State Switching Model Research Articles

Host Profit Maximization: Leveraging Performance Incentives and User Flexibility

The social network host has knowledge of the network structure and user characteristics and can earn a profit by providing merchants with viral marketing campaigns. We investigate the problem ofhost profit maximizationby leveraging performance incentives and user flexibility. To incentivize the host's performance, we propose setting a desired influence threshold that would allow the host to receive full payment, with the possibility of a small bonus for exceeding the threshold. Unlike existing works that assume a user's choice is frozen once they are activated, we introduce the Dynamic State Switching model to capture"comparative shopping"behavior from an economic perspective, in which users have the flexibilities to change their minds about which product to adopt based on the accumulated influence and propaganda strength of each product. In addition, the incentivized cost of a user serving as an influence source is treated as a negative part of the host's profit.Thehost profit maximizationproblem is NP-hard, submodular, and non-monotone. To address this challenge, we propose an efficient greedy algorithm and devise a scalable version with an approximation guarantee to select the seed sets. As a side contribution, we develop two seed allocation algorithms to balance the distribution of adoptions among merchants with small profit sacrifice. Through extensive experiments on four real-world social networks, we demonstrate that our methods are effective and scalable.

Ambient light at night causes desynchronization of rhythms in the sleep–wake switching model

The purpose of this study is to analyze the influence of the shape of the daily illumination profile on the synchronization of rhythms in the sleep–wake state switching model. Normally, the alternation of sleep and wakefulness of a person is synchronized with his circadian rhythm and with the 24-hour rhythm of illumination. There is, however, a lot of experimental evidence of a violation of this synchronism, both in the form of phase failures (for example, during air travel) and in the form of long-term mismatch of rhythms (for example, during shift work in production). Mathematical models of the process of switching between sleep and wakefulness also demonstrate the desynchronization of rhythms and are successfully used to optimize work schedules. At the same time, the influence of a number of factors on this process has not been sufficiently studied, including the nature of changes in illumination during the day. Methods. An analysis of the six-dimensional model under study shows that, in terms of nonlinear dynamics, the problem is reduced to finding and interpreting resonance regions on a three-dimensional torus. For the specific purposes of our work, it turned out to be convenient to estimate the ratio of three periods (24 hours, the circadian period, and the current duration of the sleep–wake cycle) by numerically integrating the model equations on a grid of parameter values using parallel computing technology. The main result of our work is that the presence of round-the-clock low-intensity illumination (that is, the addition of a zero-frequency signal to the daily light cycle) causes the circadian rhythm to desynchronize with respect to the daily one in a significant range of parameters. We have proposed an explanation of this effect based on the structure of the mathematical model. Conclusion. Our results raise at least two serious questions, the first of which is related to the physiological interpretation of one of the main variables of the model, sleep homeostasis, and the second is to refine the assumptions that are used in the model description of the photoreceptor response. In any case, there are interesting prospects for further research.

Recording fine-scale movement of ground beetles by two methods: Potentials and methodological pitfalls.

Movement trajectories are usually recorded as a sequence of discrete movement events described by two parameters: step length (distance) and turning angle (bearing). One of the most widespread methods to record the geocoordinates of each step is by a GPS device. Such devices have limited suitability for recording fine movements of species with low dispersal ability including flightless carabid beetles at small spatio‐temporal scales. As an alternative, the distance‐bearing approach can avoid the measurement error of GPS units since it uses directly measured distances and compass azimuths. As no quantification of measurement error between distance‐bearing and GPS approaches exists so far, we generated artificial fine‐scale trajectories and in addition radio‐tracked living carabids in a temperate forest and recorded each movement step by both methods. Trajectories obtained from distance‐bearing were compared to those obtained by a GPS device in terms of movement parameters. Consequently, both types of trajectories were segmented by state‐switching modeling into two distinct movement stages typical for carabids: random walk and directed movement. We found that the measurement error of GPS compared to distance‐bearing was 1.878 m (SEM = 0.181 m) for distances and 31.330° (SEM = 2.066°) for bearings. Moreover, these errors increased under dense forest canopy and rainy weather. Distance error did not change with increasing distance recorded by distance‐bearing but bearings were significantly more sensitive to error at short distances. State‐switching models showed only slight, not significant, differences in movement states between the two methods in favor of the random walk in the distance‐bearing approach. However, the shape of the GPS‐measured trajectories considerably differed from those recorded by distance‐bearing caused especially by bearing error at short distances. Our study showed that distance‐bearing could be more appropriate for recording movement steps not only of ground‐dwelling beetles but also other small animals at fine spatio‐temporal scales.

Toward Efficient Bayesian Approaches to Inference in Hierarchical Hidden Markov Models for Inferring Animal Behavior

The study of animal behavioral states inferred through hidden Markov models and similar state switching models has seen a significant increase in popularity in recent years. The ability to account for varying levels of behavioral scale has become possible through hierarchical hidden Markov models, but additional levels lead to higher complexity and increased correlation between model components. Maximum likelihood approaches to inference using the EM algorithm and direct optimization of likelihoods are more frequently used, with Bayesian approaches being less favored due to computational demands. Given these demands, it is vital that efficient estimation algorithms are developed when Bayesian methods are preferred. We study the use of various approaches to improve convergence times and mixing in Markov chain Monte Carlo methods applied to hierarchical hidden Markov models, including parallel tempering as an inference facilitation mechanism. The method shows promise for analysing complex stochastic models with high levels of correlation between components, but our results show that it requires careful tuning in order to maximize that potential.

A primer on coupled state-switching models for multiple interacting time series

State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend these approaches to address the case of multiple observation sequences whose underlying state variables interact. In this article, we provide an overview of the modelling techniques related to coupling in state-switching models, thereby forming a rich and flexible statistical framework particularly useful for modelling correlated time series. Simulation experiments demonstrate the relevance of being able to account for an asynchronous evolution as well as interactions between the underlying latent processes. The models are further illustrated using two case studies related to (a) interactions between a dolphin mother and her calf as inferred from movement data and (b) electronic health record data collected on 696 patients within an intensive care unit.

Fear Propagation and Return Dynamics

In this paper, we show that fear can propagate across international financial markets. Investors become more concerned about the local market tail risks when they see that the U.S. economy steps into contractions. Consistent with the rare disaster theory, risk-averse investors would require higher risk premiums, corresponding to lower stock market prices. By considering precious metals, in particular the log gold-to-platinum ratio justified by Huang and Kilic (2019), as the global market fear proxy, we show that the fear propagation shapes the return dynamics at the international level. By applying the state-switching model recently proposed by Jacobsen, Marshall, and Visaltanachoti (2019), we find the return predictability stems from the periods when the U.S. economy is in contractions but not in expansions. The evidence is robust across different business cycle definitions, and the pattern holds at multiple-horizons from one week to one year. Further evidence shows that the predictive power of this ratio during bad states is not due to the U.S. stock market spillover effect, and not subsumed by macroeconomic fundamentals and financial variables. Overall, the out-of-sample performance suggests the important implications of the proxy for international return predictability during the bad economic states.

Tonic exploration governs both flexibility and lapses.

In many cognitive tasks, lapses (spontaneous errors) are tacitly dismissed as the result of nuisance processes like sensorimotor noise, fatigue, or disengagement. However, some lapses could also be caused by exploratory noise: randomness in behavior that facilitates learning in changing environments. If so, then strategic processes would need only up-regulate (rather than generate) exploration to adapt to a changing environment. This view predicts that more frequent lapses should be associated with greater flexibility because these behaviors share a common cause. Here, we report that when rhesus macaques performed a set-shifting task, lapse rates were negatively correlated with perseverative error frequency across sessions, consistent with a common basis in exploration. The results could not be explained by local failures to learn. Furthermore, chronic exposure to cocaine, which is known to impair cognitive flexibility, did increase perseverative errors, but, surprisingly, also improved overall set-shifting task performance by reducing lapse rates. We reconcile these results with a state-switching model in which cocaine decreases exploration by deepening attractor basins corresponding to rule states. These results support the idea that exploratory noise contributes to lapses, affecting rule-based decision-making even when it has no strategic value, and suggest that one key mechanism for regulating exploration may be the depth of rule states.

Electromyography-Based Quantitative Representation Method for Upper-Limb Elbow Joint Angle in Sagittal Plane.

This paper presents a quantitative representation method for the upper-limb elbow joint angle using only electromyography (EMG) signals for continuous elbow joint voluntary flexion and extension in the sagittal plane. The dynamics relation between the musculotendon force exerted by the biceps brachii muscle and the elbow joint angle is developed for a modified musculoskeletal model. Based on the dynamics model, a quadratic-like quantitative relationship between EMG signals and the elbow joint angle is built using a Hill-type-based muscular model. Furthermore, a state switching model is designed to stabilize the transition of EMG signals between different muscle contraction motions during the whole movement. To evaluate the efficiency of the method, ten subjects performed continuous experiments during a 4-day period and five of them performed a subsequent consecutive stepping test. The results were calculated in real-time and used as control reference to drive an exoskeleton device bilaterally. The experimental results indicate that the proposed method can provide suitable prediction results with root-mean-square (RMS) errors of below 10° in continuous motion and RMS errors of below 10° in stepping motion with 20° and 30° increments. It is also easier to calibrate and implement.

Formula omitted]-state switching models with time-varying transition distributions—Does loan growth signal stronger effects of variables on inflation?

Two Bayesian sampling schemes are outlined to estimate a time-varying Markov switching transition distribution. Using data augmentation transforms the non-linear, non-normal logit transition model into a linear-normal one. A partial representation of the difference in random utility model in combination with random permutation sampling provides highest sampling efficiency. The level of the covariate in the transition distribution which balances the persistence across states is defined to be the threshold level. For illustration, we estimate a two-pillar Phillips curve for the euro area, in which loan growth affects the transition distribution.

When are Your Customers Active and is Their Buying Regular or Random? An Erlang Mixture State-Switching Model for Customer Scoring

Scoring customers with regard to the expected number of their future transactions is of fundamental interest to direct marketers. For the purpose of customer scoring, a variety of models have been developed, based on the negative binomial distribution. Extensions of such models allow for customer defection (“buy until you die”). We extend customer scoring models in two ways: (1) We assume that customers switch between an active state in which they buy and an inactive state in which they do not purchase. Switching between states can occur in both directions, implying that defection is temporary. (2) We allow for heterogeneity among households with regard to the regularity of purchasing. We achieve this by modeling purchasing in the active state as a mixture of Erlang-distributed interpurchase times. Our model nests the BG-NBD model and other variants of the NBD as special cases. We develop MCMC simulation methods for our model and apply it to five different data sets, comparing the results to several benchmark models. Our results imply that it is often erroneous to assume that customers “buy until they die”. , the results support the assumption of transient switching between an active and inactive state. We show that, when the model does not account for transient switching, customer scoring is biased. We discuss both the theoretical and managerial implications of our results, and potential areas for future research.

MS_Regress - The MATLAB Package for Markov Regime Switching Models

Markov state switching models are a type of specification which allows for the transition of states as an intrinsic property of the econometric model. Such type of statistical representations are well known and utilized in different problems in the field of economics and finance. This paper gives an overview of MS_Regress, a Matlab toolbox specially designed for the estimation, simulation and forecasting of a general markov regime switching model. The package was written in an intuitive manner so that the user have at its reach a large number of different markov switching specifications, without any change in the original code. This document introduces the main functionality of the package with the help of several empirical examples.

Evaluating the Effectiveness of State-Switching Time Series Models for U.S. Real Output

Two types of state-switching models for U.S. real output have been proposed: models that switch randomly between states and models that switch states deterministically, as in the threshold autoregressive model of Potter. These models have been justified primarily on how well they fit the sample data, yielding statistically significant estimates of the model coefficients. Here we propose a new approach to the evaluation of an estimated nonlinear time series model that provides a complement to existing methods based on in-sample fit or on out-of-sample forecasting. In this new approach, a battery of distinct nonlinearity tests is applied to the sample data, resulting in a set of p-values for rejecting the null hypothesis of a linear generating mechanism. This set of p-values is taken to be a “stylized fact” characterizing the nonlinear serial dependence in the generating mechanism of the time series. The effectiveness of an estimated nonlinear model for this time series is then evaluated in terms of the congruence between this stylized fact and a set of nonlinearity test results obtained from data simulated using the estimated model. In particular, we derive a portmanteau statistic based on this set of nonlinearity test p-values that allows us to test the proposition that a given model adequately captures the nonlinear serial dependence in the sample data. We apply the method to several estimated state-switching models of U.S. real output.

Discrete versus continuous state switching models for portfolio credit risk

Dynamic models for credit rating transitions are important ingredients for dynamic credit risk analyses. We compare the properties of two such models that have recently been put forward. The models mainly differ in their treatment of systematic risk, which can be modeled either using discrete states (e.g., expansion versus recession) or continuous states. It turns out that the implied asset correlations and default rate volatilities for discrete state switching models are implausibly low compared to empirical estimates from the literature. We conclude that care has to be taken when discrete state regime switching models are employed for dynamic credit risk management. As a side result of our analysis, we obtain indirect evidence that asset correlations may change over the business cycle.

Entropy considerations in kinetic method experiments.

In extended kinetic method experiments, relative binding enthalpies ('affinities') and relative entropies are obtained based on unimolecular dissociation kinetics. A series of ion-bound dimers A-X-B(i) is formed, in which the sample (A) and structurally similar reference molecules (B(i)) are bridged by a central cation or anion (X). The branching ratios of the A-X-B(i) set to A-X and B(i)-X are determined at different internal energies, usually by subjecting A-X-B(i) to collisionally activated dissociation at various collision energies. The dependence of the natural logarithm of the branching ratios on the corresponding B(i)-X bond enthalpies (X affinities of B(i)) is evaluated as a function of internal energy to thereby deduce the A-X bond enthalpy (X affinity of A) as well as an apparent relative entropy of the competitive dissociation channels, Delta(DeltaS(app)). Experiments with proton- and Na(+)-bound dimers show that this approach can yield accurate binding enthalpies. In contrast, the derived Delta(DeltaS(app)) values do not correlate with the corresponding thermodynamic entropy differences between the channels leading to A-X and B(i)-X, even after scaling. The observed trends are reconciled by the transition state switching model. According to this model, the kinetics of barrierless dissociations, such as those encountered in kinetic method studies, are dominated by a family of tight transition states ('entropy bottlenecks') lying lower in energy than the corresponding dissociation thresholds. In general, the relative energies of these tight transition states approximately match those of the dissociation products, but their relative entropies tend to be much smaller, as observed experimentally.

Discrete versus Continuous State Switching Models for Portfolio Credit Risk

Dynamic models for credit rating transitions are important ingredients for dynamic credit risk analyses. We compare the properties of two such models that have recently been put forward. The models mainly differ in their treatment of systematic risk, which can be modeled either using discrete states (e.g., expansion versus recession) or continuous states. It turns out that the implied asset correlations for discrete state switching models are implausibly low compared to correlation estimates in the literature. Given these limited correlations, we conclude that care has to be taken when discrete state regime switching models are employed for dynamic credit risk management. As a side result of our analysis, we obtain indirect evidence that default correlations may change over the business cycle.

Unimolecular and bimolecular reactions in the C 6H 6+· system. Experiment and theory

The results of an experimental and theoretical study of unimolecular and bimolecular reactions in the C 6H 6 +· system are reported. The kinetic energy release distributions for the fragmentation of metastable C 6H 6 +· ions were measured and the bimolecular reactions between C 6H 4 +· and H 2, cyclic C 4H 4 +· and C 2H 2, linear C 4H 4 +· and C 2H 2, and between C 2H 2 +· and linear C 4H 4 have been studied. The results of these experiments and absolute unimolecular rate constants and product branching ratios from PIPECO studies are compared with the predictions of the transition state switching model form of statistical rate theory. In general, good agreement was found between the experimental results and the calculations. The calculated total unimolecular rate constants are in excellent agreement with the experimental data (for total energies of 15.0–15.7 eV). Below total energies of 16.5 eV the measured and calculated branching ratios are in good agreement. Above 16.5 eV the agreement becomes increasingly poor. These results were interpreted as indicating that above 16.5 eV the rate of fragmentation is no longer slow compared to the rate of isomerization and so products derived from simple bond cleavages are favored over reactions requiring isomerization to different ion structures. The measured kinetic energy distribution for C 6H 5 + is broader than the calculated distribution; for C 4H 4 +· the measured and calculated distributions are in good agreement, and for C 3H 3 + the measured distribution is narrower than the calculated distribution. The measured distribution for C 6H 4 +· peaks at large values of kinetic energy, indicating a substantial barrier along the reaction coordinate in this channel. No reaction was observed between cyclic C 4H 4 +· and C 2H 2 and between C 6H 4 +· and H 2. Reaction between linear C 4H 4 +· and C 2H 2 occurs at a rate slower than the collision rate, and the experimental and theoretical results indicate that the reaction occurs through a long-lived C 6H 6 +·* intermediate complex. Charge transfer between C 2H 2 +· and C 4H 4 occurs at the collision rate. Most of the charge transfer is direct. However, the experimental and theoretical results indicate that some trajectories sample the deep C 6H 6 +· well.

Unimolecular and bimolecular reactions in the C4H6+⋅ system: Experiment and theory

New experimental data on the metastable reactions of C4H6+⋅ are presented. The bimolecular reactions between C2H2+⋅ and C2H4 and between C2H4+⋅ and C2H2 have been reinvestigated using a tandem ICR. Total rate constants and branching ratios were measured and isotopic scrambling investigated using deuterium labeling. The experimental data reported here and the PIPECO data of Werner and Baer [J. Chem. Phys. 62, 2900 (1975)] are compared with the predictions of the transition state switching model. Good agreement was found between the predictions of the model and the experimental data. The branching ratios were found to be strong functions of both energy and angular momentum. In the bimolecular reaction between C2H2+ and C2H4 charge transfer appears to occur predominently via a loosely bound intermediate which only samples a small volume of the available C4H+⋅6 phase space.

Multiple transition states in unimolecular reactions: A transition state switching model. Application to the C4H8 +⋅ system

A transition state switching model is developed for use in systems where more than one transition state occurs along the reaction coordinate. The model is cast in the perspective of both the unified statistical theory (UST) of Miller and of variational transition state theory. The basic assumptions are those common to transition state theory and RRKM–QET. A reaction branching analysis leads to reaction probabilities for a number of potential surfaces and appropriate expressions are delineated for both unimolecular and bimolecular reactions. The theory is developed from a microcanonical viewpoint and rigorously conserves both energy E and angular momentum J. Comparison is made with experimental data for the C4H8 +⋅ system where absolute unimolecular rate constants and branching ratios have been measured as a function of energy, bimolecular rate constants, and branching ratios measured at room temperature (the ethylene ion–molecule reaction), the lifetime of C4H8 +⋅ measured when formed by the ethylene ion–molecule reaction, and product kinetic energy distributions measured. The principal conclusions of the work are (i) a multiple transition state switching mechanism is required if the experimental data is to be adequetely fit by theory; (ii) at least two transition states (i.e., dividing surfaces at points of minimum flux along the reaction coordinate) naturally occur in unimolecular reactions, one a tight (i.e., configurational) TS occuring near the unimolecular reactant and the second an orbiting (i.e., centrifugal) TS occuring near the bimolecular products; (iii) tight transition states naturally occur at energies E‡ less than the threshold energy for reaction E0 when the system energy E is significantly greater than E0; (iv) the relative abundance of the three product channels C2H4 +⋅+C2H4, C3H5 ++CH3⋅, and C4H+7+H⋅ are strong functions of both energy and angular momentum in the reactant C4H8 +⋅ ion.