A cyclically adjusted spatio-temporal kernel density estimation method for predictive crime hotspot analysis

Research on output distribution modeling of photovoltaic modules based on kernel density estimation method and its application in anomaly identification

Sampling timestamps enhance the reliability of spatiotemporal trajectory density estimation. Existing kernel density estimation (KDE) methods leverage sampling time to modify kernel shapes or weight specifications. However, controlling two concurrent errors remains challenging: density over/underestimation due to temporal autocorrelation, and nonzero density assignments to unreachable locations. This study proposes a time-aware KDE (t-KDE) method for irregular sampling intervals, adopting a divide-and-conquer strategy that synergistically integrates time geography and temporal autocorrelation. By establishing two temporal mappings—from time to kernel functions and to weight coefficients—t-KDE retrospectively mitigates the above errors through KDE recalibration. The approach aims to maximize temporal information utilization to reduce estimation uncertainty, providing a theoretical basis for unbiased density modeling. Empirical analysis demonstrates that t-KDE outperforms state-of-the-art methods in accuracy and reliability.

Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most current big data applications. Several strategies, such as tree-based or hashing-based estimators, have been proposed to improve the efficiency of the kernel density estimation method. The novel density kernel density estimation method (DMKDE) uses density matrices, a quantum mechanical formalism, and random Fourier features, an explicit kernel approximation, to produce density estimates. This method has its roots in the KDE and can be considered as an approximation method, without its memory-based restriction. In this paper, we systematically evaluate the novel DMKDE algorithm and compare it with other state-of-the-art fast procedures for approximating the kernel density estimation method on different synthetic data sets. Our experimental results show that DMKDE is on par with its competitors for computing density estimates and advantages are shown when performed on high-dimensional data. We have made all the code available as an open source software repository.

Abstract: Home‐range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home‐range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home‐range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space‐use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home‐range estimation: 1) KDE with reference bandwidths, 2) KDE with least‐squares cross‐validation, 3) KDE with plug‐in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home‐range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home‐range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home‐range estimation.

The carbon trading market is directed by policy and responsive to a multitude of factors, experiencing considerable price volatility that mirrors the supply–demand dynamics of greenhouse gas emissions rights and the economic expenses of carbon reduction measures. Improving prediction accuracy of carbon prices is crucial for investors and policymakers. It can help investors avoid risks and provide a basis for policymakers to formulate effective policies. The study employed a lightweight hybrid model to forecast carbon prices. Firstly, Marine Predators Algorithm Optimized Variational Mode Decomposition (MPA-VMD) was applied to decompose the original carbon price time series to obtain optimal parameters and subsequences. Secondly, the Minimal Gated Memory Network (MGM), a simplified network structure, was proposed to forecasting subsequences, reducing training time without compromising prediction accuracy. Thirdly, the MGM was integrated with quantile regression (QR) to predict the conditional quantiles of each subsequence. Fourthly, the probability density function was estimated based on the conditional quantiles of the carbon price using the Kernel Density Estimation (KDE) method. Finally, the final forecasting values of point prediction, interval prediction and comprehensive probability were obtained through the linear superposition of each subsequence, respectively. Experimental results showed that the performance of the proposed model was validated across five aspects: the superiority of the decomposition method, point prediction accuracy, suitable prediction interval, comprehensive probability prediction performance, and training time relative to six benchmark models.

Geological hazards caused by strong earthquakes have caused continuous social and economic losses and destruction of the ecological environment in the hazard area, and are mostly manifested in the areas with frequent occurrence of geological hazards or the clustering of geological hazards. Considering the long-term nature of earthquakes and geological disasters in this region, this paper takes ten earthquake-stricken areas in Wenchuan earthquake zone as examples to collect shallow landslide data in 2010, combined with the spatial location of landslides and other factors. Kernel density estimation (KDE) method is used to analyze the spatial characteristics of shallow landslide. Taking the space of shallow landslide as the characteristic variable and fully considering the regulating factors of earthquake-induced landslide: terrain complexity, distance to river, distance to fault, distance to road, lithology, normalized vegetation difference index (NDVI) and ground peak acceleration (PGA) as independent variables, based on KDE and polynomial logistic regression (MLR), A quantitative model of shallow landslide in the earthquake area is constructed. The results show that: (1) PGA has the greatest impact on landslide in the study area. (2) Compared with the two-category logistic regression (two-category LR) model, the susceptibility map of landslide prediction results based on the KDE-MLR landslide susceptibility prediction model is more consistent with the actual situation. (3) The prediction accuracy of the model validation set is 70.7%, indicating that the landslide susceptibility prediction model based on KDE-MLR can effectively highlight the spatial characteristics of shallow landslides in 10 extreme disaster areas. The research results can provide decision-making basis for shallow landslide warning and post-disaster reconstruction in earthquake-stricken areas.

In addition to its vital significance in combustion and atmospheric chemistry, the reaction between H' and HO2 on the ground triplet state represents a prototype with multiple product channels, including H2 + O2, OH + OH, O + H2O, and H + H'O2. In this work, a full-dimensional accurate potential energy surface (PES) for the title reaction was developed to provide reliable descriptions for all dynamically relevant regions. Using this PES, we adopted the quasi-classical trajectory approach to study the corresponding reaction dynamics, including the reactivity of each product channel and the associated product branching ratio, the product energy distributions, product angular distributions, and associated microscopic mechanisms. For representing distributions of the product energies, such as product translational energy as well as product rotational and vibrational energies, both the traditional histogram and the kernel density estimation (KDE) methods were used and compared. It seems that the features of the resulting distributions in this work are very similar to each other among different methods. The KDE method is suggested for statistics, particularly for those populations with small oscillations in the histogram plot.

Combined probability density model for medium term load forecasting based on quantile regression and kernel density estimation

In kernel density estimation methods, an approximation of the data probability density function is achieved by locating a kernel function at each data location. The smoothness of the functional approximation and the modelling ability are controlled by the kernel bandwidth. In this paper we propose a Bayesian estimation method for finding the kernel bandwidth. The distribution corresponding to the bandwidth is estimated from distributions characterizing the second order statistics estimates calculated from local neighbourhoods. The proposed bandwidth estimation method is applied in three different kernel density estimation based approaches: scale space, mean shift and quantum clustering. The third method is a novel pattern recognition approach using the principles of quantum mechanics.

Identification of high-risk regions of schistosomiasis is important for rational resource allocation and effective control strategies. We conducted the first study to apply the newly developed method of adaptive kernel density estimation (KDE)-based spatial relative risk function (sRRF) to detect the high-risk regions of schistosomiasis in the Guichi region of China and compared it with the fixed KDE-based sRRF. We found that the adaptive KDE-based sRRF had a better ability to depict the heterogeneity of risk regions, but was more sensitive to altering the user-defined smoothing parameters. Specifically, the impact of bandwidths on the estimated risk value and risk significance (P value) was higher for the adaptive KDE-based sRRF, but lower on the estimated risk variation standard error (s.e.) compared with the fixed KDE-based sRRF. Based on this application the adaptive and fixed KDE-based sRRF have their respective advantages and disadvantages and the joint application of the two approaches can warrant the best possible identification of high-risk subregions of diseases.

Bulk fluid injection into low permeability geologic formations been observed to trigger microearthquakes (MEQs). Triggering of MEQ events has been linked to pore pressure, temperature, and in-situ stress variations. The resulting clouds of micro-seismic events are believed to carry information about the underlying coupled flow, geomechanics, and thermal processes and, hence, rock hydraulic and mechanical properties. We develop a framework for integrating injection-induced microseismic events as monitoring data to infer reservoir property distributions. To model the reservoir stimulation and induced microseismicity, we use a fully coupled thermo-poroelastic model with coupled heat transport, fluid flow, and rock deformation capabilities as forward model and apply the ensemble Kalman filter (EnKF) data assimilation algorithm invert MEQ measurements. Because discrete MEQ events are not amenable to continuous estimation methods, we first use a kernel density estimation (KDE) method to convert the observed cloud of MEQ events into a continuous seismicity density map. We then apply a variant of the EnKF to integrate the resulting continuous seismicity density map to estimate, individually and jointly, heterogeneous hydraulic and geomechanical rock property distributions such as permeability, Young's modulus, tensile strength and Cohesion. We apply a spectral projection approach to decorrelate the spatially correlated observation of MEQ for improved EnKF implementation. We use numerical experiments to evaluate the performance of the developed methods.

Fault detection and diagnosis (FDD) using smart thermostat data is a relatively new field of research, but one with immediate practical application to residential indoor climate control. This two-part article proposes a statistics-based method for using aggregated data from many residential HVAC systems to identify outliers. These outlier systems can then be related to operational problems, such as inadequate capacity, malfunctioning control strategies, or other soft faults. The first part of the article presents the analytical methodology. For this study, historical and real-time data from thousands of cloud-based thermostats are used to extract features during the cooling mode of operation. First, the data are parsed to identify time segments that are characteristic periods of pseudo-steady-state operation. Then, a multistage fault detection method compares the features among all systems to find statistical outliers. Each feature is analyzed independently using kernel density estimation (KDE) methods. Additionally, multiple features are analyzed simultaneously using multivariate statistics and the Mahalanobis distance () to determine outliers. Anomalous systems are sorted heuristically, and information from univariate and multivariate methods is combined to more precisely classify systems exhibiting specific faulty behavior. The second part of this article provides some typical case studies, illustrating how this method can be used to identify aberrant behavior across a large number of monitored systems.

Due to the uncertainties and the dynamic parameters from design, manufacturing, and working conditions, many engineering structures usually show uncertain and dynamic properties. This paper proposes a novel time-variant reliability analysis method using failure processes decomposition to transform the time-variant reliability problems to the time-invariant problems for dynamic structures under uncertainties. The transformation is achieved via a two-stage failure processes decomposition. First, the limit state function with high dimensional input variables and high order temporal parameters is transformed to a quadratic function of time based on the optimized time point in the first-stage failure processes decomposition. Second, based on the characteristics of the quadratic function and reliability criterion, the time-variant reliability problem is then transformed to a time-invariant system reliability problem in the second-stage failure processes decomposition. Then, the kernel density estimation (KDE) method is finally employed for the system reliability evaluation. Several examples are used to verify the effectiveness of the proposed method to demonstrate its efficiency and accuracy.

The aim of this study was to provide scientific support for the creation of policy on inbound tourism. A comprehensive and thorough understanding of fine-grained spatiotemporal dynamic patterns is crucial for tourism management, planning and policymaking. In spite of spatiotemporal pattern analysis on tourism movements, environment- and society-related topics have been developed to stimulate tourism. However, few studies have focused on the fine-grained spatiotemporal analysis of tourist behavior. Depending on a fine-grained Flickr data source, we investigated the spatiotemporal dynamic patterns of inbound tourism in the context of fine granularity in the spatial and temporal dimensions. The proposed approach based on fine-grained Flickr data and the emerging spatiotemporal analysis method was to first conduct a refined temporal variation analysis based on the annual, monthly, and daily variation; second, a thorough analysis of the seasonality of tourism was conducted with the kernel density estimation (KDE) method; third, the correlation between the attraction grade and popularity was complementarily exploited with both qualitative and quantitative methods; and finally, the patterns were identified and visualized with the space-time cube in the context of fine granularity. The results from the analysis revealed that the downtown region of Beijing was the most popular place throughout the year due to the many famous Chinese cultural heritage attractions. In contrast, the landscape sites and thematic parks were nearly cold spots because of their strong seasonality. Our approach can also be applied to other crowdsourced data, such as that from Twitter and Instagram. Spatiotemporal analysis and empirical research have interesting implications for other cities in China or other developing countries.

Radio source counts provide a fundamental census of cosmic radio emission, yet their estimation is usually based on coarse histograms that suffer from bin-choice bias, boundary effects, and survey incompleteness. We apply and rigorously evaluate kernel density estimation (KDE) as a nonparametric alternative to the conventional binned method for estimating differential radio source counts. Using simulated flux-limited samples derived from an input luminosity function model, we compare the performance of standard KDE, adaptive KDE, and traditional binning methods. Our results show that KDE-based approaches yield more accurate and stable estimates, particularly in the high-flux regime where data are sparse and conventional methods struggle. We also apply the adaptive KDE method to real observational data from the LOFAR Two-Metre Sky Survey Deep Fields. Our analysis robustly confirms the pronounced “drop and bump” feature at sub-mJy flux densities, but also reveals that a secondary, modest bump seen in the binned data at ∼10 mJy is likely a binning artifact. We also demonstrate the flexibility of KDE in addressing observational incompleteness through weighted estimation, which applies weights continuously at the level of individual sources rather than averaging them in discrete bins. These strengths make KDE a powerful tool for source-count analyses in current and future radio surveys and, more broadly, in analogous studies at other wavelengths. All computations in this study are implemented with AstroKDE , a Python package we have developed for astronomical applications.