Empirical Distribution Research Articles

An Effective Method for Estimating the Population Mean That Utilizes Dual Auxiliary Information

To improve the effectiveness of population estimators, researchers have recently implemented dual supplementary information. They employed traditional rankings, the empirical cumulative distribution function, and indicator functions as supplementary sources of information in their analysis. An improved family of population mean estimators is introduced in this article, which utilizes the relative ranks of the auxiliary information’s configurations to incorporate the relevant information. A first-order approximation is employed to derive the mathematical expressions for the bias and the mean-squared error (MSE) of the proposed family of estimators. The empirical analysis is investigated to demonstrate the practicality of the proposed estimators in real-world scenarios. Additionally, the theoretical conclusions are effectively validated by the Monte Carlo simulation integration. Our results unequivocally indicate that the proposed family of estimators surpasses their current counterparts.

Evaluating Meaningful Changes in Patient-Reported Outcome Measurement Information System-Fatigue Scores from Three Phase 3 Clinical Trials of Sarilumab for Patients With Rheumatoid Arthritis.

The aim of this study was to evaluate changes in fatigue measured by Patient-Reported Outcome Measurement Information System (PROMIS)-Fatigue scores in patients with rheumatoid arthritis (RA) who received sarilumab and to assess the proportion of patients achieving clinically meaningful change. Data from three phase 3 randomized controlled trials of patients with RA who received sarilumab-MOBILITY, TARGET, and MONARCH-were evaluated. The 10 RA-relevant items from the 13-item Functional Assessment of Chronic Illness Therapy (FACIT)-Fatigue were scored in the PROMIS T score metric. Mean changes in 10-item PROMIS-Fatigue T score (PROMIS-Fatigue 10a) were compared, proportions of patients reporting meaningful within-person change thresholds were assessed, and results were visualized using empirical cumulative distribution function (eCDF) curves. Patients with RA reported high baseline fatigue. Using PROMIS-Fatigue 10a, at week 24, patients receiving 150 or 200 mg sarilumab every other week in MOBILITY and TARGET had rapidly and significantly improved mean levels of fatigue compared to those who received placebo. When compared to patients who received adalimumab in MONARCH, patients who received sarilumab had a trend toward increased improvement. eCDF curves showed separation between active treatment versus placebo with both sarilumab doses and across the score range for improvement. Higher proportions of patients reported three-, five-, and seven-point improvements in PROMIS-Fatigue scores in groups who received active treatment. Substantial proportions of patients with RA who received sarilumab reported meaningful change in fatigue measured by PROMIS-Fatigue 10a over time. This study demonstrates the ability to convert FACIT-Fatigue score onto the PROMIS T score metric, the rapid reduction in fatigue with biologic therapies, and the use of novel eCDF curves to show individual patient-level change.

Identifying thresholds for meaningful improvements in NTDT-PRO scores to support conclusions about treatment benefit in clinical studies of patients with non-transfusion-dependent beta-thalassaemia: analysis of pooled data from a phase 2, double-blind, placebo-controlled, randomised trial

ObjectivesTo estimate thresholds for defining meaningful within-patient improvement from baseline to weeks 13–24 and interpreting meaningfulness of between-group difference for the non-transfusion-dependent beta-thalassaemia patient-reported outcome (NTDT-PRO) tiredness/weakness (T/W) and shortness...

NIMG-55. DEVELOPING A COMPUTATIONAL PIPELINE TO FORECAST AND SPATIALLY MAP HIGH-GRADE GLIOMA RESPONSE TO RADIOTHERAPY USING BIOPHYSICAL MODELS AND DATA-DRIVEN STATISTICAL ANALYSIS

Abstract High-grade glioma (HGG) presents significant treatment challenges, particularly in identifying less responsive tumor areas to target with adaptive radiotherapy (RT). This study introduces a patient-specific computational pipeline designed to predict and spatially map HGG response to RT, focusing on regions demonstrating resilience to RT. Our computational pipeline is centered around a family of 3D biophysical models describing tumor cell invasion, proliferation, and response to RT which can be personalized for individual patients using longitudinal multiparametric MRI data. Utilizing longitudinal multiparametric MRI data reporting on cell density (diffusion weighted MRI) and the extent of disease (T2-FLAIR and contrast-enhanced T1-weighted MRIs) from 21 patients, ranging from baseline to three weeks into RT, we calibrated a family of biophysical models to forecast tumor cell density up to the final week of RT and one-month follow-up. By employing pareto tail analysis on empirical cumulative distribution function fits of voxel-wise changes in apparent diffusion coefficient maps (ΔADC) between the future images (end of RT, one-month follow-up) and pre-treatment images, we identified areas of increased tumor cellularity on both the ground truth and model predicted cellularity maps. The analysis differentiated tumor voxels into “non-responding” and “responding” categories, based on cutoffs determined through ROC analysis across various conditions—including assessments of both enhancing and non-enhancing tumor regions at different time points. Optimal ΔADC cutoffs for predicted and measured data were established, leading to high area under curve (AUC; ranging from 0.803 to 0.934) values and significant Youden’s index scores (ranging from 0.526 to 0.765) across all conditions. Our findings demonstrate the feasibility of this novel pipeline in delineating biologically relevant RT targets, offering a potential tool for enhancing the efficacy of adaptive RT strategies in treating HGG.

Gumbel–Logistic Unit Distribution with Application in Telecommunications Data Modeling

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

Strong convergence of the empirical spectral distribution of a unified matrix model

Let [Formula: see text] is a positive definite matrix and [Formula: see text] with [Formula: see text] being independent and identically distributed (i.i.d.) centered real random variables. Consider the matrix [Formula: see text] where [Formula: see text] and [Formula: see text] are two projection matrices (deterministic or random) satisfying [Formula: see text] and [Formula: see text]. Additionally, if [Formula: see text] and [Formula: see text] are random matrices, they are independent of [Formula: see text]. In this paper, we demonstrate that the empirical spectral distribution of [Formula: see text] converges almost surely to a non-random distribution when [Formula: see text] and [Formula: see text], assuming [Formula: see text] has finite second moment.

Pharmacometric and statistical considerations for dose optimization.

The probability of target attainment (PTA) is a common metric in drug dose optimization, but it requires a specific known target concentration threshold. Such target thresholds are not always available for some treatments, and patient and disease groups, particularly when treating children. This study performed pharmacokinetic and pharmacokinetic-pharmacodynamic (PKPD) simulations to explore different statistical approaches for determining the optimal dose for unknown PK and PKPD targets. To determine an optimal dose, PK and PKPD outcomes in typical patients with a standard adult dosing regimen were simulated and set as the reference profile, and compared to simulated outcomes for different dosing regimens in the population of interest. Statistical distances between the empirical cumulative distribution functions of the outcomes from all possible dosing regimens were calculated and compared to the reference profile. An optimal dose for known PK and PKPD target outcomes was selected to maintain the outcome above the assigned target, while optimal dosing in a population of interest with an unknown target was selected to generate equivalent PK and PKPD outcomes as the typical population. All of the dose optimization methods with commonly used PK and PKPD models and covariates were implemented as an open source freely available Shiny web-application. The developed pharmacometric method for dose optimization in populations with known and unknown target levels were robust and reproducible, and the implementation of a freely accessible Shiny web-application ensures widespread use and could be a useful tool for dose optimization in populations of interest.

Violation of Leggett–Garg Inequality in Perceiving Cup-Like Objects and Cognitive Contextuality

This paper is devoted to an experimental investigation of cognitive contextuality inspired by quantum contextuality research. This contextuality is related to, but not identical to context-sensitivity which is well-studied in cognitive psychology and decision making. This paper is a part of quantum-like modeling, i.e., exploring the methodology of quantum theory outside of physics. We examined the bistable perception of cup-like objects, which strongly depends on experimental contexts. Our experimental data confirmed the existence of cognitive hysteresis, the important role of memory, and the non-commutative structure of cognitive observables. In physics, quantum contextuality is assessed using Bell-CHSH inequalities, and their violation is incorrectly believed to imply the nonlocality of Nature. The violation of Bell-type inequalities in cognitive and social science strongly indicates that the metaphysical implications of these inequalities are quite limited. In our experiments, modified Leggett–Garg inequalities were also significantly violated, but this only means that experimental data from experiments performed in different contexts cannot be modeled by a unique set of noncontextual, jointly distributed random variables. In our experiments, we know the empirical probability distributions measured in different contexts; thus, we can obtain much more detailed and reliable information about contextuality in human cognition by performing nonparametric compatibility tests.

The Carrot and the Stick: Bank Bailouts and the Disciplining Role of Board Appointments

We empirically examine the Capital Purchase Program (CPP) used by the US government to bail out distressed banks and its implications for regulatory policy. We find strong evidence that a feature of the CPP—the government’s ability to appoint independent directors on the board of an assisted bank that missed six dividend payments to the Treasury—had a significant effect on bank behavior. Banks were averse to these appointments—the empirical distribution of missed payments exhibits a sharp discontinuity at five. Director appointments by the Treasury were associated with improved bank performance and lower CEO pay. (JEL G21, G28, G32, G34, G35, G38, H81)

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling aims at determining the job sequence with the best desired performance, and provides the basic building block for more advanced scheduling problems. In the present study, a single machine scheduling model with uncertain processing time is considered by incorporating the job release time and due date. The job processing time follows unknown probability distribution, and can be estimated via the historical data. To model the uncertainty, the processing time distribution is defined over a Wasserstein ball ambiguity set, which covers all feasible probability distributions within the confidence radius of the empirical distribution, known as the center of the ball. Then a data-driven distributionally robust scheduling model is constructed with individual chance constraints. In particular, two equivalent reformulations are derived with respect to the ℓ1-norm and ℓ2-norm metrics of the Wasserstein ball, namely, a mixed-integer linear programming and a mixed-integer second order cone programming model, respectively. To accelerate the solving of large-scale instances, a tailored constraint generation algorithm is introduced. In the numerical analysis, the proposed distributionally robust scheduling approach is compared with the state-of-the-art methods in terms of out-of-sample performance.

Investigating genotype by environment interaction for beef cattle fertility traits in commercial herds in northern Australia with multi-trait analysis

BackgroundGenotype by environment interactions (GxE) affect a range of production traits in beef cattle. Quantifying the effect of GxE in commercial and multi-breed herds is challenging due to unknown genetic linkage between animals across environment levels. The primary aim of this study was to use multi-trait models to investigate GxE for three heifer fertility traits, corpus luteum (CL) presence, first pregnancy and second pregnancy, in a large tropical beef multibreed dataset (n = 21,037). Environmental levels were defined by two different descriptors, burden of heat load (temperature humidity index, THI) and nutritional availability (based on mean average daily gain for the herd, ADWG). To separate the effects of genetic linkage and real GxE across the environments, 1000 replicates of a simulated phenotype were generated by simulating QTL effects with no GxE onto real marker genotypes from the population, to determine the genetic correlations that could be expected across environments due to the existing genetic linkage only. Correlations from the real phenotypes were then compared to the empirical distribution under the null hypothesis from the simulated data. By adopting this approach, this study attempted to establish if low genetic correlations between environmental levels were due to GxE or insufficient genetic linkage between animals in each environmental level.ResultsThe correlations (being less than <0.8) for the real phenotypes were indicative of GxE for CL presence between ADWG environmental levels and in pregnancy traits. However, none of the correlations for CL presence or first pregnancy between ADWG levels were below the 5th percentile value for the empirical distribution under the null hypothesis from the simulated data. Only one statistically significant (P < 0.05) indication of GxE for first pregnancy was found between THI environmental levels, where rg = 0.28 and 5th percentile value = 0.29, and this result was marginal.ConclusionsOnly one case of statistically significant GxE for fertility traits was detected for first pregnancy between THI environmental levels 2 and 3. Other initial indications of GxE that were observed from the real phenotypes did not prove significant when compared to an empirical null distribution from simulated phenotypes. The lack of compelling evidence of GxE indicates that direct selection for fertility traits can be made accurately, using a single evaluation, regardless of environment.

Semi-supervised distribution learning

Abstract This study addresses the challenge of distribution estimation and inference in a semi-supervised setting. In contrast to prior research focusing on parameter inference, this work explores the complexities of semi-supervised distribution estimation, particularly the uniformity problem inherent in functional processes. To tackle this issue, we introduce a versatile framework designed to extract valuable information from unlabelled data by approximating a conditional distribution on covariates. The proposed estimator is derived from the K-fold cross-fitting strategy, exhibiting both consistency and asymptotic Gaussian process properties. Under mild conditions, the proposed estimator outperforms the empirical cumulative distribution function in terms of asymptotic efficiency. Several applications of the methodology are given, including parameter inference and goodness-of-fit tests.

Stripped Helium Star and Compact Object Binaries in Coeval Populations: Predictions Based on Detailed Binary Evolution Models

Massive stars mainly form in close binaries, where their mutual interactions can profoundly alter their evolutionary paths. Evolved binaries consisting of a massive OB-type main-sequence star with a stripped helium star or a compact companion represent a crucial stage in the evolution toward double compact objects, whose mergers are (potentially) detectable via gravitational waves. The recent detection of X-ray-quiet OB+black hole binaries and OB+stripped helium star binaries has set the stage for discovering more of these systems in the near future. In this work, based on 3670 detailed binary-evolution models and using empirical distributions of initial binary parameters, we compute the expected population of such evolved massive binaries in coeval stellar populations, including stars in star clusters and in galaxies with starburst activities, for ages up to 100 Myr. Our results are vividly illustrated in an animation that shows the evolution of these binaries in the color–magnitude diagram over time. We find that the number of OB+black hole binaries peaks around 10 Myr, and OB+neutron star binaries are most abundant at approximately 20 Myr. Both black holes and neutron stars can potentially be found in populations with ages up to 90 Myr. Additionally, we analyze the properties of such binaries at specific ages. We find that OB+helium stars and OB+black hole binaries are likely to be identifiable as single-lined spectroscopic binaries. Our research serves as a guide for future observational efforts to discover such binaries in young star clusters and starburst environments.

Modeling Groundwater Levels in California's Central Valley by Hierarchical Gaussian Process and Neural Network Regression

AbstractModeling groundwater levels continuously across California's Central Valley (CV) hydrological system is challenging due to low‐quality well data which is sparsely and noisily sampled across time and space. The lack of consistent well data makes it difficult to evaluate the impact of 2017 and 2019 wet years on CV groundwater following a severe drought during 2012–2015. A novel machine learning method is formulated for modeling groundwater levels by learning from a 3D lithological texture model of the CV aquifer. The proposed formulation performs multivariate regression by combining Gaussian processes (GP) and deep neural networks (DNN). The hierarchical modeling approach constitutes training the DNN to learn a lithologically informed latent space where non‐parametric regression with GP is performed. We demonstrate the efficacy of GP‐DNN regression for modeling non‐stationary features in the well data with fast and reliable uncertainty quantification, as validated to be statistically consistent with the empirical data distribution from 90 blind wells across CV. We show how the model predictions may be used to supplement hydrological understanding of aquifer responses in basins with irregular well data. Our results indicate that on average the 2017 and 2019 wet years in California were largely ineffective in replenishing the groundwater loss caused during previous drought years.

A non-stationary bias adjustment method for improving the inter-annual variability and persistence of projected precipitation

Hydrological studies depend heavily on environmental variables, such as precipitation and resulting runoff, which exhibit highly seasonal and intermittent behaviour in semiarid basins. In these basins, the use of traditional methods to adjust biases in time series projections can lead to inaccurate results regarding the impacts of climate change. This study introduces a non-stationary bias adjustment methodology (NS) specifically designed for environmental variables characterized by sporadic events and substantial intensity variability, such as precipitation. The methodology involves establishing a probability threshold to adapt the occurrence of precipitation events and utilizes a quantile mapping method based on a non-stationary theoretical and parametric distribution to adjust biases associated with precipitation intensity. The NS method is applied to daily precipitation projections from seven regional climatic models under the RCP 8.5 scenario spanning 2006–2100, alongside historical concurrent data from 1970 to 2005. The present method is compared to the widely used quantile delta mapping approach (QDM), revealing significant differences in performance related to the distribution of precipitation events throughout the year and the behaviour of mean and extreme intensity values. Both approaches show reliable performance, with root mean square errors between the empirical distribution functions of the corrected hindcast time series and the observations being lower than or close to 1 mm for the percentiles smaller than 50th. The error increases with the percentiles, particularly at stations located at higher altitudes. In these locations, QDM doubles or triples the error obtained with the non-stationary approach for percentiles higher than 75th, reaching up to 34 mm. The proposed methodology demonstrates promising potential in reducing uncertainties associated with systematic errors in inter-annual precipitation variability. It is a first step to jointly apply a similar approach to all involved driving variables. Such methods are key to assessing hydrological responses and associated impacts in semi-arid mountainous basins all around the Globe.

Evidence of association between gender and physical fitness in physically active people in Colombia

Abstract Background Physical Condition (PC) is an important health marker (Colley, 2019), as a predictor of morbidity and mortality from cardiovascular diseases, among other causes (Cruz, 2018). Aim To perform association tests between gender (G) and CP in physically active people in Colombia. This study is observational cross-sectional, 1,503 people participated, 1,019 Women (W) (68.6%) and 485 Men (M) (31.4%) in Colombia, mean age 52±16.2 in W and 42±17.8 in M. Data were analyzed with Rstudio v2022.12.0. The statistical protocol was: 1- Empirical distribution. 2- Normality tests with Kolmogorov-Smirnov. 3- Tests of independence with Chi-square (χ²). The mean (X¯), percentage (%) and standard deviation (±) were taken into account. PC was measured in body composition variables; Body Mass Index (BMI), Body Adiposity Index (BAI) and Abdominal Circumference (AC), Grip Strength (GS) and Maximal Oxygen Consumption (Vo2max). Results In W, 38.3% (27.2±1.37) were overweight (Ow) and 19.1% (33.0±2.83) obese (Ob), 69.6% (90.9±8.14) cardiovascular risk (CVR) for AC and 50.4% (32±4.73) risk for BAI. Regarding GS 43.4% (15.8±6.38) is weak and 54.6% (27.7±4.98) Vo2max is low. In M 35.6% (26.9±1.48) presented Ow and 10.6% (32.7±2.39) in Ob, 39.7% (98.4±6.8) with Rcv by AC and 24.3% (29.7±3.45) at risk by BAI. As for GS 41.5% (27.1±6.39) are weak and 32.3% (33.3±6.33) under Vo2max. According to independence tests with χ² there is association between the G and BMI (χ²=1452.1, df = 1427, p-value=0. 315), G and AC (χ²=394.9, df = 382, p-value=0. 313), G and Vo2max (χ²=155.5, df = 6, p-value&amp;lt;2. 2e-16), G and BAI (χ²=2970.3, df = 1502, p-value&amp;lt;2.2e-16), G and GS (χ²=6015.5, df = 1502, p-value&amp;lt;2.2e-16). This project has been approved by the bioethics committee. Conclusions Test of independence with (χ²), being a non-homogeneous sample, there is a strong association between G and PC with BMI, BAI, AC, GS and Vo2max, each variable depending on the others, evidencing higher Rcv in women with respect to men. Key messages • Several studies consider Physical Condition (PC) is an important health marker (Colley, 2019), as a predictor of morbidity and mortality of cardiovascular disease, among other causes (Cruz, 2018). • There is a strong association between G and the levels of BMI, BAI, AC, SG and Vo2max variables, each variable depending on the others, showing a higher Rcv in women compared to men.

The fluency vs. disfluency dichotomy in writing processes as reflected in the structure of the inter-key intervals empirical distribution

ABSTRACT The broader aim of this study is the corpus-based investigation of the written language production process. To this end, temporal markers have been keylog recorded alongside the writing processes to exploit pauses to segment the speech product into linear units of performance. However, identifying these pauses requires selecting the relevant interkey intervals (IKI) between production microevents. Different models have been applied to identify such components in the empirical distribution of these delays, in particular Gaussian mixture models (GMM), yet no consensus has emerged regarding the number and interpretation of these components. Here, we analyze IKI distributions from a corpus of keylogs and show that a model with two components is robustly selected across a large range of participants. Furthermore, we show that the contents of these modes are consistent with a fluency vs. disfluency interpretation of the modes by identifying which kinds of events fall into each mode.

Machine learning methods for propensity and disease risk score estimation in high-dimensional data: a plasmode simulation and real-world data cohort analysis.

Machine learning (ML) methods are promising and scalable alternatives for propensity score (PS) estimation, but their comparative performance in disease risk score (DRS) estimation remains unexplored. We used real-world data comparing antihypertensive users to non-users with 69 negative control outcomes, and plasmode simulations to study the performance of ML methods in PS and DRS estimation. We conducted a cohort study using UK primary care records. Further, we conducted a plasmode simulation with synthetic treatment and outcome mimicking empirical data distributions. We compared four PS and DRS estimation methods: 1. Reference: Logistic regression including clinically chosen confounders. 2. Logistic regression with L1 regularisation (LASSO). 3. Multi-layer perceptron (MLP). 4. Extreme Gradient Boosting (XgBoost). Covariate balance, coverage of the null effect of negative control outcomes (real-world data) and bias based on the absolute difference between observed and true effects (for plasmode) were estimated. 632,201 antihypertensive users and nonusers were included. ML methods outperformed the reference method for PS estimation in some scenarios, both in terms of covariate balance and coverage/bias. Specifically, XgBoost achieved the best performance. DRS-based methods performed worse than PS in all tested scenarios. We found that ML methods could be reliable alternatives for PS estimation. ML-based DRS methods performed worse than PS ones, likely given the rarity of outcomes.

Association between fitness levels and physical activity in apparently healthy Colombian men

Abstract Physical condition (PC) such as strength and endurance favor functional independence and disease prevention (Melo, 2014). Objective: To characterize the levels of Physical Activity (PA) and CP in apparently healthy men who practice PA in different settings in Bogotá-Colombia. This study is observational cross-sectional, 485 Men (M) participated, mean age 42±17.8 years. To measure the levels PA the IPAQ (International Physical Activity Questionnaires) was applied. The Confidence Interval (CI) and Standard Error (SE) were taken into account. For PA levels, data were analyzed with Rstudio v2022.12.0, with empirical distribution tests, Kolmogorov-Smirnov normality and independence with Chi-Square (χ²), in addition, mean (X¯), percentage (%) and standard deviation (±). 90.6% of the H met the overall PA recommendations (Leisure Time+Active Transportation) with 95% CI (88.0-93.0) and SE (0.012). The PC variables such as; Body Mass Index (BMI), Body Adiposity Index (BAI), Abdominal Circumference (AC), Grip Strength (GS) and Maximal Oxygen Consumption (Vo2max). The results showed that 35.6% (26.9±1.48) of H were Overweight (Ow) and 10.6% (32.7±2.39) were Obese (Ob), 39.7% (98.4±6.8) with Cardiovascular Risk (Rcv) by AC and 24.3% (29.7±3.45) with risk by BAI. As for GS 41.5% (27.1±6.39) is weak and 32.3% (33.3±6.3) is low Vo2max. According to independence tests with χ² there is association between the G and BMI (χ²=1452.1, df = 1427, p-value=0. 315), G and AC (χ²=394.9, df = 382, p-value=0. 313), G and Vo2max (χ²=155.5, df = 6, p-value&amp;lt;2.2e-16), G and BAI (χ²=2970.3, df = 1502, p-value&amp;lt;2.2e-16), G and GS (χ²=6015.5, df = 1502, p-value&amp;lt;2.2e-16). This project was approved by the bioethics committee. Conclusions 149 men corresponding to 30.7% of the sample present an increased possibility of Rcv, despite compliance with global PA recommendations. It is recommended that PA programs reinforce the improvement and promotion of PC to prevent possible Rcv. Key messages • The capacities that define physical fitness (FC) such as strength and endurance favor functional independence and disease prevention (Melo, 2014). • Apparently healthy men in Colombia present a higher possibility of Cardiovascular Risk due to low levels of physical fitness, despite compliance with global BP recommendations.

About Air Quality Assessment using Time Series Analysis Techniques on Air Particles Data

This study investigates the dynamics of air pollution caused by particulate matter (PM10 and PM2.5) in Omsk, Russia. Data collected from the Sensor.Community network between 2021 and 2023 were analyzed using time series analysis methods. The findings reveal a subtle weekly seasonality in the data, potentially attributed to fluctuations in industrial activity and traffic patterns throughout the week. Additionally, a concerning trend of deteriorating air quality was identified, characterized by increasing annual average concentrations of PM10 and PM2.5. The study employed various time series analysis techniques, including Empirical Cumulative Distribution Function (ECDF), Seasonal and Trend decomposition using Loess (STL), and autocorrelation function (ACF) analysis. These methods allowed for the visualization and examination of data distribution, trend identification, and seasonality detection. Furthermore, the Mann-Kendall test confirmed a statistically significant trend of increasing pollution levels over the three-year period. To enhance the accuracy of spatial analysis, data interpolation was performed using kriging with a Gaussian model. This method, compared to simple interpolation, provides a more precise assessment of the spatial distribution of pollutants. The study also implemented Long Short-Term Memory (LSTM) for forecasting hourly pollution values. LSTM exhibited promising results, demonstrating its potential for developing early warning systems, particularly when combined with meteorological data such as wind forecasts. The results highlight the need for effective measures to mitigate air pollution in Omsk and emphasize the importance of utilizing data from diverse sources, including official air quality monitoring stations, to ensure accuracy and reliability in air quality assessments.