Stochastic Process Approach Research Articles

A doubly stochastic point process approach for spatio-temporal dynamics of crime data

Crime, in general, is at the base of crucial issues for many societies living in large cities worldwide. Indeed, crime and neighbourhood disorder may negatively impact the health of urban residents. Thus, the crime rate reduction is at the core of many local policies driven by active plans supported by police action and local authorities. Considering crime reports as a spatio-temporal point pattern, we propose spatio-temporal log-Gaussian Cox processes as a modelling framework for crimes in space and time. We model the spatial and temporal variation through generalized parametric additive and linear models, and a Gaussian space-time process approximates the residual variation. The inference is performed via Markov chain Monte Carlo through MALA algorithms. We provide short-term forecasts of future crimes and suggest a surveillance system that operates by reporting predictive probabilities. Our data come from the reported crimes in the locality of Kennedy (Bogota) over several years and several types of crimes. The police department may use our method to help allocate police resources and design crime prevention strategies and policies, such as surveillance, in specific zonal planning units.

Stochastic Process Approaches for Modeling of Games

Stochastic Process Approaches for Modeling of Games

Remaining useful life prediction method based on stacked autoencoder and generalized wiener process for degrading bearing

Abstract Remaining Useful Life (RUL) prediction using deep learning networks primarily produces point estimates of RUL, but capturing the inherent uncertainty in RUL prediction is difficult. The use of the stochastic process approach can reflect the uncertainty in RUL predictions. However, the amount of data generated during equipment operation cannot be effectively utilized. This paper aims to propose an adaptive RUL prediction method tailored for extensive datasets and prediction uncertainty, effectively harnessing the strengths of deep learning methods in managing massive data and stochastic process techniques in quantifying uncertainties. RUL prediction method, based on Stacked Autoencoder (SAE) combined with Generalized Wiener Process, employs SAE to extract profound underlying features from the monitoring signals. Principal Component Analysis (PCA) is then used to select highly trending features as inputs. The output of PCA accurately reflects health status. A Generalized Wiener Process is used to construct a model for the evolution of the health indicators. The estimation values for the model parameters are determined using the Maximum Likelihood Estimation method. Furthermore, an adaptive update is performed based on Bayesian theory. Utilizing the sense of the first hitting time concept, the Probability Density Function for RUL prediction is derived accurately. Finally, the effectiveness and superiority of the proposed method is verified using numerical simulations and experimental studies of bearing degradation data. The method improves the life prediction accuracy while reducing the prediction uncertainty.

The decline of incrementalism in U.S. lawmaking

AbstractPunctuated equilibrium theory (PET) posits that policy change is incremental for long periods of time with occasional shifts in problem definition and governing authority that produce large changes. Incrementalism results from shared norms and standard operating procedures within policy subsystems. The U.S. Congress experienced a series of institutional changes in the 1990s that both introduced more partisanship into subsystem interactions and made it easier for majority party leaders to enact their agenda. These changes have disrupted many of the processes that produce incrementalism. Using data from 1949 to 2022, I find that U.S. policy outputs, measured through public laws, have experienced fewer incremental changes from one term to the next and more moderate and very large changes since 1995. The shift in outputs has been driven primarily by increased partisan conflict within congressional committees. This study highlights the utility of using the stochastic process approach to compare distributions of outputs across time and not only across countries or institutions.

Financial stability in the Indonesian monetary policy analysis

Financial stability is one of the main factors for a country’s economic sustainability nowadays. Financial instability has adverse effects on the economy which can lead to the financial crisis. This research tries to answer how monetary policy related to Indonesian financial stability in the short and long term, how specific the relations between its parts such as money supply, interest rate, and exchange rate to indonesian financial stability, and which one of these parts that have ways more effective to influence Indonesian financial stability. This research data use time series quarterly as quantitative data in Indonesia. By employing econometric models of error correction on quarter data that consist of the stationary stochastic process, long-run model and cointegration approach and error correction model, this model can indicate how quickly the effect of the money supply, interest rate or exchange rate is fully accepted by the financial stability in the short term. The finding of this study showed that the increase in interest rate began to be able to improve indonesian financial stability responsively in four times the period, namely an increase of one percent in interest rate could increase 0.4161 percent of financial stability in Indonesia.

A comparison of microbial composition under three tree ecosystems using the stochastic process and network complexity approaches.

Soil microbes act as “players” in regulating biogeochemical cycles, whereas environmental heterogeneity drives microbial community assembly patterns and is influenced by stochastic and deterministic ecological processes. Currently, the limited understanding of soil microbial community assembly patterns and interactions under temperate forest stand differences pose a challenge in studying the soil microbial involvement during the succession from coniferous to broad-leaved forests. This study investigated the changes in soil bacterial and fungal community diversity and community structure at the regional scale and identified the pathways influencing soil microbial assembly patterns and their interactions. The results showed that broad-leaved forest cover in temperate forests significantly increased soil pH, and effectively increased soil water content, total carbon (TC), total nitrogen (TN), and total phosphorus (TP) contents. Both soil bacterial and fungal alpha diversity indices were correlated with soil physicochemical properties, especially in broad-leaved forest. The bacterial and fungal community composition of coniferous forest was dominated by deterministic process (bacteria: 69.4%; fungi: 88.9%), while the bacterial community composition of broad-leaved forest was dominated by stochastic process (77.8%) and the fungal community composition was dominated by deterministic process (52.8%). Proteobacteria, Acidobacteriota, Actinobacteriota, and Verrucomicrobiota were the dominant phyla of soil bacterial communities in temperate forests. Whereas Ascomycota, Mortierellomycota, Basidiomycota, and Rozellomycota were the dominant phyla of soil fungal communities in temperate forests. Most members of dominant phylum were regulated by soil physical and chemical properties. In addition, the succession from temperate coniferous forest to broad-leaved forest was conducive to maintaining the complex network of soil bacteria and fungi, and the top 20 degree of the major taxa in the network reflected the positive response of microbial interactions to the changes of soil nutrients during forest succession. This study not only shows the mechanism by which species differences in temperate forests of northern China affect soil microbial community assembly processes, but also further emphasizes the importance of the soil microbiome as a key ecosystem factor through co-occurrence network analysis.

An open source package to perform basic and advanced statistical analysis of turbulence data and other complex systems

We present an open-source package that helps the user to perform a basic statistical analysis of a given turbulence dataset. We believe that this package is useful to the entire turbulence community. It can be used to estimate statistical quantities of turbulence such as the spectral density, turbulence intensity, integral length scale, Taylor microscale, Kolmogorov scale, and dissipation rate as well as velocity increments, structure functions, and their scaling exponents. Different well-known methods available in the literature were selected so that they can be compared. This package also performs an advanced analysis that includes the scale-dependent statistical description of turbulent cascade using the Fokker–Planck equation, consequently leading to the assessment of integral fluctuation theorems. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. This is utilized to estimate the drift and diffusion coefficients of the Fokker–Planck equation. The total entropy production for each independent cascade trajectory can be determined using a Fokker–Planck equation. Estimating total entropy production admits a rigorous law of non-equilibrium stochastic thermodynamics, namely, the integral fluctuation theorem, which must be valid if Markov properties hold and the Fokker–Planck equation is correct. This approach to the turbulent cascade process has the potential for a new way to link the statistical description of turbulence, non-equilibrium stochastic thermodynamics, and local turbulent flow structures. Finally, we emphasize that the presented package can be used for the analysis of other data with turbulent-like complexity as well.

On the Dynamics in Decoupling Buffers in Mass Manufacturing Lines: A Stochastic Approach

This paper analyzes the flow of the contents of interleaved buffers with continuously operating machines in a mass production line. Under this framework, the products to be manufactured advance from station to station to receive a physical–chemical transformation that adds value as they progress in the process. The existence of decoupling buffers between operations (between two consecutive workstations) is a common practice in order to alleviate the pressure that is ahead due to the lack of synchronization between consecutive operations, which causes leisure and/or bottlenecks in the system. In this proposal, we analyze the dynamics of a mass manufacturing line with intermediate decoupling buffers. To do that, we use a regenerative stochastic process approach to build a model where the products stored in each buffer are taken all at once by the consecutive machine. In a second approach, we use a homogeneous birth–death process with constant input–output and assume that the products are taken one by one by the consecutive machine. Finally, we use a non-homogeneous birth–death process to analyze the dynamics of a system whose inputs and outputs depend on time. These proposals are accompanied by numerical examples that illustrate its practical utility.

Performance evaluation of IoT networks: A product density approach

Mobile cellular-based Internet of Things (IoT) networking is set to be enhanced with the addition of two important pillars of 5G — massive Machine Type Communications and ultra-Reliable Low Latency Communications. Temporal traffic uncertainty from diverse applications in IoT networks mandates novel modeling approaches for performance evaluation. This paper introduces a novel stochastic point process approach that can be used to evaluate the time-dependent performance of IoT base stations. Special correlation functions called Product Densities are used to (a) evaluate time-dependent offered traffic, and (b) analyze delay performance. These performance measures are evaluated at IoT base station for Poisson as well as non-Homogeneous Poisson (Beta distributed) traffic arrival processes suggested by 3rd Generation Partnership Project(3GPP). The Product Density estimates of offered traffic are found to be more accurate than the point-wise stationary approximation (PSA) under non-stationary traffic arrival rates. Results from the proposed analytical model are compared with results from a simulation of two queuing models of the base station; infinite server model for offered traffic and multi-server model for delay performance. Analytical results from Product Density functions also correlate with the simulation outcomes suggesting that the proposed Product Density technique is effective when modeling the time-dependent performance of IoT networks subjected to non-stationary traffic conditions, which reflects the real-world scenario.

On an Absolute Autoregressive Model and Skew Symmetric Distributions

By exploiting the connection between a popular construction of a well-known skew-normal distribution and an absolute autoregressive process, we show how the stochastic process approach can lead to other skew symmetric distributions, including a skew-Cauchy distribution and some singular distributions. In so doing, we also correct an erroneous skew-Cauchy-distribution in the literature. We discuss the estimation, for dependent data, of the key parameter relating to the skewness.

Adaptive PI Control for Synchronization of Complex Networks With Stochastic Coupling and Nonlinear Dynamics

In the paper, synchronization of nonlinear dynamical complex networks with stochastic coupling under adaptive PI control is considered. In light of the relative states information of the network nodes, node- and edge-based adaptive PI synchronization protocols are proposed and several sufficient conditions are derived. By employing stochastic analysis techniques combined with a version of the LaSalle’s invariant principles applied to stochastic process and Lyapunov function approaches, synchronization of complex networks with nonlinear dynamics and stochastic coupling reaches in mean square via these two types of adaptive PI control protocols are proved. The proposed adaptive PI control protocols for synchronization of complex dynamical networks are useful for future realistic engineering systems design. Numerical examples are finally simulated to validate the theoretical analysis.

System reliability computation and estimation based on a cumulative damage–threshold–shock model

PurposeThis article considers a reliability model where the failure is due to cumulative damage exceeding a threshold level. The concept that the threshold level of cumulative damage at each arrival of shock can change based on whether the magnitude of each shock exceeds its defined threshold level is considered to compute the system reliability.Design/methodology/approachThe stochastic process approach is used to obtain the cumulative damage based on Poisson arrival of shocks. The general expression for reliability is obtained using the conditional probability over each arrival of shock. The method of maximum likelihood estimation is used to obtain the estimators of the parameters and system reliability. A sensitivity analysis is performed to measure the effect of the parameter representing the rate of arrival of shock.FindingsThe maximum likelihood estimates of the reliability approach the actual reliability for increasing sample size. A sensitivity analysis study on the parameter representing the rate of arrival of shock shows that as the values of parameter increase (decrease), the reliability value decreases (increases).Originality/valueObtained a new expression for the cumulative damage–shock model and the findings are positively supported by presenting the general trend of estimated values of reliability approaching the actual value of reliability. The sensitivity analysis also genuinely supports our findings.

Strategic Assessment of Dam Overtopping Reliability Using a Stochastic Process Approach

AbstractEarth-fill dam overtopping could pose significant threats to public safety if the necessary reliability assessments are not taken into consideration in the design process. Dam overtopping i...

Size of nested cities

AbstractModels of cities based on conventional spatial market theory are unable to replicate a realistic size distribution. The stochastic process approach to size distribution, which assumes proportionate growth, does not provide an economic foundation for spatial trades. There is an apparent irreconcilability. We propose that since there is a continuum of equilibria in models of spatial markets with endogenous location, proportionate growth can work as equilibrium selection. We present computations for an urban configuration that has not been presented in the literature before. A small city locates inside a larger city's agricultural supply zone. This generates a larger variation in city size that may include a realistic size distribution.

Size of Nested Cities

Models of city systems based on market theories are unable to replicate their size distribution. The stochastic process approach to size distribution, which asserts proportional growth, does not provide a strong economic foundation. Hence an apparent irreconcilability. We propose that since there is a continuum of equilibrium set in market models of cities, as pointed out by Berliant and Kung (2006), proportional growth can work as an equilibrium selection. We compute an urban configuration that has not been presented in the literature before. A small city locates inside a larger city's agricultural supply zone. This gives a larger variation in city size that may contain Zipf's distribution.

A stochastic process approach to multilayer neutron detectors

AbstractThe sparsity of the isotope Helium‐3, ongoing since 2009, has initiated a new generation of neutron detectors. One particularly promising development line for detectors is the multilayer gaseous detector. In this paper, a stochastic process approach is used to determine the neutron energy from the additional data afforded by the multilayer nature of these novel detectors. The data from a multilayer detector consist of counts of the number of absorbed neutrons along the sequence of the detector's layers, in which the neutron absorption probability is unknown. We study the maximum likelihood estimator for the intensity and absorption probability and show its consistency and asymptotic normality, as the number of incoming neutrons goes to infinity. We combine these results with known results on the relation between the absorption probability and the wavelength to derive an estimator of the wavelength and to show its consistency and asymptotic normality.

Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

Uncertainty in electricity demand is caused by many factors. Large changes are usually attributed to extreme weather conditions and the general random usage of electricity by consumers. More understanding requires a detailed analysis using a stochastic process approach. This paper presents a Markov chain analysis to determine stationary distributions (steady state probabilities) of large daily changes in peak electricity demand. Such large changes pose challenges to system operators in the scheduling and dispatching of electrical energy to consumers. The analysis used on South African daily peak electricity demand data from 2000 to 2011 and on a simple two-state discrete-time Markov chain modelling framework was adopted to estimate steady-state probabilities of two states: positive inter-day changes (increases) and negative inter-day changes (decreases). This was extended to a three-state Markov chain by distinguishing small positive changes and extreme large positive changes. For the negative changes, a decrease state was defined. Empirical results showed that the steady state probability for an increase was 0.4022 for the two-state problem, giving a return period of 2.5 days. For the three state problem, the steady state probability of an extreme increase was 0.0234 with a return period of 43 days, giving approximately nine days in a year that experience extreme inter-day increases in electricity demand. Such an analysis was found to be important for planning, load shifting, load flow analysis and scheduling of electricity, particularly during peak periods.

Sovereign risk in the Euro area: a multivariate stochastic process approach

In this paper we jointly model financial and real components of sovereign risk, by means of correlated stochastic processes, and apply the model to Euro Area countries. For each country we consider, as a target measure, the Debt/GDP ratio. We model the time dynamics of both the Debt and the GDP by means of a linear combination of two stochastic equations: an Euro Area systematic process and a country-specific idiosyncratic process. Doing so, we provide an early warning predictive model of sovereign debt sustainability, considering both the financial and the real economy sides, and in terms of both common and country-specific factors. We provide an estimation procedure for the parameters of the processes, which allows to calculate the implied probabilities of default for each country. The empirical findings show a clear clustering effect between northern and southern countries, especially on the financial side. The inclusion of the GDP growth rate in the derivation of default probabilities partially changes the clustering structure, showing that the sovereign risk of some countries (especially that of France and Italy) is strongly affected not only by the debt evolution, but also by the growth of the GDP.

Optimal curved fibre orientations of a composite panel with cutout for improved buckling load using the Efficient Global Optimization algorithm

ABSTRACTComposite structures with cutouts (like panels with holes) are a challenge to design because discontinuities of this kind provoke stress concentrations and become critical regions. With curved fibres, the effect of these discontinuities can be decreased by choosing the fibre paths properly. In this article, fibre-path optimization to improve the buckling load of laminated composite panels with cutouts is studied. Two fibre path parameterizations are tested: the usual curvilinear Cartesian and the radial one, proposed in this article, in which the fibre orientations vary linearly with the Euclidean distance from the centre of the panel. To reduce the simulation costs associated with the optimization, the Efficient Global Optimization (EGO) algorithm is used. EGO is a technique based on a stochastic process approach (Kriging) that approximates expensive-to-evaluate functions and sequentially maximizes the expected improvement to update the surrogate at each iteration. A stiffened panel with a cutout subjected to compression and in-plane shearing loads is analysed. The results show that the buckling load when curved fibres are used is substantially higher than the buckling load for straight-fibre laminates. In addition, the optimization framework indicates a low final computational burden.

Potential of Entropic Force in Markov Systems with Nonequilibrium Steady State, Generalized Gibbs Function and Criticality

In this paper, we revisit the notion of the “minus logarithm of stationary probability” as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium thermodynamics of complex systems. It is demonstrated that this quantity arises naturally through both monotonicity results of Markov processes and as the rate function when a stochastic process approaches a deterministic limit. We then undertake a more detailed mathematical analysis of the consequences of this quantity, culminating in a necessary and sufficient condition for the criticality of stochastic systems. This condition is then discussed in the context of recent results about criticality in biological systems.