remains elusive although much algorithmic effort has been expended. The Markov chain Monte Carlo (MCMC) method such as Gibbs motif samplers has been widely employed to solve the de novo motif-finding problem through sequence local alignment. Nonetheless, the MCMC-based motif samplers still suffer from local maxima like EM. Therefore, as a prerequisite for finding good local alignments, these motif algorithms are often independently run a multitude of times, but without information exchange between different chains. Hence it would be worth a new algorithm design enabling such information exchange. This paper presents a novel motif-finding algorithm by evolving a population of Markov chains with information exchange (PMC), each of which is initialized as a random alignment and run by the Metropolis-Hastings sampler (MHS). It is progressively updated through a series of local alignments stochastically sampled. Explicitly, the PMC motif algorithm performs stochastic sampling as specified by a population-based proposal distribution rather than individual ones, and adaptively evolves the population as a whole towards a global maximum. The alignment information exchange is accomplished by taking advantage of the pooled motif site distributions. A distinct method for running multiple independent Markov chains (IMC) without information exchange, or dubbed as the IMC motif algorithm, is also devised to compare with its PMC counterpart. Experimental studies demonstrate that the performance could be improved if pooled information were used to run a population of motif samplers. The new PMC algorithm was able to improve the convergence and outperformed other popular algorithms tested using simulated and biological motif sequences.

Utilization of two web-based continuing education courses evaluated by Markov chain model

PubMed Central

Lin, Jin-Mann S; Reeves, William C

2011-01-01

Objectives To evaluate the web structure of two web-based continuing education courses, identify problems and assess the effects of web site modifications. Design Markov chain models were built from 2008 web usage data to evaluate the courses' web structure and navigation patterns. The web site was then modified to resolve identified design issues and the improvement in user activity over the subsequent 12 months was quantitatively evaluated. Measurements Web navigation paths were collected between 2008 and 2010. The probability of navigating from one web page to another was analyzed. Results The continuing education courses' sequential structure design was clearly reflected in the resulting actual web usage models, and none of the skip transitions provided was heavily used. The web navigation patterns of the two different continuing education courses were similar. Two possible design flaws were identified and fixed in only one of the two courses. Over the following 12 months, the drop-out rate in the modified course significantly decreased from 41% to 35%, but remained unchanged in the unmodified course. The web improvement effects were further verified via a second-order Markov chain model. Conclusions The results imply that differences in web content have less impact than web structure design on how learners navigate through continuing education courses. Evaluation of user navigation can help identify web design flaws and guide modifications. This study showed that Markov chain models provide a valuable tool to evaluate web-based education courses. Both the results and techniques in this study would be very useful for public health education and research specialists. PMID:21976027

Research on computer aided testing of pilot response to critical in-flight events

NASA Technical Reports Server (NTRS)

Giffin, W. C.; Rockwell, T. H.; Smith, P. J.

1984-01-01

Experiments on pilot decision making are described. The development of models of pilot decision making in critical in flight events (CIFE) are emphasized. The following tests are reported on the development of: (1) a frame system representation describing how pilots use their knowledge in a fault diagnosis task; (2) assessment of script norms, distance measures, and Markov models developed from computer aided testing (CAT) data; and (3) performance ranking of subject data. It is demonstrated that interactive computer aided testing either by touch CRT's or personal computers is a useful research and training device for measuring pilot information management in diagnosing system failures in simulated flight situations. Performance is dictated by knowledge of aircraft sybsystems, initial pilot structuring of the failure symptoms and efficient testing of plausible causal hypotheses.

Comprehensive Fault Tolerance and Science-Optimal Attitude Planning for Spacecraft Applications

NASA Astrophysics Data System (ADS)

Nasir, Ali

Spacecraft operate in a harsh environment, are costly to launch, and experience unavoidable communication delay and bandwidth constraints. These factors motivate the need for effective onboard mission and fault management. This dissertation presents an integrated framework to optimize science goal achievement while identifying and managing encountered faults. Goal-related tasks are defined by pointing the spacecraft instrumentation toward distant targets of scientific interest. The relative value of science data collection is traded with risk of failures to determine an optimal policy for mission execution. Our major innovation in fault detection and reconfiguration is to incorporate fault information obtained from two types of spacecraft models: one based on the dynamics of the spacecraft and the second based on the internal composition of the spacecraft. For fault reconfiguration, we consider possible changes in both dynamics-based control law configuration and the composition-based switching configuration. We formulate our problem as a stochastic sequential decision problem or Markov Decision Process (MDP). To avoid the computational complexity involved in a fully-integrated MDP, we decompose our problem into multiple MDPs. These MDPs include planning MDPs for different fault scenarios, a fault detection MDP based on a logic-based model of spacecraft component and system functionality, an MDP for resolving conflicts between fault information from the logic-based model and the dynamics-based spacecraft models" and the reconfiguration MDP that generates a policy optimized over the relative importance of the mission objectives versus spacecraft safety. Approximate Dynamic Programming (ADP) methods for the decomposition of the planning and fault detection MDPs are applied. To show the performance of the MDP-based frameworks and ADP methods, a suite of spacecraft attitude planning case studies are described. These case studies are used to analyze the content and behavior of computed policies in response to the changes in design parameters. A primary case study is built from the Far Ultraviolet Spectroscopic Explorer (FUSE) mission for which component models and their probabilities of failure are based on realistic mission data. A comparison of our approach with an alternative framework for spacecraft task planning and fault management is presented in the context of the FUSE mission.

Data Analysis Recipes: Using Markov Chain Monte Carlo

NASA Astrophysics Data System (ADS)

Hogg, David W.; Foreman-Mackey, Daniel

2018-05-01

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data. In this primarily pedagogical contribution, we give a brief overview of the most basic MCMC method and some practical advice for the use of MCMC in real inference problems. We give advice on method choice, tuning for performance, methods for initialization, tests of convergence, troubleshooting, and use of the chain output to produce or report parameter estimates with associated uncertainties. We argue that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest. We emphasize that sampling is a method for doing integrals; this guides our thinking about how MCMC output is best used. .

Supervised self-organization of homogeneous swarms using ergodic projections of Markov chains.

PubMed

Chattopadhyay, Ishanu; Ray, Asok

2009-12-01

This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.

Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition.

PubMed

Janko, Vito; Luštrek, Mitja

2017-12-29

The recognition of the user's context with wearable sensing systems is a common problem in ubiquitous computing. However, the typically small battery of such systems often makes continuous recognition impractical. The strain on the battery can be reduced if the sensor setting is adapted to each context. We propose a method that efficiently finds near-optimal sensor settings for each context. It uses Markov chains to simulate the behavior of the system in different configurations and the multi-objective genetic algorithm to find a set of good non-dominated configurations. The method was evaluated on three real-life datasets and found good trade-offs between the system's energy expenditure and the system's accuracy. One of the solutions, for example, consumed five-times less energy than the default one, while sacrificing only two percentage points of accuracy.

The mean field theory in EM procedures for blind Markov random field image restoration.

PubMed

Zhang, J

1993-01-01

A Markov random field (MRF) model-based EM (expectation-maximization) procedure for simultaneously estimating the degradation model and restoring the image is described. The MRF is a coupled one which provides continuity (inside regions of smooth gray tones) and discontinuity (at region boundaries) constraints for the restoration problem which is, in general, ill posed. The computational difficulty associated with the EM procedure for MRFs is resolved by using the mean field theory from statistical mechanics. An orthonormal blur decomposition is used to reduce the chances of undesirable locally optimal estimates. Experimental results on synthetic and real-world images show that this approach provides good blur estimates and restored images. The restored images are comparable to those obtained by a Wiener filter in mean-square error, but are most visually pleasing.

Optimal regulation in systems with stochastic time sampling

NASA Technical Reports Server (NTRS)

Montgomery, R. C.; Lee, P. S.

1980-01-01

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Sieve estimation in a Markov illness-death process under dual censoring.

PubMed

Boruvka, Audrey; Cook, Richard J

2016-04-01

Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials. © The Author 2015. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes

ERIC Educational Resources Information Center

Kapland, David

2008-01-01

This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…

Adaptive Multi-scale Prognostics and Health Management for Smart Manufacturing Systems

PubMed Central

Choo, Benjamin Y.; Adams, Stephen C.; Weiss, Brian A.; Marvel, Jeremy A.; Beling, Peter A.

2017-01-01

The Adaptive Multi-scale Prognostics and Health Management (AM-PHM) is a methodology designed to enable PHM in smart manufacturing systems. In application, PHM information is not yet fully utilized in higher-level decision-making in manufacturing systems. AM-PHM leverages and integrates lower-level PHM information such as from a machine or component with hierarchical relationships across the component, machine, work cell, and assembly line levels in a manufacturing system. The AM-PHM methodology enables the creation of actionable prognostic and diagnostic intelligence up and down the manufacturing process hierarchy. Decisions are then made with the knowledge of the current and projected health state of the system at decision points along the nodes of the hierarchical structure. To overcome the issue of exponential explosion of complexity associated with describing a large manufacturing system, the AM-PHM methodology takes a hierarchical Markov Decision Process (MDP) approach into describing the system and solving for an optimized policy. A description of the AM-PHM methodology is followed by a simulated industry-inspired example to demonstrate the effectiveness of AM-PHM. PMID:28736651

Probabilistic hazard assessment for skin sensitization potency by dose–response modeling using feature elimination instead of quantitative structure–activity relationships

PubMed Central

McKim, James M.; Hartung, Thomas; Kleensang, Andre; Sá-Rocha, Vanessa

2016-01-01

Supervised learning methods promise to improve integrated testing strategies (ITS), but must be adjusted to handle high dimensionality and dose–response data. ITS approaches are currently fueled by the increasing mechanistic understanding of adverse outcome pathways (AOP) and the development of tests reflecting these mechanisms. Simple approaches to combine skin sensitization data sets, such as weight of evidence, fail due to problems in information redundancy and high dimension-ality. The problem is further amplified when potency information (dose/response) of hazards would be estimated. Skin sensitization currently serves as the foster child for AOP and ITS development, as legislative pressures combined with a very good mechanistic understanding of contact dermatitis have led to test development and relatively large high-quality data sets. We curated such a data set and combined a recursive variable selection algorithm to evaluate the information available through in silico, in chemico and in vitro assays. Chemical similarity alone could not cluster chemicals’ potency, and in vitro models consistently ranked high in recursive feature elimination. This allows reducing the number of tests included in an ITS. Next, we analyzed with a hidden Markov model that takes advantage of an intrinsic inter-relationship among the local lymph node assay classes, i.e. the monotonous connection between local lymph node assay and dose. The dose-informed random forest/hidden Markov model was superior to the dose-naive random forest model on all data sets. Although balanced accuracy improvement may seem small, this obscures the actual improvement in misclassifications as the dose-informed hidden Markov model strongly reduced "false-negatives" (i.e. extreme sensitizers as non-sensitizer) on all data sets. PMID:26046447

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution.

PubMed

Djordjevic, Ivan B

2015-08-24

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled.

Markov Chain-Like Quantum Biological Modeling of Mutations, Aging, and Evolution

PubMed Central

Djordjevic, Ivan B.

2015-01-01

Recent evidence suggests that quantum mechanics is relevant in photosynthesis, magnetoreception, enzymatic catalytic reactions, olfactory reception, photoreception, genetics, electron-transfer in proteins, and evolution; to mention few. In our recent paper published in Life, we have derived the operator-sum representation of a biological channel based on codon basekets, and determined the quantum channel model suitable for study of the quantum biological channel capacity. However, this model is essentially memoryless and it is not able to properly model the propagation of mutation errors in time, the process of aging, and evolution of genetic information through generations. To solve for these problems, we propose novel quantum mechanical models to accurately describe the process of creation spontaneous, induced, and adaptive mutations and their propagation in time. Different biological channel models with memory, proposed in this paper, include: (i) Markovian classical model, (ii) Markovian-like quantum model, and (iii) hybrid quantum-classical model. We then apply these models in a study of aging and evolution of quantum biological channel capacity through generations. We also discuss key differences of these models with respect to a multilevel symmetric channel-based Markovian model and a Kimura model-based Markovian process. These models are quite general and applicable to many open problems in biology, not only biological channel capacity, which is the main focus of the paper. We will show that the famous quantum Master equation approach, commonly used to describe different biological processes, is just the first-order approximation of the proposed quantum Markov chain-like model, when the observation interval tends to zero. One of the important implications of this model is that the aging phenotype becomes determined by different underlying transition probabilities in both programmed and random (damage) Markov chain-like models of aging, which are mutually coupled. PMID:26305258

Probabilistic hazard assessment for skin sensitization potency by dose-response modeling using feature elimination instead of quantitative structure-activity relationships.

PubMed

Luechtefeld, Thomas; Maertens, Alexandra; McKim, James M; Hartung, Thomas; Kleensang, Andre; Sá-Rocha, Vanessa

2015-11-01

Supervised learning methods promise to improve integrated testing strategies (ITS), but must be adjusted to handle high dimensionality and dose-response data. ITS approaches are currently fueled by the increasing mechanistic understanding of adverse outcome pathways (AOP) and the development of tests reflecting these mechanisms. Simple approaches to combine skin sensitization data sets, such as weight of evidence, fail due to problems in information redundancy and high dimensionality. The problem is further amplified when potency information (dose/response) of hazards would be estimated. Skin sensitization currently serves as the foster child for AOP and ITS development, as legislative pressures combined with a very good mechanistic understanding of contact dermatitis have led to test development and relatively large high-quality data sets. We curated such a data set and combined a recursive variable selection algorithm to evaluate the information available through in silico, in chemico and in vitro assays. Chemical similarity alone could not cluster chemicals' potency, and in vitro models consistently ranked high in recursive feature elimination. This allows reducing the number of tests included in an ITS. Next, we analyzed with a hidden Markov model that takes advantage of an intrinsic inter-relationship among the local lymph node assay classes, i.e. the monotonous connection between local lymph node assay and dose. The dose-informed random forest/hidden Markov model was superior to the dose-naive random forest model on all data sets. Although balanced accuracy improvement may seem small, this obscures the actual improvement in misclassifications as the dose-informed hidden Markov model strongly reduced " false-negatives" (i.e. extreme sensitizers as non-sensitizer) on all data sets. Copyright © 2015 John Wiley & Sons, Ltd.

The use of economic evaluation in CAM: an introductory framework

PubMed Central

2010-01-01

Background For CAM to feature prominently in health care decision-making there is a need to expand the evidence-base and to further incorporate economic evaluation into research priorities. In a world of scarce health care resources and an emphasis on efficiency and clinical efficacy, CAM, as indeed do all other treatments, requires rigorous evaluation to be considered in budget decision-making. Methods Economic evaluation provides the tools to measure the costs and health consequences of CAM interventions and thereby inform decision making. This article offers CAM researchers an introductory framework for understanding, undertaking and disseminating economic evaluation. The types of economic evaluation available for the study of CAM are discussed, and decision modelling is introduced as a method for economic evaluation with much potential for use in CAM. Two types of decision models are introduced, decision trees and Markov models, along with a worked example of how each method is used to examine costs and health consequences. This is followed by a discussion of how this information is used by decision makers. Conclusions Undoubtedly, economic evaluation methods form an important part of health care decision making. Without formal training it can seem a daunting task to consider economic evaluation, however, multidisciplinary teams provide an opportunity for health economists, CAM practitioners and other interested researchers, to work together to further develop the economic evaluation of CAM. PMID:21067622

The use of economic evaluation in CAM: an introductory framework.

PubMed

Ford, Emily; Solomon, Daniela; Adams, Jon; Graves, Nicholas

2010-11-11

For CAM to feature prominently in health care decision-making there is a need to expand the evidence-base and to further incorporate economic evaluation into research priorities.In a world of scarce health care resources and an emphasis on efficiency and clinical efficacy, CAM, as indeed do all other treatments, requires rigorous evaluation to be considered in budget decision-making. Economic evaluation provides the tools to measure the costs and health consequences of CAM interventions and thereby inform decision making. This article offers CAM researchers an introductory framework for understanding, undertaking and disseminating economic evaluation. The types of economic evaluation available for the study of CAM are discussed, and decision modelling is introduced as a method for economic evaluation with much potential for use in CAM. Two types of decision models are introduced, decision trees and Markov models, along with a worked example of how each method is used to examine costs and health consequences. This is followed by a discussion of how this information is used by decision makers. Undoubtedly, economic evaluation methods form an important part of health care decision making. Without formal training it can seem a daunting task to consider economic evaluation, however, multidisciplinary teams provide an opportunity for health economists, CAM practitioners and other interested researchers, to work together to further develop the economic evaluation of CAM.

A High Performance Bayesian Computing Framework for Spatiotemporal Uncertainty Modeling

NASA Astrophysics Data System (ADS)

Cao, G.

2015-12-01

All types of spatiotemporal measurements are subject to uncertainty. With spatiotemporal data becomes increasingly involved in scientific research and decision making, it is important to appropriately model the impact of uncertainty. Quantitatively modeling spatiotemporal uncertainty, however, is a challenging problem considering the complex dependence and dataheterogeneities.State-space models provide a unifying and intuitive framework for dynamic systems modeling. In this paper, we aim to extend the conventional state-space models for uncertainty modeling in space-time contexts while accounting for spatiotemporal effects and data heterogeneities. Gaussian Markov Random Field (GMRF) models, also known as conditional autoregressive models, are arguably the most commonly used methods for modeling of spatially dependent data. GMRF models basically assume that a geo-referenced variable primarily depends on its neighborhood (Markov property), and the spatial dependence structure is described via a precision matrix. Recent study has shown that GMRFs are efficient approximation to the commonly used Gaussian fields (e.g., Kriging), and compared with Gaussian fields, GMRFs enjoy a series of appealing features, such as fast computation and easily accounting for heterogeneities in spatial data (e.g, point and areal). This paper represents each spatial dataset as a GMRF and integrates them into a state-space form to statistically model the temporal dynamics. Different types of spatial measurements (e.g., categorical, count or continuous), can be accounted for by according link functions. A fast alternative to MCMC framework, so-called Integrated Nested Laplace Approximation (INLA), was adopted for model inference.Preliminary case studies will be conducted to showcase the advantages of the described framework. In the first case, we apply the proposed method for modeling the water table elevation of Ogallala aquifer over the past decades. In the second case, we analyze the drought impacts in Texas counties in the past years, where the spatiotemporal dynamics are represented in areal data.

A systematic review of modelling approaches in economic evaluations of health interventions for drug and alcohol problems.

PubMed

Hoang, Van Phuong; Shanahan, Marian; Shukla, Nagesh; Perez, Pascal; Farrell, Michael; Ritter, Alison

2016-04-13

The overarching goal of health policies is to maximize health and societal benefits. Economic evaluations can play a vital role in assessing whether or not such benefits occur. This paper reviews the application of modelling techniques in economic evaluations of drug and alcohol interventions with regard to (i) modelling paradigms themselves; (ii) perspectives of costs and benefits and (iii) time frame. Papers that use modelling approaches for economic evaluations of drug and alcohol interventions were identified by carrying out searches of major databases. Thirty eight papers met the inclusion criteria. Overall, the cohort Markov models remain the most popular approach, followed by decision trees, Individual based model and System dynamics model (SD). Most of the papers adopted a long term time frame to reflect the long term costs and benefits of health interventions. However, it was fairly common among the reviewed papers to adopt a narrow perspective that only takes into account costs and benefits borne by the health care sector. This review paper informs policy makers about the availability of modelling techniques that can be used to enhance the quality of economic evaluations for drug and alcohol treatment interventions.

Cost-effectiveness of antiplatelet drugs after percutaneous coronary intervention

PubMed Central

Wisløff, Torbjørn; Atar, Dan

2016-01-01

Abstract Aims Clopidogrel has, for long time, been accepted as the standard treatment for patients who have undergone a percutaneous coronary intervention (PCI). The introduction of prasugrel—and more recently, ticagrelor—has introduced a decision-making problem for clinicians and governments worldwide: to use the cheaper clopidogrel or the more effective, and also more expensive prasugrel or ticagrelor. We aim to give helpful contributions to this debate by analysing the cost-effectiveness of clopidogrel, prasugrel, and ticagrelor compared with each other. Methods and results We modified a previously developed Markov model of cardiac disease progression. In the model, we followed up cohorts of patients who have recently had a PCI until 100 years or death. Possible events are revascularization, bleeding, acute myocardial infarction, and death. Our analysis shows that ticagrelor is cost-effective in 77% of simulations at an incremental cost-effectiveness ratio of €7700 compared with clopidogrel. Ticagrelor was also cost-effective against prasugrel at a cost-effectiveness ratio of €7800. Given a Norwegian cost-effectiveness threshold of €70 000, both comparisons appear to be clearly cost-effective in favour of ticagrelor. Conclusion Ticagrelor is cost-effective compared with both clopidogrel and prasugrel for patients who have undergone a PCI. PMID:29474586

Cost-effectiveness of antiplatelet drugs after percutaneous coronary intervention.

PubMed

Wisløff, Torbjørn; Atar, Dan

2016-01-01

Clopidogrel has, for long time, been accepted as the standard treatment for patients who have undergone a percutaneous coronary intervention (PCI). The introduction of prasugrel-and more recently, ticagrelor-has introduced a decision-making problem for clinicians and governments worldwide: to use the cheaper clopidogrel or the more effective, and also more expensive prasugrel or ticagrelor. We aim to give helpful contributions to this debate by analysing the cost-effectiveness of clopidogrel, prasugrel, and ticagrelor compared with each other. We modified a previously developed Markov model of cardiac disease progression. In the model, we followed up cohorts of patients who have recently had a PCI until 100 years or death. Possible events are revascularization, bleeding, acute myocardial infarction, and death. Our analysis shows that ticagrelor is cost-effective in 77% of simulations at an incremental cost-effectiveness ratio of €7700 compared with clopidogrel. Ticagrelor was also cost-effective against prasugrel at a cost-effectiveness ratio of €7800. Given a Norwegian cost-effectiveness threshold of €70 000, both comparisons appear to be clearly cost-effective in favour of ticagrelor. Ticagrelor is cost-effective compared with both clopidogrel and prasugrel for patients who have undergone a PCI.

Markov stochasticity coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eliazar, Iddo, E-mail: iddo.eliazar@intel.com

Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.

Generating probabilistic Boolean networks from a prescribed transition probability matrix.

PubMed

Ching, W-K; Chen, X; Tsing, N-K

2009-11-01

Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. This is an interesting inverse problem in network inference using steady-state data. The problem is important as most microarray data sets are assumed to be obtained from sampling the steady-state.

LMC: Logarithmantic Monte Carlo

NASA Astrophysics Data System (ADS)

Mantz, Adam B.

2017-06-01

LMC is a Markov Chain Monte Carlo engine in Python that implements adaptive Metropolis-Hastings and slice sampling, as well as the affine-invariant method of Goodman & Weare, in a flexible framework. It can be used for simple problems, but the main use case is problems where expensive likelihood evaluations are provided by less flexible third-party software, which benefit from parallelization across many nodes at the sampling level. The parallel/adaptive methods use communication through MPI, or alternatively by writing/reading files, and mostly follow the approaches pioneered by CosmoMC (ascl:1106.025).

Bayesian linkage and segregation analysis: factoring the problem.

PubMed

Matthysse, S

2000-01-01

Complex segregation analysis and linkage methods are mathematical techniques for the genetic dissection of complex diseases. They are used to delineate complex modes of familial transmission and to localize putative disease susceptibility loci to specific chromosomal locations. The computational problem of Bayesian linkage and segregation analysis is one of integration in high-dimensional spaces. In this paper, three available techniques for Bayesian linkage and segregation analysis are discussed: Markov Chain Monte Carlo (MCMC), importance sampling, and exact calculation. The contribution of each to the overall integration will be explicitly discussed.

Correlated gamma-based hidden Markov model for the smart asthma management based on rescue inhaler usage.

PubMed

Son, Junbo; Brennan, Patricia Flatley; Zhou, Shiyu

2017-05-10

Asthma is a very common chronic disease that affects a large portion of population in many nations. Driven by the fast development in sensor and mobile communication technology, a smart asthma management system has become available to continuously monitor the key health indicators of asthma patients. Such data provides opportunities for healthcare practitioners to examine patients not only in the clinic (on-site) but also outside of the clinic (off-site) in their daily life. In this paper, taking advantage from this data availability, we propose a correlated gamma-based hidden Markov model framework, which can reveal and highlight useful information from the rescue inhaler-usage profiles of individual patients for practitioners. The proposed method can provide diagnostic information about the asthma control status of individual patients and can help practitioners to make more informed therapeutic decisions accordingly. The proposed method is validated through both numerical study and case study based on real world data. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Intelligent data analysis to model and understand live cell time-lapse sequences.

PubMed

Paterson, Allan; Ashtari, M; Ribé, D; Stenbeck, G; Tucker, A

2012-01-01

One important aspect of cellular function, which is at the basis of tissue homeostasis, is the delivery of proteins to their correct destinations. Significant advances in live cell microscopy have allowed tracking of these pathways by following the dynamics of fluorescently labelled proteins in living cells. This paper explores intelligent data analysis techniques to model the dynamic behavior of proteins in living cells as well as to classify different experimental conditions. We use a combination of decision tree classification and hidden Markov models. In particular, we introduce a novel approach to "align" hidden Markov models so that hidden states from different models can be cross-compared. Our models capture the dynamics of two experimental conditions accurately with a stable hidden state for control data and multiple (less stable) states for the experimental data recapitulating the behaviour of particle trajectories within live cell time-lapse data. In addition to having successfully developed an automated framework for the classification of protein transport dynamics from live cell time-lapse data our model allows us to understand the dynamics of a complex trafficking pathway in living cells in culture.

Clustering Multivariate Time Series Using Hidden Markov Models

PubMed Central

Ghassempour, Shima; Girosi, Federico; Maeder, Anthony

2014-01-01

In this paper we describe an algorithm for clustering multivariate time series with variables taking both categorical and continuous values. Time series of this type are frequent in health care, where they represent the health trajectories of individuals. The problem is challenging because categorical variables make it difficult to define a meaningful distance between trajectories. We propose an approach based on Hidden Markov Models (HMMs), where we first map each trajectory into an HMM, then define a suitable distance between HMMs and finally proceed to cluster the HMMs with a method based on a distance matrix. We test our approach on a simulated, but realistic, data set of 1,255 trajectories of individuals of age 45 and over, on a synthetic validation set with known clustering structure, and on a smaller set of 268 trajectories extracted from the longitudinal Health and Retirement Survey. The proposed method can be implemented quite simply using standard packages in R and Matlab and may be a good candidate for solving the difficult problem of clustering multivariate time series with categorical variables using tools that do not require advanced statistic knowledge, and therefore are accessible to a wide range of researchers. PMID:24662996

Asteroid mass estimation using Markov-chain Monte Carlo

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2017-11-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to an inverse problem in at least 13 dimensions where the aim is to derive the mass of the perturbing asteroid(s) and six orbital elements for both the perturbing asteroid(s) and the test asteroid(s) based on astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations: the very rough 'marching' approximation, in which the asteroids' orbital elements are not fitted, thereby reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-chain Monte Carlo (MCMC) approach. We describe each of these algorithms with particular focus on the MCMC algorithm, and present example results using both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans.

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Abhinav, S.; Manohar, C. S.

2018-03-01

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.

Extracting duration information in a picture category decoding task using hidden Markov Models

NASA Astrophysics Data System (ADS)

Pfeiffer, Tim; Heinze, Nicolai; Frysch, Robert; Deouell, Leon Y.; Schoenfeld, Mircea A.; Knight, Robert T.; Rose, Georg

2016-04-01

Objective. Adapting classifiers for the purpose of brain signal decoding is a major challenge in brain-computer-interface (BCI) research. In a previous study we showed in principle that hidden Markov models (HMM) are a suitable alternative to the well-studied static classifiers. However, since we investigated a rather straightforward task, advantages from modeling of the signal could not be assessed. Approach. Here, we investigate a more complex data set in order to find out to what extent HMMs, as a dynamic classifier, can provide useful additional information. We show for a visual decoding problem that besides category information, HMMs can simultaneously decode picture duration without an additional training required. This decoding is based on a strong correlation that we found between picture duration and the behavior of the Viterbi paths. Main results. Decoding accuracies of up to 80% could be obtained for category and duration decoding with a single classifier trained on category information only. Significance. The extraction of multiple types of information using a single classifier enables the processing of more complex problems, while preserving good training results even on small databases. Therefore, it provides a convenient framework for online real-life BCI utilizations.

Theory of choice in bandit, information sampling and foraging tasks.

PubMed

Averbeck, Bruno B

2015-03-01

Decision making has been studied with a wide array of tasks. Here we examine the theoretical structure of bandit, information sampling and foraging tasks. These tasks move beyond tasks where the choice in the current trial does not affect future expected rewards. We have modeled these tasks using Markov decision processes (MDPs). MDPs provide a general framework for modeling tasks in which decisions affect the information on which future choices will be made. Under the assumption that agents are maximizing expected rewards, MDPs provide normative solutions. We find that all three classes of tasks pose choices among actions which trade-off immediate and future expected rewards. The tasks drive these trade-offs in unique ways, however. For bandit and information sampling tasks, increasing uncertainty or the time horizon shifts value to actions that pay-off in the future. Correspondingly, decreasing uncertainty increases the relative value of actions that pay-off immediately. For foraging tasks the time-horizon plays the dominant role, as choices do not affect future uncertainty in these tasks.

The economic impact of pig-associated parasitic zoonosis in Northern Lao PDR.

PubMed

Choudhury, Adnan Ali Khan; Conlan, James V; Racloz, Vanessa Nadine; Reid, Simon Andrew; Blacksell, Stuart D; Fenwick, Stanley G; Thompson, Andrew R C; Khamlome, Boualam; Vongxay, Khamphouth; Whittaker, Maxine

2013-03-01

The parasitic zoonoses human cysticercosis (Taenia solium), taeniasis (other Taenia species) and trichinellosis (Trichinella species) are endemic in the Lao People's Democratic Republic (Lao PDR). This study was designed to quantify the economic burden pig-associated zoonotic disease pose in Lao PDR. In particular, the analysis included estimation of the losses in the pork industry as well as losses due to human illness and lost productivity. A Markov-probability based decision-tree model was chosen to form the basis of the calculations to estimate the economic and public health impacts of taeniasis, trichinellosis and cysticercosis. Two different decision trees were run simultaneously on the model's human cohort. A third decision tree simulated the potential impacts on pig production. The human capital method was used to estimate productivity loss. The results found varied significantly depending on the rate of hospitalisation due to neurocysticerosis. This study is the first systematic estimate of the economic impact of pig-associated zoonotic diseases in Lao PDR that demonstrates the significance of the diseases in that country.

Performance evaluation of automated manufacturing systems using generalized stochastic Petri Nets. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Al-Jaar, Robert Y.; Desrochers, Alan A.

1989-01-01

The main objective of this research is to develop a generic modeling methodology with a flexible and modular framework to aid in the design and performance evaluation of integrated manufacturing systems using a unified model. After a thorough examination of the available modeling methods, the Petri Net approach was adopted. The concurrent and asynchronous nature of manufacturing systems are easily captured by Petri Net models. Three basic modules were developed: machine, buffer, and Decision Making Unit. The machine and buffer modules are used for modeling transfer lines and production networks. The Decision Making Unit models the functions of a computer node in a complex Decision Making Unit Architecture. The underlying model is a Generalized Stochastic Petri Net (GSPN) that can be used for performance evaluation and structural analysis. GSPN's were chosen because they help manage the complexity of modeling large manufacturing systems. There is no need to enumerate all the possible states of the Markov Chain since they are automatically generated from the GSPN model.

Background Adjusted Alignment-Free Dissimilarity Measures Improve the Detection of Horizontal Gene Transfer.

PubMed

Tang, Kujin; Lu, Yang Young; Sun, Fengzhu

2018-01-01

Horizontal gene transfer (HGT) plays an important role in the evolution of microbial organisms including bacteria. Alignment-free methods based on single genome compositional information have been used to detect HGT. Currently, Manhattan and Euclidean distances based on tetranucleotide frequencies are the most commonly used alignment-free dissimilarity measures to detect HGT. By testing on simulated bacterial sequences and real data sets with known horizontal transferred genomic regions, we found that more advanced alignment-free dissimilarity measures such as CVTree and [Formula: see text] that take into account the background Markov sequences can solve HGT detection problems with significantly improved performance. We also studied the influence of different factors such as evolutionary distance between host and donor sequences, size of sliding window, and host genome composition on the performances of alignment-free methods to detect HGT. Our study showed that alignment-free methods can predict HGT accurately when host and donor genomes are in different order levels. Among all methods, CVTree with word length of 3, [Formula: see text] with word length 3, Markov order 1 and [Formula: see text] with word length 4, Markov order 1 outperform others in terms of their highest F 1 -score and their robustness under the influence of different factors.

Coupling of Markov chains and cellular automata spatial models to predict land cover changes (case study: upper Ci Leungsi catchment area)

NASA Astrophysics Data System (ADS)

Marko, K.; Zulkarnain, F.; Kusratmoko, E.

2016-11-01

Land cover changes particular in urban catchment area has been rapidly occur. Land cover changes occur as a result of increasing demand for built-up area. Various kinds of environmental and hydrological problems e.g. floods and urban heat island can happen if the changes are uncontrolled. This study aims to predict land cover changes using coupling of Markov chains and cellular automata. One of the most rapid land cover changes is occurs at upper Ci Leungsi catchment area that located near Bekasi City and Jakarta Metropolitan Area. Markov chains has a good ability to predict the probability of change statistically while cellular automata believed as a powerful method in reading the spatial patterns of change. Temporal land cover data was obtained by remote sensing satellite imageries. In addition, this study also used multi-criteria analysis to determine which driving factor that could stimulate the changes such as proximity, elevation, and slope. Coupling of these two methods could give better prediction model rather than just using it separately. The prediction model was validated using existing 2015 land cover data and shown a satisfactory kappa coefficient. The most significant increasing land cover is built-up area from 24% to 53%.

Numerical simulations of piecewise deterministic Markov processes with an application to the stochastic Hodgkin-Huxley model.

PubMed

Ding, Shaojie; Qian, Min; Qian, Hong; Zhang, Xuejuan

2016-12-28

The stochastic Hodgkin-Huxley model is one of the best-known examples of piecewise deterministic Markov processes (PDMPs), in which the electrical potential across a cell membrane, V(t), is coupled with a mesoscopic Markov jump process representing the stochastic opening and closing of ion channels embedded in the membrane. The rates of the channel kinetics, in turn, are voltage-dependent. Due to this interdependence, an accurate and efficient sampling of the time evolution of the hybrid stochastic systems has been challenging. The current exact simulation methods require solving a voltage-dependent hitting time problem for multiple path-dependent intensity functions with random thresholds. This paper proposes a simulation algorithm that approximates an alternative representation of the exact solution by fitting the log-survival function of the inter-jump dwell time, H(t), with a piecewise linear one. The latter uses interpolation points that are chosen according to the time evolution of the H(t), as the numerical solution to the coupled ordinary differential equations of V(t) and H(t). This computational method can be applied to all PDMPs. Pathwise convergence of the approximated sample trajectories to the exact solution is proven, and error estimates are provided. Comparison with a previous algorithm that is based on piecewise constant approximation is also presented.

Saliency Detection via Absorbing Markov Chain With Learnt Transition Probability.

PubMed

Lihe Zhang; Jianwu Ai; Bowen Jiang; Huchuan Lu; Xiukui Li

2018-02-01

In this paper, we propose a bottom-up saliency model based on absorbing Markov chain (AMC). First, a sparsely connected graph is constructed to capture the local context information of each node. All image boundary nodes and other nodes are, respectively, treated as the absorbing nodes and transient nodes in the absorbing Markov chain. Then, the expected number of times from each transient node to all other transient nodes can be used to represent the saliency value of this node. The absorbed time depends on the weights on the path and their spatial coordinates, which are completely encoded in the transition probability matrix. Considering the importance of this matrix, we adopt different hierarchies of deep features extracted from fully convolutional networks and learn a transition probability matrix, which is called learnt transition probability matrix. Although the performance is significantly promoted, salient objects are not uniformly highlighted very well. To solve this problem, an angular embedding technique is investigated to refine the saliency results. Based on pairwise local orderings, which are produced by the saliency maps of AMC and boundary maps, we rearrange the global orderings (saliency value) of all nodes. Extensive experiments demonstrate that the proposed algorithm outperforms the state-of-the-art methods on six publicly available benchmark data sets.

Development of reversible jump Markov Chain Monte Carlo algorithm in the Bayesian mixture modeling for microarray data in Indonesia

NASA Astrophysics Data System (ADS)

Astuti, Ani Budi; Iriawan, Nur; Irhamah, Kuswanto, Heri

2017-12-01

In the Bayesian mixture modeling requires stages the identification number of the most appropriate mixture components thus obtained mixture models fit the data through data driven concept. Reversible Jump Markov Chain Monte Carlo (RJMCMC) is a combination of the reversible jump (RJ) concept and the Markov Chain Monte Carlo (MCMC) concept used by some researchers to solve the problem of identifying the number of mixture components which are not known with certainty number. In its application, RJMCMC using the concept of the birth/death and the split-merge with six types of movement, that are w updating, θ updating, z updating, hyperparameter β updating, split-merge for components and birth/death from blank components. The development of the RJMCMC algorithm needs to be done according to the observed case. The purpose of this study is to know the performance of RJMCMC algorithm development in identifying the number of mixture components which are not known with certainty number in the Bayesian mixture modeling for microarray data in Indonesia. The results of this study represent that the concept RJMCMC algorithm development able to properly identify the number of mixture components in the Bayesian normal mixture model wherein the component mixture in the case of microarray data in Indonesia is not known for certain number.

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

NASA Astrophysics Data System (ADS)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; Huang, Maoyi; Bao, Jie; Swiler, Laura

2017-12-01

In this study we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach is used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated - reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.

Allele Age Under Non-Classical Assumptions is Clarified by an Exact Computational Markov Chain Approach.

PubMed

De Sanctis, Bianca; Krukov, Ivan; de Koning, A P Jason

2017-09-19

Determination of the age of an allele based on its population frequency is a well-studied problem in population genetics, for which a variety of approximations have been proposed. We present a new result that, surprisingly, allows the expectation and variance of allele age to be computed exactly (within machine precision) for any finite absorbing Markov chain model in a matter of seconds. This approach makes none of the classical assumptions (e.g., weak selection, reversibility, infinite sites), exploits modern sparse linear algebra techniques, integrates over all sample paths, and is rapidly computable for Wright-Fisher populations up to N e  = 100,000. With this approach, we study the joint effect of recurrent mutation, dominance, and selection, and demonstrate new examples of "selective strolls" where the classical symmetry of allele age with respect to selection is violated by weakly selected alleles that are older than neutral alleles at the same frequency. We also show evidence for a strong age imbalance, where rare deleterious alleles are expected to be substantially older than advantageous alleles observed at the same frequency when population-scaled mutation rates are large. These results highlight the under-appreciated utility of computational methods for the direct analysis of Markov chain models in population genetics.

Markov-chain model of classified atomistic transition states for discrete kinetic Monte Carlo simulations.

PubMed

Numazawa, Satoshi; Smith, Roger

2011-10-01

Classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The scheme is then used to determine transitions that can be applied in a lattice-based kinetic Monte Carlo (KMC) atomistic simulation model. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multidimensional Boolean valued functions in three-dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology-dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. Excellent agreement with observed experimental results is obtained.

A compositional framework for Markov processes

NASA Astrophysics Data System (ADS)

Baez, John C.; Fong, Brendan; Pollard, Blake S.

2016-03-01

We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.

Atmospheric Tracer Inverse Modeling Using Markov Chain Monte Carlo (MCMC)

NASA Astrophysics Data System (ADS)

Kasibhatla, P.

2004-12-01

In recent years, there has been an increasing emphasis on the use of Bayesian statistical estimation techniques to characterize the temporal and spatial variability of atmospheric trace gas sources and sinks. The applications have been varied in terms of the particular species of interest, as well as in terms of the spatial and temporal resolution of the estimated fluxes. However, one common characteristic has been the use of relatively simple statistical models for describing the measurement and chemical transport model error statistics and prior source statistics. For example, multivariate normal probability distribution functions (pdfs) are commonly used to model these quantities and inverse source estimates are derived for fixed values of pdf paramaters. While the advantage of this approach is that closed form analytical solutions for the a posteriori pdfs of interest are available, it is worth exploring Bayesian analysis approaches which allow for a more general treatment of error and prior source statistics. Here, we present an application of the Markov Chain Monte Carlo (MCMC) methodology to an atmospheric tracer inversion problem to demonstrate how more gereral statistical models for errors can be incorporated into the analysis in a relatively straightforward manner. The MCMC approach to Bayesian analysis, which has found wide application in a variety of fields, is a statistical simulation approach that involves computing moments of interest of the a posteriori pdf by efficiently sampling this pdf. The specific inverse problem that we focus on is the annual mean CO2 source/sink estimation problem considered by the TransCom3 project. TransCom3 was a collaborative effort involving various modeling groups and followed a common modeling and analysis protocoal. As such, this problem provides a convenient case study to demonstrate the applicability of the MCMC methodology to atmospheric tracer source/sink estimation problems.

Un formalisme de systemes a sauts pour la recirculation optimale des casses dans une machine a papier

NASA Astrophysics Data System (ADS)

Khanbaghi, Maryam

Increasing closure of white water circuits is making mill productivity and quality of paper produced increasingly affected by the occurrence of paper breaks. In this thesis the main objective is the development of white water and broke recirculation policies. The thesis consists of three main parts, respectively corresponding to the synthesis of a statistical model of paper breaks in a paper mill, the basic mathematical setup for the formulation of white water and broke recirculation policies in the mill as a jump linear quadratic regulation problem, and finally the tuning of the control law based on first passage-time theory, and its extension to the case of control sensitive paper break rates. More specifically, in the first part a statistical model of paper machine breaks is developed. We start from the hypothesis that the breaks process is a Markov chain with three states: the first state is the operational one, while the two others are associated with the general types of paper-breaks that can take place in the mill (wet breaks and dry breaks). The Markovian hypothesis is empirically validated. We also establish how paper-break rates are correlated with machine speed and broke recirculation ratio. Subsequently, we show how the obtained Markov chain model of paper-breaks can be used to formulate a machine operating speed parameter optimization problem. In the second part, upon recognizing that paper breaks can be modelled as a Markov chain type of process which, when interacting with the continuous mill dynamics, yields a jump Markov model, jump linear theory is proposed as a means of constructing white water and broke recirculation strategies which minimize process variability. Reduced process variability comes at the expense of relatively large swings in white water and broke tanks level. Since the linear design does not specifically account for constraints on the state-space, under the resulting law, damaging events of tank overflow or emptiness can occur. A heuristic simulation-based approach is proposed to choose the performance measure design parameters to keep the mean time between incidents of fluid in broke and white water tanks either overflowing, or reaching dangerously low levels, sufficiently long. In the third part, a methodology, mainly founded on the first passage-time theory of stochastic processes, is proposed to choose the performance measure design parameters to limit process variability while accounting for the possibility of undesirable tank overflows or tank emptiness. The heart of the approach is an approximation technique for evaluating mean first passage-times of the controlled tanks levels. This technique appears to have an applicability which largely exceeds the problem area it was designed for. Furthermore, the introduction of control sensitive break rates and the analysis of the ensuing control problem are presented. This is to account for the experimentally observed increase in breaks concomitant with flow rate variability.

Electrophysiological correlates reflect the integration of model-based and model-free decision information.

PubMed

Eppinger, Ben; Walter, Maik; Li, Shu-Chen

2017-04-01

In this study, we investigated the interplay of habitual (model-free) and goal-directed (model-based) decision processes by using a two-stage Markov decision task in combination with event-related potentials (ERPs) and computational modeling. To manipulate the demands on model-based decision making, we applied two experimental conditions with different probabilities of transitioning from the first to the second stage of the task. As we expected, when the stage transitions were more predictable, participants showed greater model-based (planning) behavior. Consistent with this result, we found that stimulus-evoked parietal (P300) activity at the second stage of the task increased with the predictability of the state transitions. However, the parietal activity also reflected model-free information about the expected values of the stimuli, indicating that at this stage of the task both types of information are integrated to guide decision making. Outcome-related ERP components only reflected reward-related processes: Specifically, a medial prefrontal ERP component (the feedback-related negativity) was sensitive to negative outcomes, whereas a component that is elicited by reward (the feedback-related positivity) increased as a function of positive prediction errors. Taken together, our data indicate that stimulus-locked parietal activity reflects the integration of model-based and model-free information during decision making, whereas feedback-related medial prefrontal signals primarily reflect reward-related decision processes.

Optimizing basin-scale coupled water quantity and water quality man-agement with stochastic dynamic programming

NASA Astrophysics Data System (ADS)

Davidsen, Claus; Liu, Suxia; Mo, Xingguo; Engelund Holm, Peter; Trapp, Stefan; Rosbjerg, Dan; Bauer-Gottwein, Peter

2015-04-01

Few studies address water quality in hydro-economic models, which often focus primarily on optimal allocation of water quantities. Water quality and water quantity are closely coupled, and optimal management with focus solely on either quantity or quality may cause large costs in terms of the oth-er component. In this study, we couple water quality and water quantity in a joint hydro-economic catchment-scale optimization problem. Stochastic dynamic programming (SDP) is used to minimize the basin-wide total costs arising from water allocation, water curtailment and water treatment. The simple water quality module can handle conservative pollutants, first order depletion and non-linear reactions. For demonstration purposes, we model pollutant releases as biochemical oxygen demand (BOD) and use the Streeter-Phelps equation for oxygen deficit to compute the resulting min-imum dissolved oxygen concentrations. Inelastic water demands, fixed water allocation curtailment costs and fixed wastewater treatment costs (before and after use) are estimated for the water users (agriculture, industry and domestic). If the BOD concentration exceeds a given user pollution thresh-old, the user will need to pay for pre-treatment of the water before use. Similarly, treatment of the return flow can reduce the BOD load to the river. A traditional SDP approach is used to solve one-step-ahead sub-problems for all combinations of discrete reservoir storage, Markov Chain inflow clas-ses and monthly time steps. Pollution concentration nodes are introduced for each user group and untreated return flow from the users contribute to increased BOD concentrations in the river. The pollutant concentrations in each node depend on multiple decision variables (allocation and wastewater treatment) rendering the objective function non-linear. Therefore, the pollution concen-tration decisions are outsourced to a genetic algorithm, which calls a linear program to determine the remainder of the decision variables. This hybrid formulation keeps the optimization problem computationally feasible and represents a flexible and customizable method. The method has been applied to the Ziya River basin, an economic hotspot located on the North China Plain in Northern China. The basin is subject to severe water scarcity, and the rivers are heavily polluted with wastewater and nutrients from diffuse sources. The coupled hydro-economic optimiza-tion model can be used to assess costs of meeting additional constraints such as minimum water qual-ity or to economically prioritize investments in waste water treatment facilities based on economic criteria.

Wheat forecast economics effect study. [value of improved information on crop inventories, production, imports and exports

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Rouhani, R.; Jones, S.; Schick, I.

1980-01-01

A model to assess the value of improved information regarding the inventories, productions, exports, and imports of crop on a worldwide basis is discussed. A previously proposed model is interpreted in a stochastic control setting and the underlying assumptions of the model are revealed. In solving the stochastic optimization problem, the Markov programming approach is much more powerful and exact as compared to the dynamic programming-simulation approach of the original model. The convergence of a dual variable Markov programming algorithm is shown to be fast and efficient. A computer program for the general model of multicountry-multiperiod is developed. As an example, the case of one country-two periods is treated and the results are presented in detail. A comparison with the original model results reveals certain interesting aspects of the algorithms and the dependence of the value of information on the incremental cost function.

Passive Acoustic Leak Detection for Sodium Cooled Fast Reactors Using Hidden Markov Models

NASA Astrophysics Data System (ADS)

Marklund, A. Riber; Kishore, S.; Prakash, V.; Rajan, K. K.; Michel, F.

2016-06-01

Acoustic leak detection for steam generators of sodium fast reactors have been an active research topic since the early 1970s and several methods have been tested over the years. Inspired by its success in the field of automatic speech recognition, we here apply hidden Markov models (HMM) in combination with Gaussian mixture models (GMM) to the problem. To achieve this, we propose a new feature calculation scheme, based on the temporal evolution of the power spectral density (PSD) of the signal. Using acoustic signals recorded during steam/water injection experiments done at the Indira Gandhi Centre for Atomic Research (IGCAR), the proposed method is tested. We perform parametric studies on the HMM+GMM model size and demonstrate that the proposed method a) performs well without a priori knowledge of injection noise, b) can incorporate several noise models and c) has an output distribution that simplifies false alarm rate control.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Quantum Mechanics, Pattern Recognition, and the Mammalian Brain

NASA Astrophysics Data System (ADS)

Chapline, George

2008-10-01

Although the usual way of representing Markov processes is time asymmetric, there is a way of describing Markov processes, due to Schrodinger, which is time symmetric. This observation provides a link between quantum mechanics and the layered Bayesian networks that are often used in automated pattern recognition systems. In particular, there is a striking formal similarity between quantum mechanics and a particular type of Bayesian network, the Helmholtz machine, which provides a plausible model for how the mammalian brain recognizes important environmental situations. One interesting aspect of this relationship is that the "wake-sleep" algorithm for training a Helmholtz machine is very similar to the problem of finding the potential for the multi-channel Schrodinger equation. As a practical application of this insight it may be possible to use inverse scattering techniques to study the relationship between human brain wave patterns, pattern recognition, and learning. We also comment on whether there is a relationship between quantum measurements and consciousness.

ECG signal analysis through hidden Markov models.

PubMed

Andreão, Rodrigo V; Dorizzi, Bernadette; Boudy, Jérôme

2006-08-01

This paper presents an original hidden Markov model (HMM) approach for online beat segmentation and classification of electrocardiograms. The HMM framework has been visited because of its ability of beat detection, segmentation and classification, highly suitable to the electrocardiogram (ECG) problem. Our approach addresses a large panel of topics some of them never studied before in other HMM related works: waveforms modeling, multichannel beat segmentation and classification, and unsupervised adaptation to the patient's ECG. The performance was evaluated on the two-channel QT database in terms of waveform segmentation precision, beat detection and classification. Our waveform segmentation results compare favorably to other systems in the literature. We also obtained high beat detection performance with sensitivity of 99.79% and a positive predictivity of 99.96%, using a test set of 59 recordings. Moreover, premature ventricular contraction beats were detected using an original classification strategy. The results obtained validate our approach for real world application.

Acquisition of Robotic Giant-swing Motion Using Reinforcement Learning and Its Consideration of Motion Forms

NASA Astrophysics Data System (ADS)

Sakai, Naoki; Kawabe, Naoto; Hara, Masayuki; Toyoda, Nozomi; Yabuta, Tetsuro

This paper argues how a compact humanoid robot can acquire a giant-swing motion without any robotic models by using Q-Learning method. Generally, it is widely said that Q-Learning is not appropriated for learning dynamic motions because Markov property is not necessarily guaranteed during the dynamic task. However, we tried to solve this problem by embedding the angular velocity state into state definition and averaging Q-Learning method to reduce dynamic effects, although there remain non-Markov effects in the learning results. The result shows how the robot can acquire a giant-swing motion by using Q-Learning algorithm. The successful acquired motions are analyzed in the view point of dynamics in order to realize a functionally giant-swing motion. Finally, the result shows how this method can avoid the stagnant action loop at around the bottom of the horizontal bar during the early stage of giant-swing motion.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

Using Markov Chains and Multi-Objective Optimization for Energy-Efficient Context Recognition †

PubMed Central

Janko, Vito

2017-01-01

The recognition of the user’s context with wearable sensing systems is a common problem in ubiquitous computing. However, the typically small battery of such systems often makes continuous recognition impractical. The strain on the battery can be reduced if the sensor setting is adapted to each context. We propose a method that efficiently finds near-optimal sensor settings for each context. It uses Markov chains to simulate the behavior of the system in different configurations and the multi-objective genetic algorithm to find a set of good non-dominated configurations. The method was evaluated on three real-life datasets and found good trade-offs between the system’s energy expenditure and the system’s accuracy. One of the solutions, for example, consumed five-times less energy than the default one, while sacrificing only two percentage points of accuracy. PMID:29286301

Adaptive learning compressive tracking based on Markov location prediction

NASA Astrophysics Data System (ADS)

Zhou, Xingyu; Fu, Dongmei; Yang, Tao; Shi, Yanan

2017-03-01

Object tracking is an interdisciplinary research topic in image processing, pattern recognition, and computer vision which has theoretical and practical application value in video surveillance, virtual reality, and automatic navigation. Compressive tracking (CT) has many advantages, such as efficiency and accuracy. However, when there are object occlusion, abrupt motion and blur, similar objects, and scale changing, the CT has the problem of tracking drift. We propose the Markov object location prediction to get the initial position of the object. Then CT is used to locate the object accurately, and the classifier parameter adaptive updating strategy is given based on the confidence map. At the same time according to the object location, extract the scale features, which is able to deal with object scale variations effectively. Experimental results show that the proposed algorithm has better tracking accuracy and robustness than current advanced algorithms and achieves real-time performance.

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

NASA Astrophysics Data System (ADS)

Liu, Boda; Liang, Yan

2017-04-01

Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.

PubMed

Kapfer, Sebastian C; Krauth, Werner

2017-12-15

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium

NASA Astrophysics Data System (ADS)

Kapfer, Sebastian C.; Krauth, Werner

2017-12-01

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Structured Set Intra Prediction With Discriminative Learning in a Max-Margin Markov Network for High Efficiency Video Coding

PubMed Central

Dai, Wenrui; Xiong, Hongkai; Jiang, Xiaoqian; Chen, Chang Wen

2014-01-01

This paper proposes a novel model on intra coding for High Efficiency Video Coding (HEVC), which simultaneously predicts blocks of pixels with optimal rate distortion. It utilizes the spatial statistical correlation for the optimal prediction based on 2-D contexts, in addition to formulating the data-driven structural interdependences to make the prediction error coherent with the probability distribution, which is desirable for successful transform and coding. The structured set prediction model incorporates a max-margin Markov network (M3N) to regulate and optimize multiple block predictions. The model parameters are learned by discriminating the actual pixel value from other possible estimates to maximize the margin (i.e., decision boundary bandwidth). Compared to existing methods that focus on minimizing prediction error, the M3N-based model adaptively maintains the coherence for a set of predictions. Specifically, the proposed model concurrently optimizes a set of predictions by associating the loss for individual blocks to the joint distribution of succeeding discrete cosine transform coefficients. When the sample size grows, the prediction error is asymptotically upper bounded by the training error under the decomposable loss function. As an internal step, we optimize the underlying Markov network structure to find states that achieve the maximal energy using expectation propagation. For validation, we integrate the proposed model into HEVC for optimal mode selection on rate-distortion optimization. The proposed prediction model obtains up to 2.85% bit rate reduction and achieves better visual quality in comparison to the HEVC intra coding. PMID:25505829

Finite grade pheromone ant colony optimization for image segmentation

NASA Astrophysics Data System (ADS)

Yuanjing, F.; Li, Y.; Liangjun, K.

2008-06-01

By combining the decision process of ant colony optimization (ACO) with the multistage decision process of image segmentation based on active contour model (ACM), an algorithm called finite grade ACO (FACO) for image segmentation is proposed. This algorithm classifies pheromone into finite grades and updating of the pheromone is achieved by changing the grades and the updated quantity of pheromone is independent from the objective function. The algorithm that provides a new approach to obtain precise contour is proved to converge to the global optimal solutions linearly by means of finite Markov chains. The segmentation experiments with ultrasound heart image show the effectiveness of the algorithm. Comparing the results for segmentation of left ventricle images shows that the ACO for image segmentation is more effective than the GA approach and the new pheromone updating strategy appears good time performance in optimization process.

[Use the Markov-decision tree model to optimize vaccination strategies of hepatitis E among women aged 15 to 49].

PubMed

Chen, Z M; Ji, S B; Shi, X L; Zhao, Y Y; Zhang, X F; Jin, H

2017-02-10

Objective: To evaluate the cost-utility of different hepatitis E vaccination strategies in women aged 15 to 49. Methods: The Markov-decision tree model was constructed to evaluate the cost-utility of three hepatitis E virus vaccination strategies. Parameters of the models were estimated on the basis of published studies and experience of experts. Both methods on sensitivity and threshold analysis were used to evaluate the uncertainties of the model. Results: Compared with non-vaccination group, strategy on post-screening vaccination with rate as 100%, could save 0.10 quality-adjusted life years per capital in the women from the societal perspectives. After implementation of screening program and with the vaccination rate reaching 100%, the incremental cost utility ratio (ICUR) of vaccination appeared as 5 651.89 and 6 385.33 Yuan/QALY, respectively. Vaccination post to the implementation of a screening program, the result showed better benefit than the vaccination rate of 100%. Results from the sensitivity analysis showed that both the cost of hepatitis E vaccine and the inoculation compliance rate presented significant effects. If the cost were lower than 191.56 Yuan (RMB) or the inoculation compliance rate lower than 0.23, the vaccination rate of 100% strategy was better than the post-screening vaccination strategy, otherwise the post-screening vaccination strategy appeared the optimal strategy. Conclusion: Post-screening vaccination for women aged 15 to 49 from social perspectives seemed the optimal one but it had to depend on the change of vaccine cost and the rate of inoculation compliance.

Semi-Markov adjunction to the Computer-Aided Markov Evaluator (CAME)

NASA Technical Reports Server (NTRS)

Rosch, Gene; Hutchins, Monica A.; Leong, Frank J.; Babcock, Philip S., IV

1988-01-01

The rule-based Computer-Aided Markov Evaluator (CAME) program was expanded in its ability to incorporate the effect of fault-handling processes into the construction of a reliability model. The fault-handling processes are modeled as semi-Markov events and CAME constructs and appropriate semi-Markov model. To solve the model, the program outputs it in a form which can be directly solved with the Semi-Markov Unreliability Range Evaluator (SURE) program. As a means of evaluating the alterations made to the CAME program, the program is used to model the reliability of portions of the Integrated Airframe/Propulsion Control System Architecture (IAPSA 2) reference configuration. The reliability predictions are compared with a previous analysis. The results bear out the feasibility of utilizing CAME to generate appropriate semi-Markov models to model fault-handling processes.

American option pricing in Gauss-Markov interest rate models

NASA Astrophysics Data System (ADS)

Galluccio, Stefano

1999-07-01

In the context of Gaussian non-homogeneous interest-rate models, we study the problem of American bond option pricing. In particular, we show how to efficiently compute the exercise boundary in these models in order to decompose the price as a sum of a European option and an American premium. Generalizations to coupon-bearing bonds and jump-diffusion processes for the interest rates are also discussed.

exocartographer: Constraining surface maps orbital parameters of exoplanets

NASA Astrophysics Data System (ADS)

Farr, Ben; Farr, Will M.; Cowan, Nicolas B.; Haggard, Hal M.; Robinson, Tyler

2018-05-01

exocartographer solves the exo-cartography inverse problem. This flexible forward-modeling framework, written in Python, retrieves the albedo map and spin geometry of a planet based on time-resolved photometry; it uses a Markov chain Monte Carlo method to extract albedo maps and planet spin and their uncertainties. Gaussian Processes use the data to fit for the characteristic length scale of the map and enforce smooth maps.

The Existence of Smooth Densities for the Prediction, Filtering and Smoothing Problems

DTIC Science & Technology

1990-12-20

128 - 139. [14] With D. COLWELL and P.E. KOPP, Martingale representation and hedging policies. Stochastic Processes and Applications. (Accepted) [5j...Martingale Representation and Hedging Policies David B. COLWELL Robert J. ELLIOTT P. Ekkehard KOPP* Department of Statistics and Applied Probability...is determined by elementary methods in the Markov situation. Applications to hedging portfolios in finance are described. martingale representation

Open Markov Processes and Reaction Networks

ERIC Educational Resources Information Center

Swistock Pollard, Blake Stephen

2017-01-01

We begin by defining the concept of "open" Markov processes, which are continuous-time Markov chains where probability can flow in and out through certain "boundary" states. We study open Markov processes which in the absence of such boundary flows admit equilibrium states satisfying detailed balance, meaning that the net flow…

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dascaliuc, Radu; Thomann, Enrique; Waymire, Edward C., E-mail: waymire@math.oregonstate.edu

2015-07-15

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturallymore » arise as a result of this investigation.« less

Symmetry breaking and uniqueness for the incompressible Navier-Stokes equations.

PubMed

Dascaliuc, Radu; Michalowski, Nicholas; Thomann, Enrique; Waymire, Edward C

2015-07-01

The present article establishes connections between the structure of the deterministic Navier-Stokes equations and the structure of (similarity) equations that govern self-similar solutions as expected values of certain naturally associated stochastic cascades. A principle result is that explosion criteria for the stochastic cascades involved in the probabilistic representations of solutions to the respective equations coincide. While the uniqueness problem itself remains unresolved, these connections provide interesting problems and possible methods for investigating symmetry breaking and the uniqueness problem for Navier-Stokes equations. In particular, new branching Markov chains, including a dilogarithmic branching random walk on the multiplicative group (0, ∞), naturally arise as a result of this investigation.

Supercomputer optimizations for stochastic optimal control applications

NASA Technical Reports Server (NTRS)

Chung, Siu-Leung; Hanson, Floyd B.; Xu, Huihuang

1991-01-01

Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.

The explicit form of the rate function for semi-Markov processes and its contractions

NASA Astrophysics Data System (ADS)

Sughiyama, Yuki; Kobayashi, Testuya J.

2018-03-01

We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.

Applications of decision analysis and related techniques to industrial engineering problems at KSC

NASA Technical Reports Server (NTRS)

Evans, Gerald W.

1995-01-01

This report provides: (1) a discussion of the origination of decision analysis problems (well-structured problems) from ill-structured problems; (2) a review of the various methodologies and software packages for decision analysis and related problem areas; (3) a discussion of how the characteristics of a decision analysis problem affect the choice of modeling methodologies, thus providing a guide as to when to choose a particular methodology; and (4) examples of applications of decision analysis to particular problems encountered by the IE Group at KSC. With respect to the specific applications at KSC, particular emphasis is placed on the use of the Demos software package (Lumina Decision Systems, 1993).

Communication: Introducing prescribed biases in out-of-equilibrium Markov models

NASA Astrophysics Data System (ADS)

Dixit, Purushottam D.

2018-03-01

Markov models are often used in modeling complex out-of-equilibrium chemical and biochemical systems. However, many times their predictions do not agree with experiments. We need a systematic framework to update existing Markov models to make them consistent with constraints that are derived from experiments. Here, we present a framework based on the principle of maximum relative path entropy (minimum Kullback-Leibler divergence) to update Markov models using stationary state and dynamical trajectory-based constraints. We illustrate the framework using a biochemical model network of growth factor-based signaling. We also show how to find the closest detailed balanced Markov model to a given Markov model. Further applications and generalizations are discussed.

Poissonian steady states: from stationary densities to stationary intensities.

PubMed

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

Poissonian steady states: From stationary densities to stationary intensities

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

On a Result for Finite Markov Chains

ERIC Educational Resources Information Center

Kulathinal, Sangita; Ghosh, Lagnojita

2006-01-01

In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…

The Markov blankets of life: autonomy, active inference and the free energy principle

PubMed Central

Palacios, Ensor; Friston, Karl; Kiverstein, Julian

2018-01-01

This work addresses the autonomous organization of biological systems. It does so by considering the boundaries of biological systems, from individual cells to Home sapiens, in terms of the presence of Markov blankets under the active inference scheme—a corollary of the free energy principle. A Markov blanket defines the boundaries of a system in a statistical sense. Here we consider how a collective of Markov blankets can self-assemble into a global system that itself has a Markov blanket; thereby providing an illustration of how autonomous systems can be understood as having layers of nested and self-sustaining boundaries. This allows us to show that: (i) any living system is a Markov blanketed system and (ii) the boundaries of such systems need not be co-extensive with the biophysical boundaries of a living organism. In other words, autonomous systems are hierarchically composed of Markov blankets of Markov blankets—all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment. PMID:29343629

Honest Importance Sampling with Multiple Markov Chains

PubMed Central

Tan, Aixin; Doss, Hani; Hobert, James P.

2017-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π1, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π1 is replaced by a Harris ergodic Markov chain with invariant density π1, then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π1, …, πk, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection. PMID:28701855

Honest Importance Sampling with Multiple Markov Chains.

PubMed

Tan, Aixin; Doss, Hani; Hobert, James P

2015-01-01

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.

Large Deviations for Stationary Probabilities of a Family of Continuous Time Markov Chains via Aubry-Mather Theory

NASA Astrophysics Data System (ADS)

Lopes, Artur O.; Neumann, Adriana

2015-05-01

In the present paper, we consider a family of continuous time symmetric random walks indexed by , . For each the matching random walk take values in the finite set of states ; notice that is a subset of , where is the unitary circle. The infinitesimal generator of such chain is denoted by . The stationary probability for such process converges to the uniform distribution on the circle, when . Here we want to study other natural measures, obtained via a limit on , that are concentrated on some points of . We will disturb this process by a potential and study for each the perturbed stationary measures of this new process when . We disturb the system considering a fixed potential and we will denote by the restriction of to . Then, we define a non-stochastic semigroup generated by the matrix , where is the infinifesimal generator of . From the continuous time Perron's Theorem one can normalized such semigroup, and, then we get another stochastic semigroup which generates a continuous time Markov Chain taking values on . This new chain is called the continuous time Gibbs state associated to the potential , see (Lopes et al. in J Stat Phys 152:894-933, 2013). The stationary probability vector for such Markov Chain is denoted by . We assume that the maximum of is attained in a unique point of , and from this will follow that . Thus, here, our main goal is to analyze the large deviation principle for the family , when . The deviation function , which is defined on , will be obtained from a procedure based on fixed points of the Lax-Oleinik operator and Aubry-Mather theory. In order to obtain the associated Lax-Oleinik operator we use the Varadhan's Lemma for the process . For a careful analysis of the problem we present full details of the proof of the Large Deviation Principle, in the Skorohod space, for such family of Markov Chains, when . Finally, we compute the entropy of the invariant probabilities on the Skorohod space associated to the Markov Chains we analyze.

Entanglement revival can occur only when the system-environment state is not a Markov state

NASA Astrophysics Data System (ADS)

Sargolzahi, Iman

2018-06-01

Markov states have been defined for tripartite quantum systems. In this paper, we generalize the definition of the Markov states to arbitrary multipartite case and find the general structure of an important subset of them, which we will call strong Markov states. In addition, we focus on an important property of the Markov states: If the initial state of the whole system-environment is a Markov state, then each localized dynamics of the whole system-environment reduces to a localized subdynamics of the system. This provides us a necessary condition for entanglement revival in an open quantum system: Entanglement revival can occur only when the system-environment state is not a Markov state. To illustrate (a part of) our results, we consider the case that the environment is modeled as classical. In this case, though the correlation between the system and the environment remains classical during the evolution, the change of the state of the system-environment, from its initial Markov state to a state which is not a Markov one, leads to the entanglement revival in the system. This shows that the non-Markovianity of a state is not equivalent to the existence of non-classical correlation in it, in general.

Power optimization of wireless media systems with space-time block codes.

PubMed

Yousefi'zadeh, Homayoun; Jafarkhani, Hamid; Moshfeghi, Mehran

2004-07-01

We present analytical and numerical solutions to the problem of power control in wireless media systems with multiple antennas. We formulate a set of optimization problems aimed at minimizing total power consumption of wireless media systems subject to a given level of QoS and an available bit rate. Our formulation takes into consideration the power consumption related to source coding, channel coding, and transmission of multiple-transmit antennas. In our study, we consider Gauss-Markov and video source models, Rayleigh fading channels along with the Bernoulli/Gilbert-Elliott loss models, and space-time block codes.

Principles of health economic evaluations of lipid-lowering strategies.

PubMed

Ara, Roberta; Basarir, Hasan; Ward, Sue Elizabeth

2012-08-01

Policy decision-making in cardiovascular disease is increasingly informed by the results generated from decision-analytic models (DAMs). The methodological approaches and assumptions used in these DAMs impact on the results generated and can influence a policy decision based on a cost per quality-adjusted life year (QALY) threshold. Decision makers need to be provided with a clear understanding of the key sources of evidence and how they are used in the DAM to make an informed judgement on the quality and appropriateness of the results generated. Our review identified 12 studies exploring the cost-effectiveness of pharmaceutical lipid-lowering interventions published since January 2010. All studies used Markov models with annual cycles to represent the long-term clinical pathway. Important differences in the model structures and evidence base used within the DAMs were identified. Whereas the reporting standards were reasonably good, there were many instances when reporting of methods could be improved, particularly relating to baseline risk levels, long-term benefit of treatment and health state utility values. There is a scope for improvement in the reporting of evidence and modelling approaches used within DAMs to provide decision makers with a clearer understanding of the quality and validity of the results generated. This would be assisted by fuller publication of models, perhaps through detailed web appendices.

Markov chain Monte Carlo techniques and spatial-temporal modelling for medical EIT.

PubMed

West, Robert M; Aykroyd, Robert G; Meng, Sha; Williams, Richard A

2004-02-01

Many imaging problems such as imaging with electrical impedance tomography (EIT) can be shown to be inverse problems: that is either there is no unique solution or the solution does not depend continuously on the data. As a consequence solution of inverse problems based on measured data alone is unstable, particularly if the mapping between the solution distribution and the measurements is also nonlinear as in EIT. To deliver a practical stable solution, it is necessary to make considerable use of prior information or regularization techniques. The role of a Bayesian approach is therefore of fundamental importance, especially when coupled with Markov chain Monte Carlo (MCMC) sampling to provide information about solution behaviour. Spatial smoothing is a commonly used approach to regularization. In the human thorax EIT example considered here nonlinearity increases the difficulty of imaging, using only boundary data, leading to reconstructions which are often rather too smooth. In particular, in medical imaging the resistivity distribution usually contains substantial jumps at the boundaries of different anatomical regions. With spatial smoothing these boundaries can be masked by blurring. This paper focuses on the medical application of EIT to monitor lung and cardiac function and uses explicit geometric information regarding anatomical structure and incorporates temporal correlation. Some simple properties are assumed known, or at least reliably estimated from separate studies, whereas others are estimated from the voltage measurements. This structural formulation will also allow direct estimation of clinically important quantities, such as ejection fraction and residual capacity, along with assessment of precision.

Estimating Model Probabilities using Thermodynamic Markov Chain Monte Carlo Methods

NASA Astrophysics Data System (ADS)

Ye, M.; Liu, P.; Beerli, P.; Lu, D.; Hill, M. C.

2014-12-01

Markov chain Monte Carlo (MCMC) methods are widely used to evaluate model probability for quantifying model uncertainty. In a general procedure, MCMC simulations are first conducted for each individual model, and MCMC parameter samples are then used to approximate marginal likelihood of the model by calculating the geometric mean of the joint likelihood of the model and its parameters. It has been found the method of evaluating geometric mean suffers from the numerical problem of low convergence rate. A simple test case shows that even millions of MCMC samples are insufficient to yield accurate estimation of the marginal likelihood. To resolve this problem, a thermodynamic method is used to have multiple MCMC runs with different values of a heating coefficient between zero and one. When the heating coefficient is zero, the MCMC run is equivalent to a random walk MC in the prior parameter space; when the heating coefficient is one, the MCMC run is the conventional one. For a simple case with analytical form of the marginal likelihood, the thermodynamic method yields more accurate estimate than the method of using geometric mean. This is also demonstrated for a case of groundwater modeling with consideration of four alternative models postulated based on different conceptualization of a confining layer. This groundwater example shows that model probabilities estimated using the thermodynamic method are more reasonable than those obtained using the geometric method. The thermodynamic method is general, and can be used for a wide range of environmental problem for model uncertainty quantification.

Beyond utilitarianism: a method for analyzing competing ethical principles in a decision analysis of liver transplantation.

PubMed

Volk, Michael L; Lok, Anna S F; Ubel, Peter A; Vijan, Sandeep

2008-01-01

The utilitarian foundation of decision analysis limits its usefulness for many social policy decisions. In this study, the authors examine a method to incorporate competing ethical principles in a decision analysis of liver transplantation for a patient with acute liver failure (ALF). A Markov model was constructed to compare the benefit of transplantation for a patient with ALF versus the harm caused to other patients on the waiting list and to determine the lowest acceptable 5-y posttransplant survival for the ALF patient. The weighting of the ALF patient and other patients was then adjusted using a multiattribute variable incorporating utilitarianism, urgency, and other principles such as fair chances. In the base-case analysis, the strategy of transplanting the ALF patient resulted in a 0.8% increase in the risk of death and a utility loss of 7.8 quality-adjusted days of life for each of the other patients on the waiting list. These harms cumulatively outweighed the benefit of transplantation for an ALF patient having a posttransplant survival of less than 48% at 5 y. However, the threshold for an acceptable posttransplant survival for the ALF patient ranged from 25% to 56% at 5 y, depending on the ethical principles involved. The results of the decision analysis vary depending on the ethical perspective. This study demonstrates how competing ethical principles can be numerically incorporated in a decision analysis.

Bridging the gap between uncertainty analysis for complex watershed models and decision-making for watershed-scale water management

NASA Astrophysics Data System (ADS)

Zheng, Y.; Han, F.; Wu, B.

2013-12-01

Process-based, spatially distributed and dynamic models provide desirable resolutions to watershed-scale water management. However, their reliability in solving real management problems has been seriously questioned, since the model simulation usually involves significant uncertainty with complicated origins. Uncertainty analysis (UA) for complex hydrological models has been a hot topic in the past decade, and a variety of UA approaches have been developed, but mostly in a theoretical setting. Whether and how a UA could benefit real management decisions remains to be critical questions. We have conducted a series of studies to investigate the applicability of classic approaches, such as GLUE and Markov Chain Monte Carlo (MCMC) methods, in real management settings, unravel the difficulties encountered by such methods, and tailor the methods to better serve the management. Frameworks and new algorithms, such as Probabilistic Collocation Method (PCM)-based approaches, were also proposed for specific management issues. This presentation summarize our past and ongoing studies on the role of UA in real water management. Challenges and potential strategies to bridge the gap between UA for complex models and decision-making for management will be discussed. Future directions for the research in this field will also be suggested. Two common water management settings were examined. One is the Total Maximum Daily Loads (TMDLs) management for surface water quality protection. The other is integrated water resources management for watershed sustainability. For the first setting, nutrients and pesticides TMDLs in the Newport Bay Watershed (Orange Country, California, USA) were discussed. It is a highly urbanized region with a semi-arid Mediterranean climate, typical of the western U.S. For the second setting, the water resources management in the Zhangye Basin (the midstream part of Heihe Baisn, China), where the famous 'Silk Road' came through, was investigated. The Zhangye Basin has a Gobi-oasis system typical of the western China, with extensive agriculture in its oasis.

Utility indifference pricing of insurance catastrophe derivatives.

PubMed

Eichler, Andreas; Leobacher, Gunther; Szölgyenyi, Michaela

2017-01-01

We propose a model for an insurance loss index and the claims process of a single insurance company holding a fraction of the total number of contracts that captures both ordinary losses and losses due to catastrophes. In this model we price a catastrophe derivative by the method of utility indifference pricing. The associated stochastic optimization problem is treated by techniques for piecewise deterministic Markov processes. A numerical study illustrates our results.

LATTE Linking Acoustic Tests and Tagging Using Statistical Estimation

DTIC Science & Technology

2015-09-30

the complexity of the model: (from simplest to most complex) Kalman filter , Markov chain Monte-Carlo (MCMC) and ABC. Many of these methods have been...using SMMs fitted using Kalman filters . Therefore, using the DTAG data, we can estimate the distributions associated with 2D horizontal displacement...speed (a key problem in the previous Kalman filter implementation). This new approach also allows the animal’s horizontal movement direction to differ

Did the ever dead outnumber the living and when? A birth-and-death approach

NASA Astrophysics Data System (ADS)

Avan, Jean; Grosjean, Nicolas; Huillet, Thierry

2015-02-01

This paper is an attempt to formalize analytically the question raised in 'World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?' Huffington Post, Howard (2012). We start developing simple deterministic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both linear birth and death Markov chain models and age-structured models.

A Bayesian Approach to a Multiple-Group Latent Class-Profile Analysis: The Timing of Drinking Onset and Subsequent Drinking Behaviors among U.S. Adolescents

ERIC Educational Resources Information Center

Chung, Hwan; Anthony, James C.

2013-01-01

This article presents a multiple-group latent class-profile analysis (LCPA) by taking a Bayesian approach in which a Markov chain Monte Carlo simulation is employed to achieve more robust estimates for latent growth patterns. This article describes and addresses a label-switching problem that involves the LCPA likelihood function, which has…

Improving Learning of Markov Logic Networks using Transfer and Bottom-Up Induction

DTIC Science & Technology

2007-05-01

Texas at Austin Austin, TX 78712 lilyanam@cs.utexas.edu Doctoral Dissertation Proposal Supervising Professor: Raymond J. Mooney Abstract Statistical...maxima and plateaus. It is therefore an important research problem to develop learning algorithms that improve the speed and accuracy of this process. The...of Texas at Austin,Department of Computer Sciences,Austin,TX,78712 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S

Harnessing graphical structure in Markov chain Monte Carlo learning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stolorz, P.E.; Chew P.C.

1996-12-31

The Monte Carlo method is recognized as a useful tool in learning and probabilistic inference methods common to many datamining problems. Generalized Hidden Markov Models and Bayes nets are especially popular applications. However, the presence of multiple modes in many relevant integrands and summands often renders the method slow and cumbersome. Recent mean field alternatives designed to speed things up have been inspired by experience gleaned from physics. The current work adopts an approach very similar to this in spirit, but focusses instead upon dynamic programming notions as a basis for producing systematic Monte Carlo improvements. The idea is tomore » approximate a given model by a dynamic programming-style decomposition, which then forms a scaffold upon which to build successively more accurate Monte Carlo approximations. Dynamic programming ideas alone fail to account for non-local structure, while standard Monte Carlo methods essentially ignore all structure. However, suitably-crafted hybrids can successfully exploit the strengths of each method, resulting in algorithms that combine speed with accuracy. The approach relies on the presence of significant {open_quotes}local{close_quotes} information in the problem at hand. This turns out to be a plausible assumption for many important applications. Example calculations are presented, and the overall strengths and weaknesses of the approach are discussed.« less

Asteroid mass estimation using Markov-Chain Monte Carlo techniques

NASA Astrophysics Data System (ADS)

Siltala, Lauri; Granvik, Mikael

2016-10-01

Estimates for asteroid masses are based on their gravitational perturbations on the orbits of other objects such as Mars, spacecraft, or other asteroids and/or their satellites. In the case of asteroid-asteroid perturbations, this leads to a 13-dimensional inverse problem where the aim is to derive the mass of the perturbing asteroid and six orbital elements for both the perturbing asteroid and the test asteroid using astrometric observations. We have developed and implemented three different mass estimation algorithms utilizing asteroid-asteroid perturbations into the OpenOrb asteroid-orbit-computation software: the very rough 'marching' approximation, in which the asteroid orbits are fixed at a given epoch, reducing the problem to a one-dimensional estimation of the mass, an implementation of the Nelder-Mead simplex method, and most significantly, a Markov-Chain Monte Carlo (MCMC) approach. We will introduce each of these algorithms with particular focus on the MCMC algorithm, and present example results for both synthetic and real data. Our results agree with the published mass estimates, but suggest that the published uncertainties may be misleading as a consequence of using linearized mass-estimation methods. Finally, we discuss remaining challenges with the algorithms as well as future plans, particularly in connection with ESA's Gaia mission.

Robust Hidden Markov Model based intelligent blood vessel detection of fundus images.

PubMed

Hassan, Mehdi; Amin, Muhammad; Murtza, Iqbal; Khan, Asifullah; Chaudhry, Asmatullah

2017-11-01

In this paper, we consider the challenging problem of detecting retinal vessel networks. Precise detection of retinal vessel networks is vital for accurate eye disease diagnosis. Most of the blood vessel tracking techniques may not properly track vessels in presence of vessels' occlusion. Owing to problem in sensor resolution or acquisition of fundus images, it is possible that some part of vessel may occlude. In this scenario, it becomes a challenging task to accurately trace these vital vessels. For this purpose, we have proposed a new robust and intelligent retinal vessel detection technique on Hidden Markov Model. The proposed model is able to successfully track vessels in the presence of occlusion. The effectiveness of the proposed technique is evaluated on publically available standard DRIVE dataset of the fundus images. The experiments show that the proposed technique not only outperforms the other state of the art methodologies of retinal blood vessels segmentation, but it is also capable of accurate occlusion handling in retinal vessel networks. The proposed technique offers better average classification accuracy, sensitivity, specificity, and area under the curve (AUC) of 95.7%, 81.0%, 97.0%, and 90.0% respectively, which shows the usefulness of the proposed technique. Copyright © 2017 Elsevier B.V. All rights reserved.

Decision-Making, Cognitive Distortions and Alcohol Use in Adolescent Problem and Non-problem Gamblers: An Experimental Study.

PubMed

Ciccarelli, Maria; Griffiths, Mark D; Nigro, Giovanna; Cosenza, Marina

2016-12-01

In the psychological literature, many studies have investigated the neuropsychological and behavioral changes that occur developmentally during adolescence. These studies have consistently observed a deficit in the decision-making ability of children and adolescents. This deficit has been ascribed to incomplete brain development. The same deficit has also been observed in adult problem and pathological gamblers. However, to date, no study has examined decision-making in adolescents with and without gambling problems. Furthermore, no study has ever examined associations between problem gambling, decision-making, cognitive distortions and alcohol use in youth. To address these issues, 104 male adolescents participated in this study. They were equally divided in two groups, problem gamblers and non-problem gamblers, based on South Oaks Gambling Screen Revised for Adolescents scores. All participants performed the Iowa gambling task and completed the Gambling Related Cognitions Scale and the alcohol use disorders identification test. Adolescent problem gamblers displayed impaired decision-making, reported high cognitive distortions, and had more problematic alcohol use compared to non-problem gamblers. Strong correlations between problem gambling, alcohol use, and cognitive distortions were observed. Decision-making correlated with interpretative bias. This study demonstrated that adolescent problem gamblers appear to have the same psychological profile as adult problem gamblers and that gambling involvement can negatively impact on decision-making ability that, in adolescence, is still developing. The correlations between interpretative bias and decision-making suggested that the beliefs in the ability to influence gambling outcomes may facilitate decision-making impairment.

Interference effects of categorization on decision making.

PubMed

Wang, Zheng; Busemeyer, Jerome R

2016-05-01

Many decision making tasks in life involve a categorization process, but the effects of categorization on subsequent decision making has rarely been studied. This issue was explored in three experiments (N=721), in which participants were shown a face stimulus on each trial and performed variations of categorization-decision tasks. On C-D trials, they categorized the stimulus and then made an action decision; on X-D trials, they were told the category and then made an action decision; on D-alone trials, they only made an action decision. An interference effect emerged in some of the conditions, such that the probability of an action on the D-alone trials (i.e., when there was no explicit categorization before the decision) differed from the total probability of the same action on the C-D or X-D trials (i.e., when there was explicit categorization before the decision). Interference effects are important because they indicate a violation of the classical law of total probability, which is assumed by many cognitive models. Across all three experiments, a complex pattern of interference effects systematically occurred for different types of stimuli and for different types of categorization-decision tasks. These interference effects present a challenge for traditional cognitive models, such as Markov and signal detection models, but a quantum cognition model, called the belief-action entanglement (BAE) model, predicted that these results could occur. The BAE model employs the quantum principles of superposition and entanglement to explain the psychological mechanisms underlying the puzzling interference effects. The model can be applied to many important and practical categorization-decision situations in life. Copyright © 2016 Elsevier B.V. All rights reserved.

Vacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery

NASA Astrophysics Data System (ADS)

Jain, Madhu; Meena, Rakesh Kumar

2018-03-01

Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the pre-specified workload of failed machines is build up. The first (second) repairman turns on only when the work load of N1 (N2) failed machines is accumulated in the system. The both servers may go for vacation in case when all the machines are in good condition and there are no pending repair jobs for the repairmen. Runge-Kutta method is implemented to solve the set of governing equations used to formulate the Markov model. Various system metrics including the mean queue length, machine availability, throughput, etc., are derived to determine the performance of the machining system. To provide the computational tractability of the present investigation, a numerical illustration is provided. A cost function is also constructed to determine the optimal repair rate of the server by minimizing the expected cost incurred on the system. The hybrid soft computing method is considered to develop the adaptive neuro-fuzzy inference system (ANFIS). The validation of the numerical results obtained by Runge-Kutta approach is also facilitated by computational results generated by ANFIS.

Neyman, Markov processes and survival analysis.

PubMed

Yang, Grace

2013-07-01

J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE PAGES

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan; ...

2017-10-17

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Bayesian inversion of seismic and electromagnetic data for marine gas reservoir characterization using multi-chain Markov chain Monte Carlo sampling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Huiying; Ray, Jaideep; Hou, Zhangshuan

In this paper we developed an efficient Bayesian inversion framework for interpreting marine seismic Amplitude Versus Angle and Controlled-Source Electromagnetic data for marine reservoir characterization. The framework uses a multi-chain Markov-chain Monte Carlo sampler, which is a hybrid of DiffeRential Evolution Adaptive Metropolis and Adaptive Metropolis samplers. The inversion framework is tested by estimating reservoir-fluid saturations and porosity based on marine seismic and Controlled-Source Electromagnetic data. The multi-chain Markov-chain Monte Carlo is scalable in terms of the number of chains, and is useful for computationally demanding Bayesian model calibration in scientific and engineering problems. As a demonstration, the approach ismore » used to efficiently and accurately estimate the porosity and saturations in a representative layered synthetic reservoir. The results indicate that the seismic Amplitude Versus Angle and Controlled-Source Electromagnetic joint inversion provides better estimation of reservoir saturations than the seismic Amplitude Versus Angle only inversion, especially for the parameters in deep layers. The performance of the inversion approach for various levels of noise in observational data was evaluated — reasonable estimates can be obtained with noise levels up to 25%. Sampling efficiency due to the use of multiple chains was also checked and was found to have almost linear scalability.« less

Estimating the Societal Benefits of THA After Accounting for Work Status and Productivity: A Markov Model Approach.

PubMed

Koenig, Lane; Zhang, Qian; Austin, Matthew S; Demiralp, Berna; Fehring, Thomas K; Feng, Chaoling; Mather, Richard C; Nguyen, Jennifer T; Saavoss, Asha; Springer, Bryan D; Yates, Adolph J

2016-12-01

Demand for total hip arthroplasty (THA) is high and expected to continue to grow during the next decade. Although much of this growth includes working-aged patients, cost-effectiveness studies on THA have not fully incorporated the productivity effects from surgery. We asked: (1) What is the expected effect of THA on patients' employment and earnings? (2) How does accounting for these effects influence the cost-effectiveness of THA relative to nonsurgical treatment? Taking a societal perspective, we used a Markov model to assess the overall cost-effectiveness of THA compared with nonsurgical treatment. We estimated direct medical costs using Medicare claims data and indirect costs (employment status and worker earnings) using regression models and nonparametric simulations. For direct costs, we estimated average spending 1 year before and after surgery. Spending estimates included physician and related services, hospital inpatient and outpatient care, and postacute care. For indirect costs, we estimated the relationship between functional status and productivity, using data from the National Health Interview Survey and regression analysis. Using regression coefficients and patient survey data, we ran a nonparametric simulation to estimate productivity (probability of working multiplied by earnings if working minus the value of missed work days) before and after THA. We used the Australian Orthopaedic Association National Joint Replacement Registry to obtain revision rates because it contained osteoarthritis-specific THA revision rates by age and gender, which were unavailable in other registry reports. Other model assumptions were extracted from a previously published cost-effectiveness analysis that included a comprehensive literature review. We incorporated all parameter estimates into Markov models to assess THA effects on quality-adjusted life years and lifetime costs. We conducted threshold and sensitivity analyses on direct costs, indirect costs, and revision rates to assess the robustness of our Markov model results. Compared with nonsurgical treatments, THA increased average annual productivity of patients by USD 9503 (95% CI, USD 1446-USD 17,812). We found that THA increases average lifetime direct costs by USD 30,365, which were offset by USD 63,314 in lifetime savings from increased productivity. With net societal savings of USD 32,948 per patient, total lifetime societal savings were estimated at almost USD 10 billion from more than 300,000 THAs performed in the United States each year. Using a Markov model approach, we show that THA produces societal benefits that can offset the costs of THA. When comparing THA with other nonsurgical treatments, policymakers should consider the long-term benefits associated with increased productivity from surgery. Level III, economic and decision analysis.

A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models.

PubMed

Jones, Edmund; Epstein, David; García-Mochón, Leticia

2017-10-01

For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.

Derivation of Markov processes that violate detailed balance

NASA Astrophysics Data System (ADS)

Lee, Julian

2018-03-01

Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.

Markov chains at the interface of combinatorics, computing, and statistical physics

NASA Astrophysics Data System (ADS)

Streib, Amanda Pascoe

The fields of statistical physics, discrete probability, combinatorics, and theoretical computer science have converged around efforts to understand random structures and algorithms. Recent activity in the interface of these fields has enabled tremendous breakthroughs in each domain and has supplied a new set of techniques for researchers approaching related problems. This thesis makes progress on several problems in this interface whose solutions all build on insights from multiple disciplinary perspectives. First, we consider a dynamic growth process arising in the context of DNA-based self-assembly. The assembly process can be modeled as a simple Markov chain. We prove that the chain is rapidly mixing for large enough bias in regions of Zd. The proof uses a geometric distance function and a variant of path coupling in order to handle distances that can be exponentially large. We also provide the first results in the case of fluctuating bias, where the bias can vary depending on the location of the tile, which arises in the nanotechnology application. Moreover, we use intuition from statistical physics to construct a choice of the biases for which the Markov chain Mmon requires exponential time to converge. Second, we consider a related problem regarding the convergence rate of biased permutations that arises in the context of self-organizing lists. The Markov chain Mnn in this case is a nearest-neighbor chain that allows adjacent transpositions, and the rate of these exchanges is governed by various input parameters. It was conjectured that the chain is always rapidly mixing when the inversion probabilities are positively biased, i.e., we put nearest neighbor pair x < y in order with bias 1/2 ≤ pxy ≤ 1 and out of order with bias 1 - pxy. The Markov chain Mmon was known to have connections to a simplified version of this biased card-shuffling. We provide new connections between Mnn and Mmon by using simple combinatorial bijections, and we prove that Mnn is always rapidly mixing for two general classes of positively biased { pxy}. More significantly, we also prove that the general conjecture is false by exhibiting values for the pxy, with 1/2 ≤ pxy ≤ 1 for all x < y, but for which the transposition chain will require exponential time to converge. Finally, we consider a model of colloids, which are binary mixtures of molecules with one type of molecule suspended in another. It is believed that at low density typical configurations will be well-mixed throughout, while at high density they will separate into clusters. This clustering has proved elusive to verify, since all local sampling algorithms are known to be inefficient at high density, and in fact a new nonlocal algorithm was recently shown to require exponential time in some cases. We characterize the high and low density phases for a general family of discrete interfering binary mixtures by showing that they exhibit a "clustering property" at high density and not at low density. The clustering property states that there will be a region that has very high area, very small perimeter, and high density of one type of molecule. Special cases of interfering binary mixtures include the Ising model at fixed magnetization and independent sets.

Identifying and correcting non-Markov states in peptide conformational dynamics

NASA Astrophysics Data System (ADS)

Nerukh, Dmitry; Jensen, Christian H.; Glen, Robert C.

2010-02-01

Conformational transitions in proteins define their biological activity and can be investigated in detail using the Markov state model. The fundamental assumption on the transitions between the states, their Markov property, is critical in this framework. We test this assumption by analyzing the transitions obtained directly from the dynamics of a molecular dynamics simulated peptide valine-proline-alanine-leucine and states defined phenomenologically using clustering in dihedral space. We find that the transitions are Markovian at the time scale of ≈50 ps and longer. However, at the time scale of 30-40 ps the dynamics loses its Markov property. Our methodology reveals the mechanism that leads to non-Markov behavior. It also provides a way of regrouping the conformations into new states that now possess the required Markov property of their dynamics.

A linear programming approach to max-sum problem: a review.

PubMed

Werner, Tomás

2007-07-01

The max-sum labeling problem, defined as maximizing a sum of binary (i.e., pairwise) functions of discrete variables, is a general NP-hard optimization problem with many applications, such as computing the MAP configuration of a Markov random field. We review a not widely known approach to the problem, developed by Ukrainian researchers Schlesinger et al. in 1976, and show how it contributes to recent results, most importantly, those on the convex combination of trees and tree-reweighted max-product. In particular, we review Schlesinger et al.'s upper bound on the max-sum criterion, its minimization by equivalent transformations, its relation to the constraint satisfaction problem, the fact that this minimization is dual to a linear programming relaxation of the original problem, and the three kinds of consistency necessary for optimality of the upper bound. We revisit problems with Boolean variables and supermodular problems. We describe two algorithms for decreasing the upper bound. We present an example application for structural image analysis.

Sell in May and Go Away? Learning and Risk Taking in Nonmonotonic Decision Problems

ERIC Educational Resources Information Center

Frey, Renato; Rieskamp, Jörg; Hertwig, Ralph

2015-01-01

In nonmonotonic decision problems, the magnitude of outcomes can both increase and decrease over time depending on the state of the decision problem. These increases and decreases may occur repeatedly and result in a variety of possible outcome distributions. In many previously investigated sequential decision problems, in contrast, outcomes (or…

Representing Lumped Markov Chains by Minimal Polynomials over Field GF(q)

NASA Astrophysics Data System (ADS)

Zakharov, V. M.; Shalagin, S. V.; Eminov, B. F.

2018-05-01

A method has been proposed to represent lumped Markov chains by minimal polynomials over a finite field. The accuracy of representing lumped stochastic matrices, the law of lumped Markov chains depends linearly on the minimum degree of polynomials over field GF(q). The method allows constructing the realizations of lumped Markov chains on linear shift registers with a pre-defined “linear complexity”.

A new class of accelerated kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bulatov, V V; Oppelstrup, T; Athenes, M

2011-11-30

Kinetic (aka dynamic) Monte Carlo (KMC) is a powerful method for numerical simulations of time dependent evolution applied in a wide range of contexts including biology, chemistry, physics, nuclear sciences, financial engineering, etc. Generally, in a KMC the time evolution takes place one event at a time, where the sequence of events and the time intervals between them are selected (or sampled) using random numbers. While details of the method implementation vary depending on the model and context, there exist certain common issues that limit KMC applicability in almost all applications. Among such is the notorious 'flicker problem' where themore » same states of the systems are repeatedly visited but otherwise no essential evolution is observed. In its simplest form the flicker problem arises when two states are connected to each other by transitions whose rates far exceed the rates of all other transitions out of the same two states. In such cases, the model will endlessly hop between the two states otherwise producing no meaningful evolution. In most situation of practical interest, the trapping cluster includes more than two states making the flicker somewhat more difficult to detect and to deal with. Several methods have been proposed to overcome or mitigate the flicker problem, exactly [1-3] or approximately [4,5]. Of the exact methods, the one proposed by Novotny [1] is perhaps most relevant to our research. Novotny formulates the problem of escaping from a trapping cluster as a Markov system with absorbing states. Given an initial state inside the cluster, it is in principle possible to solve the Master Equation for the time dependent probabilities to find the walker in a given state (transient or absorbing) of the cluster at any time in the future. Novotny then proceeds to demonstrate implementation of his general method to trapping clusters containing the initial state plus one or two transient states and all of their absorbing states. Similar methods have been subsequently proposed in [refs] but applied in a different context. The most serious deficiency of the earlier methods is that size of the trapping cluster size is fixed and often too small to bring substantial simulation speedup. Furthermore, the overhead associated with solving for the probability distribution on the trapping cluster sometimes makes such simulations less efficient than the standard KMC. Here we report on a general and exact accelerated kinetic Monte Carlo algorithm generally applicable to arbitrary Markov models1. Two different implementations are attempted both based on incremental expansion of trapping sub-set of Markov states: (1) numerical solution of the Master Equation with absorbing states and (2) incremental graph reduction followed by randomization. Of the two implementations, the 2nd one performs better allowing, for the first time, to overcome trapping basins spanning several million Markov states. The new method is used for simulations of anomalous diffusion on a 2D substrate and of the kinetics of diffusive 1st order phase transformations in binary alloys. Depending on temperature and (alloy) super-saturation conditions, speedups of 3 to 7 orders of magnitude are demonstrated, with no compromise of simulation accuracy.« less

Context Analysis of Customer Requests using a Hybrid Adaptive Neuro Fuzzy Inference System and Hidden Markov Models in the Natural Language Call Routing Problem

NASA Astrophysics Data System (ADS)

Rustamov, Samir; Mustafayev, Elshan; Clements, Mark A.

2018-04-01

The context analysis of customer requests in a natural language call routing problem is investigated in the paper. One of the most significant problems in natural language call routing is a comprehension of client request. With the aim of finding a solution to this issue, the Hybrid HMM and ANFIS models become a subject to an examination. Combining different types of models (ANFIS and HMM) can prevent misunderstanding by the system for identification of user intention in dialogue system. Based on these models, the hybrid system may be employed in various language and call routing domains due to nonusage of lexical or syntactic analysis in classification process.

Crossing over...Markov meets Mendel.

PubMed

Mneimneh, Saad

2012-01-01

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition.

Crossing Over…Markov Meets Mendel

PubMed Central

Mneimneh, Saad

2012-01-01

Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage—one of the first efforts towards a computational approach to biology—relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the mathematically more elaborate parts. I kept those as separate sections in the exposition. PMID:22629235

Information dynamics algorithm for detecting communities in networks

NASA Astrophysics Data System (ADS)

Massaro, Emanuele; Bagnoli, Franco; Guazzini, Andrea; Lió, Pietro

2012-11-01

The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network-inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen's Markov Cluster algorithm (MCL) method [4] by considering networks' nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect. The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.

Urban growth simulation from "first principles".

PubMed

Andersson, Claes; Lindgren, Kristian; Rasmussen, Steen; White, Roger

2002-08-01

General and mathematically transparent models of urban growth have so far suffered from a lack in microscopic realism. Physical models that have been used for this purpose, i.e., diffusion-limited aggregation, dielectric breakdown models, and correlated percolation all have microscopic dynamics for which analogies with urban growth appear stretched. Based on a Markov random field formulation we have developed a model that is capable of reproducing a variety of important characteristic urban morphologies and that has realistic microscopic dynamics. The results presented in this paper are particularly important in relation to "urban sprawl," an important aspect of which is aggressively spreading low-density land uses. This type of growth is increasingly causing environmental, social, and economical problems around the world. The microdynamics of our model, or its "first principles," can be mapped to human decisions and motivations and thus potentially also to policies and regulations. We measure statistical properties of macrostates generated by the urban growth mechanism that we propose, and we compare these to empirical measurements as well as to results from other models. To showcase the open-endedness of the model and to thereby relate our work to applied urban planning we have also included a simulated city consisting of a large number of land use classes in which also topographical data have been used.

Automatic spin-chain learning to explore the quantum speed limit

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Ming; Cui, Zi-Wei; Wang, Xin; Yung, Man-Hong

2018-05-01

One of the ambitious goals of artificial intelligence is to build a machine that outperforms human intelligence, even if limited knowledge and data are provided. Reinforcement learning (RL) provides one such possibility to reach this goal. In this work, we consider a specific task from quantum physics, i.e., quantum state transfer in a one-dimensional spin chain. The mission for the machine is to find transfer schemes with the fastest speeds while maintaining high transfer fidelities. The first scenario we consider is when the Hamiltonian is time independent. We update the coupling strength by minimizing a loss function dependent on both the fidelity and the speed. Compared with a scheme proven to be at the quantum speed limit for the perfect state transfer, the scheme provided by RL is faster while maintaining the infidelity below 5 ×10-4 . In the second scenario where a time-dependent external field is introduced, we convert the state transfer process into a Markov decision process that can be understood by the machine. We solve it with the deep Q-learning algorithm. After training, the machine successfully finds transfer schemes with high fidelities and speeds, which are faster than previously known ones. These results show that reinforcement learning can be a powerful tool for quantum control problems.

Optimal maintenance policy incorporating system level and unit level for mechanical systems

NASA Astrophysics Data System (ADS)

Duan, Chaoqun; Deng, Chao; Wang, Bingran

2018-04-01

The study works on a multi-level maintenance policy combining system level and unit level under soft and hard failure modes. The system experiences system-level preventive maintenance (SLPM) when the conditional reliability of entire system exceeds SLPM threshold, and also undergoes a two-level maintenance for each single unit, which is initiated when a single unit exceeds its preventive maintenance (PM) threshold, and the other is performed simultaneously the moment when any unit is going for maintenance. The units experience both periodic inspections and aperiodic inspections provided by failures of hard-type units. To model the practical situations, two types of economic dependence have been taken into account, which are set-up cost dependence and maintenance expertise dependence due to the same technology and tool/equipment can be utilised. The optimisation problem is formulated and solved in a semi-Markov decision process framework. The objective is to find the optimal system-level threshold and unit-level thresholds by minimising the long-run expected average cost per unit time. A formula for the mean residual life is derived for the proposed multi-level maintenance policy. The method is illustrated by a real case study of feed subsystem from a boring machine, and a comparison with other policies demonstrates the effectiveness of our approach.

Intelligent cognitive radio jamming - a game-theoretical approach

NASA Astrophysics Data System (ADS)

Dabcevic, Kresimir; Betancourt, Alejandro; Marcenaro, Lucio; Regazzoni, Carlo S.

2014-12-01

Cognitive radio (CR) promises to be a solution for the spectrum underutilization problems. However, security issues pertaining to cognitive radio technology are still an understudied topic. One of the prevailing such issues are intelligent radio frequency (RF) jamming attacks, where adversaries are able to exploit on-the-fly reconfigurability potentials and learning mechanisms of cognitive radios in order to devise and deploy advanced jamming tactics. In this paper, we use a game-theoretical approach to analyze jamming/anti-jamming behavior between cognitive radio systems. A non-zero-sum game with incomplete information on an opponent's strategy and payoff is modelled as an extension of Markov decision process (MDP). Learning algorithms based on adaptive payoff play and fictitious play are considered. A combination of frequency hopping and power alteration is deployed as an anti-jamming scheme. A real-life software-defined radio (SDR) platform is used in order to perform measurements useful for quantifying the jamming impacts, as well as to infer relevant hardware-related properties. Results of these measurements are then used as parameters for the modelled jamming/anti-jamming game and are compared to the Nash equilibrium of the game. Simulation results indicate, among other, the benefit provided to the jammer when it is employed with the spectrum sensing algorithm in proactive frequency hopping and power alteration schemes.

Optimal Policy of Cross-Layer Design for Channel Access and Transmission Rate Adaptation in Cognitive Radio Networks

NASA Astrophysics Data System (ADS)

He, Hao; Wang, Jun; Zhu, Jiang; Li, Shaoqian

2010-12-01

In this paper, we investigate the cross-layer design of joint channel access and transmission rate adaptation in CR networks with multiple channels for both centralized and decentralized cases. Our target is to maximize the throughput of CR network under transmission power constraint by taking spectrum sensing errors into account. In centralized case, this problem is formulated as a special constrained Markov decision process (CMDP), which can be solved by standard linear programming (LP) method. As the complexity of finding the optimal policy by LP increases exponentially with the size of action space and state space, we further apply action set reduction and state aggregation to reduce the complexity without loss of optimality. Meanwhile, for the convenience of implementation, we also consider the pure policy design and analyze the corresponding characteristics. In decentralized case, where only local information is available and there is no coordination among the CR users, we prove the existence of the constrained Nash equilibrium and obtain the optimal decentralized policy. Finally, in the case that the traffic load parameters of the licensed users are unknown for the CR users, we propose two methods to estimate the parameters for two different cases. Numerical results validate the theoretic analysis.

Segmentized Clear Channel Assessment for IEEE 802.15.4 Networks.

PubMed

Son, Kyou Jung; Hong, Sung Hyeuck; Moon, Seong-Pil; Chang, Tae Gyu; Cho, Hanjin

2016-06-03

This paper proposed segmentized clear channel assessment (CCA) which increases the performance of IEEE 802.15.4 networks by improving carrier sense multiple access with collision avoidance (CSMA/CA). Improving CSMA/CA is important because the low-power consumption feature and throughput performance of IEEE 802.15.4 are greatly affected by CSMA/CA behavior. To improve the performance of CSMA/CA, this paper focused on increasing the chance to transmit a packet by assessing precise channel status. The previous method used in CCA, which is employed by CSMA/CA, assesses the channel by measuring the energy level of the channel. However, this method shows limited channel assessing behavior, which comes from simple threshold dependent channel busy evaluation. The proposed method solves this limited channel decision problem by dividing CCA into two groups. Two groups of CCA compare their energy levels to get precise channel status. To evaluate the performance of the segmentized CCA method, a Markov chain model has been developed. The validation of analytic results is confirmed by comparing them with simulation results. Additionally, simulation results show the proposed method is improving a maximum 8.76% of throughput and decreasing a maximum 3.9% of the average number of CCAs per packet transmission than the IEEE 802.15.4 CCA method.

Segmentized Clear Channel Assessment for IEEE 802.15.4 Networks

PubMed Central

Son, Kyou Jung; Hong, Sung Hyeuck; Moon, Seong-Pil; Chang, Tae Gyu; Cho, Hanjin

2016-01-01

This paper proposed segmentized clear channel assessment (CCA) which increases the performance of IEEE 802.15.4 networks by improving carrier sense multiple access with collision avoidance (CSMA/CA). Improving CSMA/CA is important because the low-power consumption feature and throughput performance of IEEE 802.15.4 are greatly affected by CSMA/CA behavior. To improve the performance of CSMA/CA, this paper focused on increasing the chance to transmit a packet by assessing precise channel status. The previous method used in CCA, which is employed by CSMA/CA, assesses the channel by measuring the energy level of the channel. However, this method shows limited channel assessing behavior, which comes from simple threshold dependent channel busy evaluation. The proposed method solves this limited channel decision problem by dividing CCA into two groups. Two groups of CCA compare their energy levels to get precise channel status. To evaluate the performance of the segmentized CCA method, a Markov chain model has been developed. The validation of analytic results is confirmed by comparing them with simulation results. Additionally, simulation results show the proposed method is improving a maximum 8.76% of throughput and decreasing a maximum 3.9% of the average number of CCAs per packet transmission than the IEEE 802.15.4 CCA method. PMID:27271626

Determining A Purely Symbolic Transfer Function from Symbol Streams: Theory and Algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Griffin, Christopher H

Transfer function modeling is a \\emph{standard technique} in classical Linear Time Invariant and Statistical Process Control. The work of Box and Jenkins was seminal in developing methods for identifying parameters associated with classicalmore » $(r,s,k)$$ transfer functions. Discrete event systems are often \\emph{used} for modeling hybrid control structures and high-level decision problems. \\emph{Examples include} discrete time, discrete strategy repeated games. For these games, a \\emph{discrete transfer function in the form of} an accurate hidden Markov model of input-output relations \\emph{could be used to derive optimal response strategies.} In this paper, we develop an algorithm \\emph{for} creating probabilistic \\textit{Mealy machines} that act as transfer function models for discrete event dynamic systems (DEDS). Our models are defined by three parameters, $$(l_1, l_2, k)$ just as the Box-Jenkins transfer function models. Here $$l_1$$ is the maximal input history lengths to consider, $$l_2$$ is the maximal output history lengths to consider and $k$ is the response lag. Using related results, We show that our Mealy machine transfer functions are optimal in the sense that they maximize the mutual information between the current known state of the DEDS and the next observed input/output pair.« less

Comparative effectiveness research on patients with acute ischemic stroke using Markov decision processes

PubMed Central

2012-01-01

Background Several methodological issues with non-randomized comparative clinical studies have been raised, one of which is whether the methods used can adequately identify uncertainties that evolve dynamically with time in real-world systems. The objective of this study is to compare the effectiveness of different combinations of Traditional Chinese Medicine (TCM) treatments and combinations of TCM and Western medicine interventions in patients with acute ischemic stroke (AIS) by using Markov decision process (MDP) theory. MDP theory appears to be a promising new method for use in comparative effectiveness research. Methods The electronic health records (EHR) of patients with AIS hospitalized at the 2nd Affiliated Hospital of Guangzhou University of Chinese Medicine between May 2005 and July 2008 were collected. Each record was portioned into two "state-action-reward" stages divided by three time points: the first, third, and last day of hospital stay. We used the well-developed optimality technique in MDP theory with the finite horizon criterion to make the dynamic comparison of different treatment combinations. Results A total of 1504 records with a primary diagnosis of AIS were identified. Only states with more than 10 (including 10) patients' information were included, which gave 960 records to be enrolled in the MDP model. Optimal combinations were obtained for 30 types of patient condition. Conclusion MDP theory makes it possible to dynamically compare the effectiveness of different combinations of treatments. However, the optimal interventions obtained by the MDP theory here require further validation in clinical practice. Further exploratory studies with MDP theory in other areas in which complex interventions are common would be worthwhile. PMID:22400712

Making do with less: Must sparse data preclude informed harvest strategies for European waterbirds?

USGS Publications Warehouse

Johnson, Fred A.; Alhainen, Mikko; Fox, Anthony D.; Madsen, Jesper; Guillemain, Matthieu

2018-01-01

The demography of many European waterbirds is not well understood because most countries have conducted little monitoring and assessment, and coordination among countries on waterbird management has little precedent. Yet intergovernmental treaties now mandate the use of sustainable, adaptive harvest strategies, whose development is challenged by a paucity of demographic information. In this study, we explore how a combination of allometric relationships, fragmentary monitoring and research information, and expert judgment can be used to estimate the parameters of a theta-logistic population model, which in turn can be used in a Markov decision process to derive optimal harvesting strategies. We show how to account for considerable parametric uncertainty, as well as for different management objectives. We illustrate our methodology with a poorly understood population of taiga bean geese (Anser fabalis fabalis), which is a popular game bird in Fennoscandia. Our results for taiga bean geese suggest that they may have demographic rates similar to other, well-studied species of geese, and our model-based predictions of population size are consistent with the limited monitoring information available. Importantly, we found that by using a Markov decision process, a simple scalar population model may be sufficient to guide harvest management of this species, even if its demography is age-structured. Finally, we demonstrated how two different management objectives can lead to very different optimal harvesting strategies, and how conflicting objectives may be traded off with each other. This approach will have broad application for European waterbirds by providing preliminary estimates of key demographic parameters, by providing insights into the monitoring and research activities needed to corroborate those estimates, and by producing harvest management strategies that are optimal with respect to the managers’ objectives, options, and available demographic information.

An empirical comparison of Markov cohort modeling and discrete event simulation in a capacity-constrained health care setting.

PubMed

Standfield, L B; Comans, T A; Scuffham, P A

2017-01-01

To empirically compare Markov cohort modeling (MM) and discrete event simulation (DES) with and without dynamic queuing (DQ) for cost-effectiveness (CE) analysis of a novel method of health services delivery where capacity constraints predominate. A common data-set comparing usual orthopedic care (UC) to an orthopedic physiotherapy screening clinic and multidisciplinary treatment service (OPSC) was used to develop a MM and a DES without (DES-no-DQ) and with DQ (DES-DQ). Model results were then compared in detail. The MM predicted an incremental CE ratio (ICER) of $495 per additional quality-adjusted life-year (QALY) for OPSC over UC. The DES-no-DQ showed OPSC dominating UC; the DES-DQ generated an ICER of $2342 per QALY. The MM and DES-no-DQ ICER estimates differed due to the MM having implicit delays built into its structure as a result of having fixed cycle lengths, which are not a feature of DES. The non-DQ models assume that queues are at a steady state. Conversely, queues in the DES-DQ develop flexibly with supply and demand for resources, in this case, leading to different estimates of resource use and CE. The choice of MM or DES (with or without DQ) would not alter the reimbursement of OPSC as it was highly cost-effective compared to UC in all analyses. However, the modeling method may influence decisions where ICERs are closer to the CE acceptability threshold, or where capacity constraints and DQ are important features of the system. In these cases, DES-DQ would be the preferred modeling technique to avoid incorrect resource allocation decisions.

ASSIST - THE ABSTRACT SEMI-MARKOV SPECIFICATION INTERFACE TO THE SURE TOOL PROGRAM (SUN VERSION)

NASA Technical Reports Server (NTRS)

Johnson, S. C.

1994-01-01

ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, is an interface that will enable reliability engineers to accurately design large semi-Markov models. The user describes the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. The abstract language allows efficient description of large, complex systems; a one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. Instead of listing the individual states of the Markov model, reliability engineers can specify the rules governing the behavior of a system, and these are used to automatically generate the model. ASSIST reads an input file describing the failure behavior of a system in an abstract language and generates a Markov model in the format needed for input to SURE, the semi-Markov Unreliability Range Evaluator program, and PAWS/STEM, the Pade Approximation with Scaling program and Scaled Taylor Exponential Matrix. A Markov model consists of a number of system states and transitions between them. Each state in the model represents a possible state of the system in terms of which components have failed, which ones have been removed, etc. Within ASSIST, each state is defined by a state vector, where each element of the vector takes on an integer value within a defined range. An element can represent any meaningful characteristic, such as the number of working components of one type in the system, or the number of faulty components of another type in use. Statements representing transitions between states in the model have three parts: a condition expression, a destination expression, and a rate expression. The first expression is a Boolean expression describing the state space variable values of states for which the transition is valid. The second expression defines the destination state for the transition in terms of state space variable values. The third expression defines the distribution of elapsed time for the transition. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. ASSIST was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The VMS version (LAR14193) is written in C-language and can be compiled with the VAX C compiler. The standard distribution medium for the VMS version of ASSIST is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The Sun version (LAR14923) is written in ANSI C-language. An ANSI compliant C compiler is required in order to compile this package. The standard distribution medium for the Sun version of ASSIST is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the documentation in PostScript, TeX, and DVI formats are provided on the distribution medium. (The VMS distribution lacks the .DVI format files, however.) ASSIST was developed in 1986 and last updated in 1992. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

ASSIST - THE ABSTRACT SEMI-MARKOV SPECIFICATION INTERFACE TO THE SURE TOOL PROGRAM (VAX VMS VERSION)

NASA Technical Reports Server (NTRS)

Johnson, S. C.

1994-01-01

ASSIST, the Abstract Semi-Markov Specification Interface to the SURE Tool program, is an interface that will enable reliability engineers to accurately design large semi-Markov models. The user describes the failure behavior of a fault-tolerant computer system in an abstract, high-level language. The ASSIST program then automatically generates a corresponding semi-Markov model. The abstract language allows efficient description of large, complex systems; a one-page ASSIST-language description may result in a semi-Markov model with thousands of states and transitions. The ASSIST program also includes model-reduction techniques to facilitate efficient modeling of large systems. Instead of listing the individual states of the Markov model, reliability engineers can specify the rules governing the behavior of a system, and these are used to automatically generate the model. ASSIST reads an input file describing the failure behavior of a system in an abstract language and generates a Markov model in the format needed for input to SURE, the semi-Markov Unreliability Range Evaluator program, and PAWS/STEM, the Pade Approximation with Scaling program and Scaled Taylor Exponential Matrix. A Markov model consists of a number of system states and transitions between them. Each state in the model represents a possible state of the system in terms of which components have failed, which ones have been removed, etc. Within ASSIST, each state is defined by a state vector, where each element of the vector takes on an integer value within a defined range. An element can represent any meaningful characteristic, such as the number of working components of one type in the system, or the number of faulty components of another type in use. Statements representing transitions between states in the model have three parts: a condition expression, a destination expression, and a rate expression. The first expression is a Boolean expression describing the state space variable values of states for which the transition is valid. The second expression defines the destination state for the transition in terms of state space variable values. The third expression defines the distribution of elapsed time for the transition. The mathematical approach chosen to solve a reliability problem may vary with the size and nature of the problem. Although different solution techniques are utilized on different programs, it is possible to have a common input language. The Systems Validation Methods group at NASA Langley Research Center has created a set of programs that form the basis for a reliability analysis workstation. The set of programs are: SURE reliability analysis program (COSMIC program LAR-13789, LAR-14921); the ASSIST specification interface program (LAR-14193, LAR-14923), PAWS/STEM reliability analysis programs (LAR-14165, LAR-14920); and the FTC fault tree tool (LAR-14586, LAR-14922). FTC is used to calculate the top-event probability for a fault tree. PAWS/STEM and SURE are programs which interpret the same SURE language, but utilize different solution methods. ASSIST is a preprocessor that generates SURE language from a more abstract definition. SURE, ASSIST, and PAWS/STEM are also offered as a bundle. Please see the abstract for COS-10039/COS-10041, SARA - SURE/ASSIST Reliability Analysis Workstation, for pricing details. ASSIST was originally developed for DEC VAX series computers running VMS and was later ported for use on Sun computers running SunOS. The VMS version (LAR14193) is written in C-language and can be compiled with the VAX C compiler. The standard distribution medium for the VMS version of ASSIST is a 9-track 1600 BPI magnetic tape in VMSINSTAL format. It is also available on a TK50 tape cartridge in VMSINSTAL format. Executables are included. The Sun version (LAR14923) is written in ANSI C-language. An ANSI compliant C compiler is required in order to compile this package. The standard distribution medium for the Sun version of ASSIST is a .25 inch streaming magnetic tape cartridge in UNIX tar format. Both Sun3 and Sun4 executables are included. Electronic copies of the documentation in PostScript, TeX, and DVI formats are provided on the distribution medium. (The VMS distribution lacks the .DVI format files, however.) ASSIST was developed in 1986 and last updated in 1992. DEC, VAX, VMS, and TK50 are trademarks of Digital Equipment Corporation. SunOS, Sun3, and Sun4 are trademarks of Sun Microsystems, Inc. UNIX is a registered trademark of AT&T Bell Laboratories.

Bayesian selection of Markov models for symbol sequences: application to microsaccadic eye movements.

PubMed

Bettenbühl, Mario; Rusconi, Marco; Engbert, Ralf; Holschneider, Matthias

2012-01-01

Complex biological dynamics often generate sequences of discrete events which can be described as a Markov process. The order of the underlying Markovian stochastic process is fundamental for characterizing statistical dependencies within sequences. As an example for this class of biological systems, we investigate the Markov order of sequences of microsaccadic eye movements from human observers. We calculate the integrated likelihood of a given sequence for various orders of the Markov process and use this in a Bayesian framework for statistical inference on the Markov order. Our analysis shows that data from most participants are best explained by a first-order Markov process. This is compatible with recent findings of a statistical coupling of subsequent microsaccade orientations. Our method might prove to be useful for a broad class of biological systems.

Combinatorial Optimization Algorithms for Dynamic Multiple Fault Diagnosis in Automotive and Aerospace Applications

NASA Astrophysics Data System (ADS)

Kodali, Anuradha

In this thesis, we develop dynamic multiple fault diagnosis (DMFD) algorithms to diagnose faults that are sporadic and coupled. Firstly, we formulate a coupled factorial hidden Markov model-based (CFHMM) framework to diagnose dependent faults occurring over time (dynamic case). Here, we implement a mixed memory Markov coupling model to determine the most likely sequence of (dependent) fault states, the one that best explains the observed test outcomes over time. An iterative Gauss-Seidel coordinate ascent optimization method is proposed for solving the problem. A soft Viterbi algorithm is also implemented within the framework for decoding dependent fault states over time. We demonstrate the algorithm on simulated and real-world systems with coupled faults; the results show that this approach improves the correct isolation rate as compared to the formulation where independent fault states are assumed. Secondly, we formulate a generalization of set-covering, termed dynamic set-covering (DSC), which involves a series of coupled set-covering problems over time. The objective of the DSC problem is to infer the most probable time sequence of a parsimonious set of failure sources that explains the observed test outcomes over time. The DSC problem is NP-hard and intractable due to the fault-test dependency matrix that couples the failed tests and faults via the constraint matrix, and the temporal dependence of failure sources over time. Here, the DSC problem is motivated from the viewpoint of a dynamic multiple fault diagnosis problem, but it has wide applications in operations research, for e.g., facility location problem. Thus, we also formulated the DSC problem in the context of a dynamically evolving facility location problem. Here, a facility can be opened, closed, or can be temporarily unavailable at any time for a given requirement of demand points. These activities are associated with costs or penalties, viz., phase-in or phase-out for the opening or closing of a facility, respectively. The set-covering matrix encapsulates the relationship among the rows (tests or demand points) and columns (faults or locations) of the system at each time. By relaxing the coupling constraints using Lagrange multipliers, the DSC problem can be decoupled into independent subproblems, one for each column. Each subproblem is solved using the Viterbi decoding algorithm, and a primal feasible solution is constructed by modifying the Viterbi solutions via a heuristic. The proposed Viterbi-Lagrangian relaxation algorithm (VLRA) provides a measure of suboptimality via an approximate duality gap. As a major practical extension of the above problem, we also consider the problem of diagnosing faults with delayed test outcomes, termed delay-dynamic set-covering (DDSC), and experiment with real-world problems that exhibit masking faults. Also, we present simulation results on OR-library datasets (set-covering formulations are predominantly validated on these matrices in the literature), posed as facility location problems. Finally, we implement these algorithms to solve problems in aerospace and automotive applications. Firstly, we address the diagnostic ambiguity problem in aerospace and automotive applications by developing a dynamic fusion framework that includes dynamic multiple fault diagnosis algorithms. This improves the correct fault isolation rate, while minimizing the false alarm rates, by considering multiple faults instead of the traditional data-driven techniques based on single fault (class)-single epoch (static) assumption. The dynamic fusion problem is formulated as a maximum a posteriori decision problem of inferring the fault sequence based on uncertain outcomes of multiple binary classifiers over time. The fusion process involves three steps: the first step transforms the multi-class problem into dichotomies using error correcting output codes (ECOC), thereby solving the concomitant binary classification problems; the second step fuses the outcomes of multiple binary classifiers over time using a sliding window or block dynamic fusion method that exploits temporal data correlations over time. We solve this NP-hard optimization problem via a Lagrangian relaxation (variational) technique. The third step optimizes the classifier parameters, viz., probabilities of detection and false alarm, using a genetic algorithm. The proposed algorithm is demonstrated by computing the diagnostic performance metrics on a twin-spool commercial jet engine, an automotive engine, and UCI datasets (problems with high classification error are specifically chosen for experimentation). We show that the primal-dual optimization framework performed consistently better than any traditional fusion technique, even when it is forced to give a single fault decision across a range of classification problems. Secondly, we implement the inference algorithms to diagnose faults in vehicle systems that are controlled by a network of electronic control units (ECUs). The faults, originating from various interactions and especially between hardware and software, are particularly challenging to address. Our basic strategy is to divide the fault universe of such cyber-physical systems in a hierarchical manner, and monitor the critical variables/signals that have impact at different levels of interactions. The proposed diagnostic strategy is validated on an electrical power generation and storage system (EPGS) controlled by two ECUs in an environment with CANoe/MATLAB co-simulation. Eleven faults are injected with the failures originating in actuator hardware, sensor, controller hardware and software components. Diagnostic matrix is established to represent the relationship between the faults and the test outcomes (also known as fault signatures) via simulations. The results show that the proposed diagnostic strategy is effective in addressing the interaction-caused faults.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models.

PubMed

Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I

2018-01-01

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Modeling of dialogue regimes of distance robot control

NASA Astrophysics Data System (ADS)

Larkin, E. V.; Privalov, A. N.

2017-02-01

Process of distance control of mobile robots is investigated. Petri-Markov net for modeling of dialogue regime is worked out. It is shown, that sequence of operations of next subjects: a human operator, a dialogue computer and an onboard computer may be simulated with use the theory of semi-Markov processes. From the semi-Markov process of the general form Markov process was obtained, which includes only states of transaction generation. It is shown, that a real transaction flow is the result of «concurrency» in states of Markov process. Iteration procedure for evaluation of transaction flow parameters, which takes into account effect of «concurrency», is proposed.

A decision model to estimate a risk threshold for venous thromboembolism prophylaxis in hospitalized medical patients.

PubMed

Le, P; Martinez, K A; Pappas, M A; Rothberg, M B

2017-06-01

Essentials Low risk patients don't require venous thromboembolism (VTE) prophylaxis; low risk is unquantified. We used a Markov model to estimate the risk threshold for VTE prophylaxis in medical inpatients. Prophylaxis was cost-effective for an average medical patient with a VTE risk of ≥ 1.0%. VTE prophylaxis can be personalized based on patient risk and age/life expectancy. Background Venous thromboembolism (VTE) is a common preventable condition in medical inpatients. Thromboprophylaxis is recommended for inpatients who are not at low risk of VTE, but no specific risk threshold for prophylaxis has been defined. Objective To determine a threshold for prophylaxis based on risk of VTE. Patients/Methods We constructed a decision model with a decision-tree following patients for 3 months after hospitalization, and a lifetime Markov model with 3-month cycles. The model tracked symptomatic deep vein thromboses and pulmonary emboli, bleeding events and heparin-induced thrombocytopenia. Long-term complications included recurrent VTE, post-thrombotic syndrome and pulmonary hypertension. For the base case, we considered medical inpatients aged 66 years, having a life expectancy of 13.5 years, VTE risk of 1.4% and bleeding risk of 2.7%. Patients received enoxaparin 40 mg day -1 for prophylaxis. Results Assuming a willingness-to-pay (WTP) threshold of $100 000/ quality-adjusted life year (QALY), prophylaxis was indicated for an average medical inpatient with a VTE risk of ≥ 1.0% up to 3 months after hospitalization. For the average patient, prophylaxis was not indicated when the bleeding risk was > 8.1%, the patient's age was > 73.4 years or the cost of enoxaparin exceeded $60/dose. If VTE risk was < 0.26% or bleeding risk was > 19%, the risks of prophylaxis outweighed benefits. The prophylaxis threshold was relatively insensitive to low-molecular-weight heparin cost and bleeding risk, but very sensitive to patient age and life expectancy. Conclusions The decision to offer prophylaxis should be personalized based on patient VTE risk, age and life expectancy. At a WTP of $100 000/QALY, prophylaxis is not warranted for most patients with a 3-month VTE risk below 1.0%. © 2017 International Society on Thrombosis and Haemostasis.

A Fast Variational Approach for Learning Markov Random Field Language Models

DTIC Science & Technology

2015-01-01

the same distribution as n- gram models, but utilize a non-linear neural network pa- rameterization. NLMs have been shown to produce com- petitive...to either resort to local optimiza- tion methods, such as those used in neural lan- guage models, or work with heavily constrained distributions. In...embeddings learned through neural language models. Central to the language modelling problem is the challenge Proceedings of the 32nd International

The Domain-Specific Software Architecture Program

DTIC Science & Technology

1992-06-01

Kang, K.C; Cohen, S.C: Jess, J.A; Novak, W.E; Peterson, A.S. Feature- Oriented Domain Analysis ( FODA ) Feasibility Study. (CMU/SEI-90-TR-21, ADA235785...perspective of a con- trols engineer solving a problem using an iterative process of simulation and analysis . The CMU/SEI-92-SR-9 1 I ~math AnalysislP...for schedulability analysis and Markov processes for the determination of reliability. Software architectures are derived from these formal models. ORA

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains

PubMed Central

Meyer, Denny; Forbes, Don; Clarke, Stephen R.

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key Points A comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition. The Markov assumption appears to be valid. However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play. Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes. PMID:24357946

Probability distributions for Markov chain based quantum walks

NASA Astrophysics Data System (ADS)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.

Statistical Analysis of Notational AFL Data Using Continuous Time Markov Chains.

PubMed

Meyer, Denny; Forbes, Don; Clarke, Stephen R

2006-01-01

Animal biologists commonly use continuous time Markov chain models to describe patterns of animal behaviour. In this paper we consider the use of these models for describing AFL football. In particular we test the assumptions for continuous time Markov chain models (CTMCs), with time, distance and speed values associated with each transition. Using a simple event categorisation it is found that a semi-Markov chain model is appropriate for this data. This validates the use of Markov Chains for future studies in which the outcomes of AFL matches are simulated. Key PointsA comparison of four AFL matches suggests similarity in terms of transition probabilities for events and the mean times, distances and speeds associated with each transition.The Markov assumption appears to be valid.However, the speed, time and distance distributions associated with each transition are not exponential suggesting that semi-Markov model can be used to model and simulate play.Team identified events and directions associated with transitions are required to develop the model into a tool for the prediction of match outcomes.

Development of a decision support tool for seasonal water supply management incorporating system uncertainties and operational constraints

NASA Astrophysics Data System (ADS)

Wang, H.; Asefa, T.

2017-12-01

A real-time decision support tool (DST) for water supply system would consider system uncertainties, e.g., uncertain streamflow and demand, as well as operational constraints and infrastructure outage (e.g., pump station shutdown, an offline reservoir due to maintenance). Such DST is often used by water managers for resource allocation and delivery for customers. Although most seasonal DST used by water managers recognize those system uncertainties and operational constraints, most use only historical information or assume deterministic outlook of water supply systems. This study presents a seasonal DST that incorporates rainfall/streamflow uncertainties, seasonal demand outlook and system operational constraints. Large scale climate-information is captured through a rainfall simulator driven by a Bayesian non-homogeneous Markov Chain Monte Carlo model that allows non-stationary transition probabilities contingent on Nino 3.4 index. An ad-hoc seasonal demand forecasting model considers weather conditions explicitly and socio-economic factors implicitly. Latin Hypercube sampling is employed to effectively sample probability density functions of flow and demand. Seasonal system operation is modelled as a mixed-integer optimization problem that aims at minimizing operational costs. It embeds the flexibility of modifying operational rules at different components, e.g., surface water treatment plants, desalination facilities, and groundwater pumping stations. The proposed framework is illustrated at a wholesale water supplier in Southeastern United States, Tampa Bay Water. The use of the tool is demonstrated in proving operational guidance in a typical drawdown and refill cycle of a regional reservoir. The DST provided: 1) probabilistic outlook of reservoir storage and chance of a successful refill by the end of rainy season; 2) operational expectations for large infrastructures (e.g., high service pumps and booster stations) throughout the season. Other potential use of such DST is also discussed.

Robust Decision Making: The Cognitive and Computational Modeling of Team Problem Solving for Decision Making under Complex and Dynamic Conditions

DTIC Science & Technology

2015-07-14

AFRL-OSR-VA-TR-2015-0202 Robust Decision Making: The Cognitive and Computational Modeling of Team Problem Solving for Decision Making under Complex...Computational Modeling of Team Problem Solving for Decision Making Under Complex and Dynamic Conditions 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-12-1...functioning as they solve complex problems, and propose the means to improve the performance of teams, under changing or adversarial conditions. By

Fisher information and asymptotic normality in system identification for quantum Markov chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guta, Madalin

2011-06-15

This paper deals with the problem of estimating the coupling constant {theta} of a mixing quantum Markov chain. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. In particular, we obtain a simple estimator of {theta} whose classical Fisher information can be optimized over different choices of measured observables. We then show that the quantum state of the output together with the system is itself asymptotically Gaussian and compute its quantum Fisher information, which sets an absolutemore » bound to the estimation error. The classical and quantum Fisher information are compared in a simple example. In the vicinity of {theta}=0 we find that the quantum Fisher information has a quadratic rather than linear scaling in output size, and asymptotically the Fisher information is localized in the system, while the output is independent of the parameter.« less

Brain tumor segmentation in 3D MRIs using an improved Markov random field model

NASA Astrophysics Data System (ADS)

Yousefi, Sahar; Azmi, Reza; Zahedi, Morteza

2011-10-01

Markov Random Field (MRF) models have been recently suggested for MRI brain segmentation by a large number of researchers. By employing Markovianity, which represents the local property, MRF models are able to solve a global optimization problem locally. But they still have a heavy computation burden, especially when they use stochastic relaxation schemes such as Simulated Annealing (SA). In this paper, a new 3D-MRF model is put forward to raise the speed of the convergence. Although, search procedure of SA is fairly localized and prevents from exploring the same diversity of solutions, it suffers from several limitations. In comparison, Genetic Algorithm (GA) has a good capability of global researching but it is weak in hill climbing. Our proposed algorithm combines SA and an improved GA (IGA) to optimize the solution which speeds up the computation time. What is more, this proposed algorithm outperforms the traditional 2D-MRF in quality of the solution.

Coherent-Anomaly Method in Self-Avoiding Walk Problems

NASA Astrophysics Data System (ADS)

Hu, Xiao; Suzuki, Masuo

Self-avoiding walk (SAW), being a nonequilibrium cooperative phenomenon, is investigated with a finite-order-restricted-walk (finite-ORW or FORW) coherent-anomaly method (CAM). The coefficient β1r in the asymptotic form Cnr ≃ βlrλn1r for the total number Cnr of r-ORW's with respect to the step number n is investigated for the first time. An asymptotic form for SAW's is thus obtained from the series of FORW approximants, Cnr ≃ brgμ(1 + a/r)n, as the envelope curve Cn ≃ b(ae/g)gμnng. Numerical results are given by Cn ≃ 1.424n0.27884.1507n and Cn ≃ 1.179n0.158710.005n for the plane triangular lattice and f.c.c. lattice, respectively. A good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite-step SAW's implies that the essential nature of SAW (non-Markov process) can be understood from FORW (Markov process) in the CAM framework.

Potential-based dynamical reweighting for Markov state models of protein dynamics.

PubMed

Weber, Jeffrey K; Pande, Vijay S

2015-06-09

As simulators attempt to replicate the dynamics of large cellular components in silico, problems related to sampling slow, glassy degrees of freedom in molecular systems will be amplified manyfold. It is tempting to augment simulation techniques with external biases to overcome such barriers with ease; biased simulations, however, offer little utility unless equilibrium properties of interest (both kinetic and thermodynamic) can be recovered from the data generated. In this Article, we present a general scheme that harnesses the power of Markov state models (MSMs) to extract equilibrium kinetic properties from molecular dynamics trajectories collected on biased potential energy surfaces. We first validate our reweighting protocol on a simple two-well potential, and we proceed to test our method on potential-biased simulations of the Trp-cage miniprotein. In both cases, we find that equilibrium populations, time scales, and dynamical processes are reliably reproduced as compared to gold standard, unbiased data sets. We go on to discuss the limitations of our dynamical reweighting approach, and we suggest auspicious target systems for further application.

CosmoSIS: A system for MC parameter estimation

DOE PAGES

Bridle, S.; Dodelson, S.; Jennings, E.; ...

2015-12-23

CosmoSIS is a modular system for cosmological parameter estimation, based on Markov Chain Monte Carlo and related techniques. It provides a series of samplers, which drive the exploration of the parameter space, and a series of modules, which calculate the likelihood of the observed data for a given physical model, determined by the location of a sample in the parameter space. While CosmoSIS ships with a set of modules that calculate quantities of interest to cosmologists, there is nothing about the framework itself, nor in the Markov Chain Monte Carlo technique, that is specific to cosmology. Thus CosmoSIS could bemore » used for parameter estimation problems in other fields, including HEP. This paper describes the features of CosmoSIS and show an example of its use outside of cosmology. Furthermore, it also discusses how collaborative development strategies differ between two different communities: that of HEP physicists, accustomed to working in large collaborations, and that of cosmologists, who have traditionally not worked in large groups.« less

Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains.

PubMed

Allefeld, Carsten; Bialonski, Stephan

2007-12-01

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.

Model reduction by trimming for a class of semi-Markov reliability models and the corresponding error bound

NASA Technical Reports Server (NTRS)

White, Allan L.; Palumbo, Daniel L.

1991-01-01

Semi-Markov processes have proved to be an effective and convenient tool to construct models of systems that achieve reliability by redundancy and reconfiguration. These models are able to depict complex system architectures and to capture the dynamics of fault arrival and system recovery. A disadvantage of this approach is that the models can be extremely large, which poses both a model and a computational problem. Techniques are needed to reduce the model size. Because these systems are used in critical applications where failure can be expensive, there must be an analytically derived bound for the error produced by the model reduction technique. A model reduction technique called trimming is presented that can be applied to a popular class of systems. Automatic model generation programs were written to help the reliability analyst produce models of complex systems. This method, trimming, is easy to implement and the error bound easy to compute. Hence, the method lends itself to inclusion in an automatic model generator.