Total factor productivity (TFP) serves as a critical indicator for measuring enterprise efficiency and technological progress. However, existing prediction methods often fail to distinguish genuine causal mechanisms from spurious correlations while neglecting inter-enterprise network dependencies. This study proposes a Causal-Temporal Graph Convolutional Network (CT-GCN) that integrates causal inference techniques with temporal graph convolutional networks for dynamic TFP prediction and optimization. The framework employs the Levinsohn-Petrin method for TFP estimation, double machine learning for causal effect identification, and constructs enterprise relationship graphs capturing supply chain linkages, geographic proximity, and technological similarity. Using panel data from 12,847 Chinese manufacturing enterprises spanning 2008-2022, empirical results demonstrate that CT-GCN achieves substantial prediction improvements over baseline models, with RMSE reductions exceeding 19%. The causal analysis identifies R&D investment, digital transformation, and human capital as genuine productivity drivers, with significant treatment effect heterogeneity across industry sectors, firm sizes, and regions. An optimization decision mechanism translates these insights into differentiated strategic recommendations. This research contributes a novel methodology bridging causal reasoning and deep learning for economic forecasting applications.

Stockout risk is a persistent challenge in supply chain management, undermining both operational efficiency and customer satisfaction. This study adopts a multi-method approach to investigate the causal effect of lead time on stockout risk by integrating causal inference techniques with predictive analytics. The proposed framework combines Propensity Score Matching (PSM), Instrumental Variables (IV-2SLS), Inverse Probability Weighting (IPW), and Doubly Robust Estimation (DRE) alongside machine learning (ML) algorithms and time series forecasting. Using a dataset of 20,000 supply chain incidents, the study estimates the Average Treatment Effect (ATE) and evaluates predictive model performance. PSM generated the most credible ATE (0.882), confirming a strong causal link between lead time and stockout risk. IV analysis using supplier distance as an instrument yielded a reduced and statistically insignificant ATE (0.5535, p = 0.3148), suggesting instrument weakness. Among ML models, Random Forest and LightGBM achieved superior predictive accuracy (R2 = 0.25; MSE = 0.736), while Moving Average forecasting effectively captured stockout patterns over time (R2 = 0.883). The findings identify PSM as the most robust technique for causal inference. This study advances the literature by integrating causal inference, ML, and time series methods, offering practical, data-driven insights to strengthen operational resilience and guide proactive inventory management.

Reliable paratransit services are essential for urban mobility, particularly for individuals with disabilities who depend on demand-responsive transportation. However, service inefficiencies in urban paratransit systems, such as travel time variability, congestion impacts, and scheduling constraints, continue to pose significant challenges. This study introduces a multitier analytical framework that integrates spatial–temporal modeling, machine learning–based outlier detection, and causal inference to systematically evaluate the reliability of paratransit services in an urban context. Leveraging trip transaction data from a metropolitan paratransit system, we develop the paratransit efficiency index (PEI) to assess travel time reliability at both system-wide and individual trip levels. We then analyze PEI's spatial–temporal variability using geographically and temporally weighted regression and identify outlier trips with high PEI using XGBoost to pinpoint service unreliability and systemic inefficiencies. Later, we utilize causal inference techniques to show that peak-hour pick-ups causally contribute to travel time inefficiency (a 19.4% relative increase in outlier probability), whereas subscription-based bookings causally improve service consistency (a 33.9% relative decrease). The findings provide actionable insights for urban planners and transit agencies to optimize scheduling, mitigate congestion effects, and explore innovative strategies such as integrating transportation network companies for high-cost or unreliable trips. By addressing critical urban transportation equity issues, this study offers data-driven solutions to enhance the efficiency and resilience of paratransit services in growing metropolitan areas.

Large language models (LLMs) have demonstrated remarkable capabilities in natural language processing. Their massive computational and memory requirements often necessitate cloud-based deployment, introducing challenges related to cost, latency, privacy, and network reliability. Deploying on-device LLMs alleviates these challenges, but is hindered by the severe resource constraints of edge hardware. This survey reviews efficient inference techniques for edge LLMs, with a focus on two key strategies of speculative decoding and model offloading. We categorize strategies into single-device and multi-device types, systematically analyzing the principles, recent advancements, implementations, and support within edge frameworks. Finally, we highlight the open challenges and future research directions that will advance the field of edge LLM inference.

Although the association between depressive symptoms and cardiovascular disease (CVD) has been extensively studied, evidence for a long-term causal relationship remains sparse. This research employed advanced causal inference techniques to evaluate this longitudinal effect and its potential reversibility. We analyzed data from 37,668 participants across three prospective cohorts: CHARLS (China), HRS (USA), and KLoSA (South Korea). Applying the Longitudinal Targeted Maximum Likelihood Estimation (LTMLE) method across five time points, we assessed the causal effect of depression (defined by CES-D scale cutoffs) on self-reported physician-diagnosed CVD. Subgroup analyses were conducted by gender and age. Multiple sensitivity analyses were conducted to validate the robustness of the findings. Across all cohorts, the risk of CVD significantly increased with longer follow-up durations under persistent depressive symptoms. For example, in CHARLS, the adjusted odds ratio (OR) increased from 1.570 (95% CI: 1.398-1.798) at Year 2 to 2.097 (95% CI: 1.659-2.651) by Year 9. Further analysis of different exposure sequences of depressive symptoms revealed that the risk of CVD increased gradually with a greater cumulative number of waves with depressive symptoms, whereas it decreased correspondingly with more waves without depressive symptoms, demonstrating a pattern consistent with reversible association. This multi-cohort study provides evidence for a longitudinal causal relationship between depressive symptoms and CVD, showing temporal cumulative effect and a risk pattern consistent with reversible association. These results highlight the need to integrate mental health care into CVD prevention.

This systematic review follows PRISMA 2020 guidelines to identify whether measurable impacts have been observed following urban air quality interventions targeting private road users. A structured search was conducted on Scopus in February 2025, identifying 2088 studies. After applying strict inclusion criteria - requiring studies to examine urban-scale air quality interventions, target private road users, and apply quantitative ex post causal inference techniques - 59 studies were included for review. Our review examines publication trends, geographic focus, outlets, methods, key variables, and overall findings, classifying impacts on air quality, economic, behavioural, and health outcomes as positive, mixed, or negative. We identify three intervention types: (1) vehicle bans by type/time, (2) access charges for urban areas, and (3) fines for non-compliant vehicles. When splitting the papers by intervention type, outcome studied, and categorisation of impact, sample sizes become small. Only for intervention types (1) and (3), is there a sample of ≥ 10 studies examining the impacts on one outcome: air quality. Of these papers, a higher proportion examining fines for non-compliance found positive effects on air quality. While studies commonly report improvements in air quality and health, results are mixed for behavioural and economic variables. This review provides an up-to-date synthesis of policy effectiveness and highlights methodological and geographic gaps in the literature, supporting future evidence-based policy design.

Reconstructing past climate conditions in boreal ecosystems remains a complex challenge due to the intricate interactions between both external and internal forcings, ecological dynamics, and methodological constraints. In this study, we present pollen- and chironomid-based temperature reconstructions from five boreal forest sites in eastern Canada, assessing their sensitivities, limitations, and potential for improving paleoclimatic interpretations. By applying multiple inference techniques and evaluating their reliability through statistical indices, we identify key internal factors that influence reconstruction accuracy. Our findings reveal that pollen-based temperature estimates are affected by multiple biases, including the impact of forest fires on vegetation dynamics, postglacial migration lags, and uncertainties in the temperature optima of overrepresented taxa. These biases vary considerably across different vegetation zones. Chironomid-based reconstructions, in contrast, generally exhibit stronger alignment with regional climate trends, but may be sensitive to local, lake-specific conditions. Integrating these insights, we refine the Holocene climatic history of eastern Canada, reconciling discrepancies with previous studies and producing more robust estimates of temperature variations during key climatic intervals, including the deglaciation, the Holocene Thermal Maximum, and the Neoglacial Period. These results enhance our understanding of past climate variability in boreal environments and provide a critical foundation for assessing future ecological responses to ongoing climate change. • Pollen- and chironomid-based temperature inferences reveal notable discrepancies. • Forest fires bias pollen-based temperature inferences by altering vegetation dynamics. • Postglacial migration lags distort pollen-based temperature inferences. • Chironomid reconstructions are sensitive to local, within-lake conditions. • Multi-proxy approaches refine Holocene climate reconstructions in eastern Canada.

ABSTRACTThe ProblemTransportability considerations are increasingly important to answer research questions in comparative effectiveness research (CER) to support the transfer of evidence on medicinal products across countries or settings. As drug development costs rise and healthcare systems and professionals face economic and resource pressures, leveraging existing data and evidence generated across borders or settings can improve efficiency and inform decisions in product development and decision‐making (regulatory, health technology assessment [HTA] and clinical care). Differences in population characteristics, healthcare systems, and data availability, including coding discrepancies, may present significant challenges to the transportability of CER evidence. Without rigorous methodological approaches, the utility of transportability analyses is limited.What we DidThis article provides a structured framework for considering transportability exercises in CER analyses. We outlined key methodological principles, when and why to use transportability exercises in CER, feasibility assessments including effect modifier identification and causal inference techniques such as weighting, outcome regression, and combined methods to guide transportability analytical approaches in CER. By synthesizing existing literature and expert insights, we identified opportunities and trade‐offs in applying transportability methods to support decisions across the product lifecycle.Strategies to Disseminate and Facilitate UseTo enhance the adoption of transportability analyses, we proposed best practices for researchers, regulators, HTA bodies, and industry stakeholders. These include early engagement with regulatory agencies and HTA bodies, transparent documentation of data assumptions, quality, fitness, and comparability assessments while ensuring robust analytical approaches. We also emphasized the need for standardized reporting guidelines and cross‐country collaborations to validate transportability methods in real‐world settings and communicate uncertainty in transported evidence.ConclusionsTransportability analyses offer a powerful tool for extending the applicability of CER findings across healthcare systems, improving evidence generation efficiency, and supporting global drug development and evaluation. By implementing best practices that promote a rigorous and transparent approach to the design and conduct of such analyses, stakeholders can maximize the value of transported treatment effects while ensuring scientific rigor and decision‐making relevance. Future research should focus on empirical testing and validation of transportability methods targeting different questions across the product lifecycle and the development of harmonized regulatory and HTA methodological standards. “This manuscript is endorsed by the International Society for Pharmacoepidemiology (ISPE).” Official Endorsement was received on 5/13/26.

Retrospective study using causal inference techniques. To apply causal inference techniques and a single-surgeon study design to more effectively address confounding by indication inherent to prior research on instrumented vs non-instrumented fusion in elderly patients. We hypothesized that non-instrumented fusion would be associated with lower rates of reoperation at two years. There has been renewed interest in non-instrumented approaches in the context of payment reform and increased sensitivity to the impact of high intensity surgery on elderly patients and those with frailty. Previously published randomized trials on instrumented vs non-instrumented procedures are not informative for elderly individuals and those with frailty. We identified individuals 65 and older who received instrumented, or non-instrumented, decompression and fusion for degenerative lumbar indications in a single surgeon practice. The primary outcome was reoperation within two years of surgery. The primary predictor was instrumented versus non-instrumented fusion. To account for confounding by indication in the decision to use instrumentation, we used propensity-score weighting that accounted for age, biologic sex, body mass index, co-morbidities, the number of levels decompressed and the number of levels fused. This study included 248 patients; 181 who underwent instrumented fusion and 67 who received non-instrumented fusion. Following propensity-score weighting, non-instrumented fusion was significantly associated with increased odds of reoperation (OR 1.83; 95% CI 1.05, 3.25; P=0.04). When limiting consideration to reoperations performed for mechanical failure, adjacent segment degeneration or symptom recurrence/incomplete resolution there was no significant difference in reoperation (OR 0.86; 95% CI 0.39, 1.84; P=0.69). When accounting for selection and indication bias, instrumented fusion results in a significantly lower rate of reoperation even in those with more advanced age and frailty. We believe that the use of instrumentation represents the preferred approach when fusion is indicated except in rare situations. III.

Background and Objectives: Whether hyperglycaemia causes hypertension, hypertension worsens glycaemic control, or both conditions arise from shared metabolic drivers remains clinically consequential yet unresolved. This study applies a triangulated causal inference framework to large-scale population data to quantify the direction, magnitude, and robustness of the glucose–blood pressure relationship. The primary objective is to test for bidirectional causal effects between glycaemic status and blood pressure; secondary objectives include quantifying effect magnitudes by multiple complementary methods and assessing robustness to unmeasured confounding. Materials and Methods: We analysed 55,386 adults from the National Health and Nutrition Examination Survey (NHANES, 1999–2023). Multiple causal inference techniques were integrated: directed acyclic graph (DAG) testing, structural equation modelling (SEM) with latent constructs, propensity score matching (PSM), inverse probability weighting (IPW), doubly robust augmented IPW (AIPW), and E-value/Rosenbaum Γ sensitivity analyses, with external replication in the Framingham Heart Study data (n = 4240). Results: All of the methods used confirmed the bidirectional effects. PSM showed that hyperglycaemia increased systolic BP by 1.76 mmHg (95% CI: 0.58–2.96, p = 0.005), and hypertension increased fasting glucose by 6.55 mg/dL (95% CI: 4.61–8.58, p < 0.001), revealing a marked asymmetry favouring the BP → glucose direction. AIPW confirmed both effects (3.51 mmHg and 6.15 mg/dL, both p < 0.001). SEM identified significant bidirectional structural paths between latent glycaemic and blood-pressure constructs, with the Glycaemic → BPState path showing a negative coefficient (β = −0.15, p = 0.043), a sign reversal attributable to conditioning on the shared latent metabolic-syndrome factor. Sensitivity analyses indicated that an unmeasured confounder would need associations of RR ≥ 1.40–1.64 with both exposure and outcome to nullify these estimates, representing moderate robustness. Conclusions: The BP → glucose pathway is the dominant causal direction, suggesting that prioritisation of hypertension control may yield underappreciated benefits for glycaemic regulation. These findings support integrated cardiometabolic management strategies.

State-dependent fornix-hippocampal communication and the impact of deep brain stimulation: Insights from supervised learning, granger causality and causal discovery analyses.

Rivers in industrial regions face significant pressure from anthropogenic activities, often resulting in degraded water quality. This study investigates long-term water quality dynamics of the Damodar River in West Bengal, India, using a multi-index approach and advanced statistics. Six established Water Quality Indices (WQIs) were computed using monthly data from 2014 to 2024 across ten monitoring sites. To reconcile the inconsistencies among individual indices, Principal Component Analysis (PCA) was applied to generate a unified metric termed the Principal Component Averaged WQI (PCAWQI). Furthermore, to quantify the causal impact of the COVID-19 lockdown (March-May 2020) on river health, we employed a Regression Discontinuity Design (RDD) using Bayesian structural time-series modeling (CausalImpact). The composite PCAWQI successfully captured spatial and temporal pollution gradients, highlighting critical midstream deterioration. Additionally, site-specific improvements in water quality were observed during the lockdown, with some sites exhibiting significant gains likely due to industrial inactivity. However, heterogeneous responses underscored the influence of socio-cultural and hydrological factors. Thus, by integrating dimensionality reduction and causal inference techniques, we developed a robust and replicable framework for water quality assessment. This framework can be utilized for environmental monitoring and policy evaluation in heavily industrialized river basins.

BackgroundDementia presents complex challenges for causal inference due to its multifactorial aetiology and slow, heterogeneous progression. Randomized controlled trials are often limited in their potential to fully address these challenges because of ethical and practical constraints. As the field evolves, observational studies incorporating advanced causal inference methods are increasingly used to estimate real-world effects in dementia research. However, the implementation of these methods varies widely and has not been systematically evaluated, with an emerging trend towards integration with techniques such as machine learning. This systematic review will critically examine how causal inference techniques are applied in dementia research, assess their methodological rigor, and identify trends, assumptions, and gaps that may inform future applications and methodological innovation in the field.MethodsFollowing PRISMA guidelines, searches will be conducted in MEDLINE, EMBASE, Web of Science, PsycINFO, Scopus, and the Cochrane Library for studies published between 1960 and 2024. Eligible studies will include observational designs that use causal inference methods to investigate outcomes such as cognitive decline, disease progression, and quality of life. Data extraction will capture study characteristics, methodological details, and key findings, with risk of bias assessed using ROBINS-I. A narrative synthesis will summarize qualitative results, and meta-analyses will be performed when methodological homogeneity permits.DiscussionThis review will address a critical gap in the evaluation of the application of causal inference methods in real-world dementia research. By identifying methodological challenges, underlying assumptions, and emerging analytical techniques, it aims to strengthen research rigor and reproducibility and inform future methodological development, with potential implications for policy and practice in dementia care.Systematic review registrationPROSPERO (CRD42024619228).Supplementary InformationThe online version contains supplementary material available at 10.1186/s13643-026-03179-w.

We investigated the potential of nature-based solutions within the context of agriculture conservation practices (ACPs) that impact watershed hydrology and water quality in Shell Creek, Nebraska, USA. This region serves as an example of a successful watershed conversion driven by the collaboration of local stakeholders and government agencies, which also offers valuable solutions for addressing future climate challenges. We utilized a high-resolution remote sensing data covering a wide range of attributes, including continuous land cover, winter vegetation health, and summer cropping, and supplemented it with hydrometeorological and water quantity and quality data. The implementation patterns of ACPs and changes in water quantity and quality were studied using trend analysis. The data were then analyzed using explainable Artificial Intelligence and causal inference techniques to understand how ACPs lead to changes in water quantity and quality attributes. In addition, we carried out flood frequency analysis to assess the impact of ACPs on extreme flows. The findings suggested that winter cover cropping has extensively increased over the past 30 years. The health of winter vegetation also significantly improved, although there was an intensification in summer cropping. In the context of water quantity, extreme flood events have become less frequent. Results also showed a noticeable decrease in turbidity, total suspended solids concentration, and total phosphorus concentration. However, these changes were not statistically significant. The overall findings suggest that different nature-based solutions have increased in recent decades and have contributed to improvements in water quality and reductions in flood frequency in the watershed.

Malnutrition, including overnutrition, undernutrition, and micronutrient deficiency, remains a major global public health challenge, closely linked to food insecurity. Among children, micronutrient deficiencies can impair cognitive development, making effective national policies vital to guide in-school micronutrient supplementation within school meal programs. This study aimed to assess how national policies on school feeding, nutrition, health, food safety, agriculture, and private sector engagement influence the implementation of micronutrient supplementation in school meal programs across countries. The study employed the Bayesian Mindsponge Framework, which combines the Granular Interaction Thinking Theory with Bayesian inference techniques. A dataset comprising responses from 126 government representatives (n = 126) responsible for large-scale school meal programs across 126 countries was analyzed to estimate the effects of various national policy domains on micronutrient supplementation outcomes. Findings revealed that school feeding policies have a small but positive effect on the implementation of micronutrient supplementation (β = 0.12, SD = 0.10). In contrast, nutrition policies exhibit a slight negative association (β = -0.12, SD = 0.10). Other policies, including those related to health, food safety, agriculture, and the private sector, demonstrated minimal or negligible influence. The study underscores the positive contribution of school feeding policies in promoting micronutrient supplementation within school meal programs. However, the negative association of nutrition policies suggests the need for critical policy reassessment to ensure coherence and effectiveness. Strengthening cross-sectoral linkages, particularly among health, food safety, agriculture, and private sector policies, may further enhance micronutrient intake and improve child health outcomes globally.

Early Detection of Diabetes with Quantum Machine Learning and Causal Inference Techniques

The increasing use of schemaless data systems has intensified the need for reliable methods to assess the quality of extracted schemas intended for downstream tasks such as data integration, query optimisation, and interoperability. Although numerous schema inference techniques have been proposed, the field still lacks standardised and method-independent criteria for evaluating the validity and accuracy of inferred schemas. This paper introduces the Schema Validation and Evaluation Framework (SVEF), a systematic evaluation model for assessing extracted schemas across six complementary dimensions that capture essential structural and semantic properties: Data Type Accuracy, Required and Optional Fields, Multiple Type Support, Collection Structure Consistency, Entity Relationships, and Temporal Evolution Detection. Each dimension is defined through formal, data-driven metrics that quantify the degree to which an inferred schema reflects characteristics observed in the underlying dataset. In the present study, the framework is instantiated and evaluated for schemaless document-oriented data represented in JSON or JSON-like form. SVEF is evaluated using controlled benchmark datasets with curated ground-truth schemas and is applied to three representative schema extraction approaches. The results show that, while existing methods achieve strong performance in basic type reconstruction, substantial differences remain in modelling conditional fields, complex collection structures, and schema evolution over time. SVEF provides a consistent and interpretable basis for comparing schema extraction strategies and supports more rigorous empirical analysis of their behaviour in dynamic document-oriented data environments.

Type of the article: Research ArticleAbstractArtificial intelligence is shaping digital governance, with global organizations emphasizing its opportunities and risks for public administration. The study aims to assess whether advancements in AI, measured by the AI Vibrancy Score (AIVS) and the Government AI Readiness Index (GAIRI), drive improvements in the E-Government Development Index (EGDI). Using panel data methods, the analysis draws on data from 36 countries for 2018–2022 (AIVS–EGDI) and 170 countries for 2020–2024 (GAIRI–EGDI), due to differing data availability and indicator coverage periods, applying fixed effects, random effects, and Mundlak specifications, combined with robust inference techniques. The results demonstrate that within-country improvements in AI readiness are positively and robustly associated with higher levels of e-government development, with the FE estimate for the Government AI Readiness Index equal to 0.17 (p &amp;amp;lt; 0.001). RE models reveal stronger cross-country correlations, with coefficients of 2.55 (p &amp;amp;lt; 0.001) for the AI Vibrancy Score and 0.35 (p &amp;amp;lt; 0.001) for AI readiness. However, Mundlak (correlated RE) specifications indicate that the between-country components are statistically insignificant. Yet, the within-country effects remain significant, suggesting that dynamic national reforms and policy-driven progress outweigh inherited structural advantages. Time effects are pronounced, with positive and significant shifts in 2020 (+7.02) and 2022 (+8.10) relative to the baseline year, reflecting the acceleration of digital public administration during the post-pandemic period. Country-specific effects exhibit substantial heterogeneity, ranging from strongly positive deviations (e.g., Denmark, Estonia, Korea) to persistently negative ones (e.g., India, South Africa), underscoring the uneven national trajectories. Robustness checks using clustered standard errors confirm the stability of all key coefficients.AcknowledgmentThis paper was prepared based on the results of a study funded by the Ministry of Education and Science of Ukraine entitled “Digitalization of the public-private partnership system as a driver of the state’s economic security in the war and post-war periods” (registration number: 0126U000543).

Understanding the source of the universe’s asymmetry between matter and antimatter is one of the major open questions in particle physics. In this work, the sensitivity of novel machine-learning-based inference techniques to C P -odd and C P -even H W W anomalous couplings is studied in the W H → ℓ ν b b ¯ channel ( ℓ = e , μ ), within the standard model effective field theory framework. Two machine-learning simulation-based inference (SBI) methods are explored: a per-event likelihood-ratio estimator, which directly approximates the ratio of probability densities between competing hypotheses, is benchmarked against a per-event optimal-observable estimator optimized for sensitivity to the parameters of interest. Both approaches are also compared to traditional summary statistics, in this case histograms of kinematic and angular observables, as commonly used in experimental analyses. SBI methods provide tighter constraints than one-dimensional summary statistics, though their performance is comparable to two-dimensional histogram analysis. The optimal-observable approach remains promising for its ability to probe multiple couplings simultaneously. Restricting the analysis to a region of high S / B also enhances sensitivity to C P -odd operators while preserving sensitivity to C P -even operators, which histogram analyses often lose. Although the likelihood-ratio estimator sometimes struggles with likelihood minima and shapes, optimizations that target its robustness could make it more sensitive than both the optimal-observable estimator and the histogram method. These results underscore the potential of advanced simulation-based inference techniques, encouraging further exploration with LHC Run 3 data to surpass current ATLAS and CMS sensitivities.

Abstract Latent Gaussian processes are widely used in latent variable models because they offer a flexible nonlinear mapping from a low-dimensional latent space to a high-dimensional space via Gaussian processes. However, these models are computationally intensive and do not scale well. In this paper, we propose a temporal categorical model that utilizes latent Gaussian processes, inducing-input approximation, and a regularization framework to model multivariate categorical processes, with and without priors on hyperparameters. We analyze the underlying properties and introduce two variational inference approaches: one based on a Monte Carlo method and the other on the delta method. We also found that latent dynamics tend to collapse into a constant zero, which hinders the reflection of dynamic information. To address this, we propose two strategies to regularize the latent dynamics for better alignment with observation dynamics: introducing a regularization term based on inducing variables and incorporating a scale prior for latent Gaussian processes. Additionally, we propose an efficient and effective stochastic variational inference technique. Finally, we demonstrate our model and inference methods using both synthetic data and real financial data.