Conditional Probability Model Research Articles

Extended Bayesian inference incorporating symmetry bias

We start by proposing a causal induction model that incorporates symmetry bias. This model has two parameters that control the strength of symmetry bias and includes conditional probability and conventional models of causal induction as special cases. We calculated the determination coefficients between assessments by participants in eight types of causal induction experiments and the estimated values using the proposed model. The mean coefficient of determination was 0.93. Thus, it can reproduce causal induction of human judgment with high accuracy. We further propose a human-like Bayesian inference method to replace the conditional probability in Bayesian inference with the aforementioned causal induction model. In this method, two components coexist: the component of Bayesian inference, which updates the degree of confidence for each hypothesis, and the component of inverse Bayesian inference that modifies the model of each hypothesis. In other words, this method allows not only inference but also simultaneous learning. Our study demonstrates that the method addresses unsteady situations where the target of inference occasionally changes not only by making inferences based on knowledge (model) and observation data, but also by modifying the model itself.

Subthalamic nucleus activity dynamics and limb movement prediction in Parkinson's disease.

Whilst exaggerated bursts of beta frequency band oscillatory synchronization in the subthalamic nucleus have been associated with motor impairment in Parkinson's disease, a plausible mechanism linking the two phenomena has been lacking. Here we test the hypothesis that increased synchronization denoted by beta bursting might compromise information coding capacity in basal ganglia networks. To this end we recorded local field potential activity in the subthalamic nucleus of 18 patients with Parkinson's disease as they executed cued upper and lower limb movements. We used the accuracy of local field potential-based classification of the limb to be moved on each trial as an index of the information held by the system with respect to intended action. Machine learning using the naïve Bayes conditional probability model was used for classification. Local field potential dynamics allowed accurate prediction of intended movements well ahead of their execution, with an area under the receiver operator characteristic curve of 0.80 ± 0.04 before imperative cues when the demanded action was known ahead of time. The presence of bursts of local field potential activity in the alpha, and even more so, in the beta frequency band significantly compromised the prediction of the limb to be moved. We conclude that low frequency bursts, particularly those in the beta band, restrict the capacity of the basal ganglia system to encode physiologically relevant information about intended actions. The current findings are also important as they suggest that local subthalamic activity may potentially be decoded to enable effector selection, in addition to force control in restorative brain-machine interface applications.

Propagation thresholds of meteorological drought for triggering hydrological drought at various levels

What the extent of meteorological drought could trigger the corresponding hydrological drought with different levels? This question is an important topic in the field of drought propagation, which however has not been resolved. Therefore, a novel model based on a Bayesian network was proposed to address this issue in this study. In this model, the drought pooling and excluding methods were applied to eliminate minor drought events. A drought matching approach based on drought propagation time was proposed to achieve the one by one matching between different types of drought. Moreover, based on the matched drought events and the copula-based conditional probability model, the drought propagation thresholds of meteorological drought for triggering hydrological drought at various levels were determined. In addition, the interval conditional probability was calculated to further explore the sensitivity of hydrological drought response to different meteorological drought conditions. Furthermore, the propagation ratio was proposed to characterize the differences of drought propagation threshold among various regions. The Wei River Basin was selected as a case study. Results indicated that the results of drought propagation threshold were reliable and accurate. The increase of interval conditional probability showed a typical S-curve, which can intuitively obtain the probability of hydrological drought occurrence at different levels under specific meteorological drought condition, so as to effectively guide drought preparedness and mitigation. The propagation ratio can describe the overall resistance of the basin to meteorological drought, and it mainly depended on the meteorological and underlying surface conditions as well as groundwater supply.

Sensitivity analysis of Bayesian networks to parameters of the conditional probability model using a Beta regression approach

Ensuring the validity and credibility of Bayesian Belief Network (BBN) as a modelling tool for expert systems requires appropriate methods for sensitivity analysis (SA), in order to test the robustness of the BBN diagnostic and prognostic with respect to the parameterisation of the conditional probability model (CPM). Yet, the most widely used techniques (based on sensitivity functions for discrete BBNs) only provide a local insight on the CPM influence, i.e. by varying only one CPM parameter at a time (or a few of them) while keeping the other ones unchanged. To overcome this limitation, the present study proposes an approach for global SA relying on Beta Regression using gradient boosting (potentially combined with stability selection analysis): it presents the benefit of keeping the presentation intuitive through a graph-based approach, while being applicable to a large number of CPM parameters. The implementation of this approach is investigated for three cases, which cover a large spectrum of situations: (1) a small discrete BBN, used to capture medical knowledge, demonstrates the proposed approach; (2) a linear Gaussian BBN, used to assess the damage of reinforced concrete structures, exemplifies a case where the number of parameters is too large to be easily processed and interpreted (>40 parameters); (3) a discrete BBN, used for reliability analysis of nuclear power plant, exemplifies a case where analytical solutions for sensitivity can hardly be derived. Finally, provided that the validity of the BBR model is carefully checked, we show that the proposed approach can provide richer information than traditional SA methods at different levels: (i) it selects the most influential parameters; (ii) it provides the functional relation between the CPM parameter and the result of the probabilistic query; and (iii) it identifies how the CPM parameters can lead to situations of high probability, while quantifying the confidence in the occurrence of these situations.

Modeling the Optimal Transportation for Acute Stroke Treatment: The Impact of the Drip-and-Drive Paradigm.

Background and Purpose- Health systems are faced with the challenge of ensuring fast access to appropriate therapy for patients with acute stroke. The paradigms primarily discussed are mothership and drip and ship. Less attention has been focused on the drip-and-drive (DD) paradigm. Our aim was to analyze whether and under what conditions DD would predict the greatest probability of good outcome for patients with suspected ischemic stroke in Northwestern Germany. Methods- Conditional probability models based on the decay curves for endovascular therapy and intravenous thrombolysis were created to determine the best transport paradigm, and results were displayed using map visualizations. Our study area consisted of the federal states of Lower Saxony, Hamburg, and Schleswig-Holstein in Northwestern Germany covering an area of 64 065 km2 with a population of 12 703 561 in 2017 (198 persons per km2). In several scenarios, the catchment area, that is, the region that would result in the greatest probability of good outcomes, was calculated for each of the mothership, drip-and-ship, and the DD paradigms. Several different treatment time parameters were varied including onset-to-first-medical-response time, ambulance-on-scene time, door-to-needle time at primary stroke center, needle-to-door time, door-to-needle time at comprehensive stroke center, door-to-groin-puncture time, needle-to-interventionalist-leave time, and interventionalist-arrival-to-groin-puncture time. Results- The mothership paradigm had the largest catchment area; however, the DD catchment area was larger than the drip-and-ship catchment area so long as the needle-to-interventionalist-leave time and the interventionalist-arrival-to-groin-puncture time remain <40 minutes each. A slowed workflow in the DD paradigm resulted in a decrease of the DD catchment area to 1221 km2 (2%). Conclusions- Our study suggests the largest catchment area for the mothership paradigm and a larger catchment area of DD paradigm compared with the drip-and-ship paradigm in Northwestern Germany in most scenarios. The existence of different paradigms allows the spread of capacities, shares the cost and hospital income, and gives primary stroke centers the possibility to provide endovascular therapy services 24/7.

Statistical Prediction for Annual Start Date and Duration of Sea-Ice Coverage at Qinhuangdao Observation Station

Qinhuangdao City is located in the mid-latitude monsoon-affected region, and the timing of sea-ice coverage changes from year to year, making sea-ice forecasting difficult. In this paper, we propose a statistical model using the 1980–2013 data collected at the Qinhuangdao observation station. The start date and the duration of ice coverage are fitted with four marginal distributions, from which the best-fitted, i.e., the Weibull distribution, is selected to form a joint probability density function (PDF), built by the Gaussian copula method, for the two variables. With a given start date forecast by the Gray-Markov model (GMM), the joint PDF becomes a conditional probability model, which predicts that the duration of ice coverage is most likely 33 days at the Qinhuangdao observation station in 2014–2015. The predicted duration value is only two days less than the actual situation. The results prove that the new prediction model is feasible and effective to predict the period of ice coverage. The general sea-ice conditions that the sea ice would most likely form on December 8 and last for 80 days at the Qinhuangdao observation station could also be obtained from the joint PDF. The statistical model provides a useful tool to forecast ice conditions for planning and management of maritime activities.

Evaluation of earthquake recurrences with different distribution models in western Anatolia

The last two strong earthquakes, 21 July 2017 Bodrum-Kos (Mw = 6.5) and 12 June 2017 Karaburun-Aegean Sea (Mw = 6.2), indicate that western Anatolia (Aegean region) is seismo-tectonically active and has experienced several destructive earthquakes. Therefore, we aim to evaluate the seismic hazard of two study regions in western Anatolia by calculating conditional probabilities of earthquake (M ≥ 5.5) recurrences according to exponential, Weibull, gamma, log-normal, and Rayleigh distribution models. The study data include earthquakes (M ≥ 5.5) that occurred in the study regions from 1900 to 2018. We calculate the distribution model parameters with maximum likelihood estimates by using the inter-event time of earthquake recurrences. The fittings of the models with data are tested with the selection criteria, which are the lnL, the Akaike information criterion, Bayesian information criteria, and the Kolmogorov–Smirnov minimum distance criterion. After evaluating these selection criteria, the best fit is provided by the log-normal distribution model and the poorest fit is from the Rayleigh distribution model in both regions. The exponential, Weibull, and log-normal model conditional probability results (> 0.50) are close in the two regions (2017, te = 0 and 2020–2042, 3 ≤ t ≤ 25). The gamma distribution conditional probability gives the highest values. The minimum conditional probability value begins at 0.10 for the Rayleigh distribution model. According to the different distribution models in the study, the conditional probability results contribute to seismic hazard assessment in the regions.

AL: autogenerating supervised learning programs

We present AL, a novel automated machine learning system that learns to generate new supervised learning pipelines from an existing corpus of supervised learning programs. In contrast to existing automated machine learning tools, which typically implement a search over manually selected machine learning functions and classes, AL learns to identify the relevant classes in an API by analyzing dynamic program traces that use the target machine learning library. AL constructs a conditional probability model from these traces to estimate the likelihood of the generated supervised learning pipelines and uses this model to guide the search to generate pipelines for new datasets. Our evaluation shows that AL can produce successful pipelines for datasets that previous systems fail to process and produces pipelines with comparable predictive performance for datasets that previous systems process successfully.

Quantification of the forecast uncertainty using conditional probability and updating models

Abstract Quantifying forecast uncertainty is of great importance for reservoir operation and flood control. However, deterministic hydrological forecasts do not consider forecast uncertainty. This study develops a conditional probability model based on copulas to quantify forecast uncertainty. Three updating models, namely auto-regressive (AR) model, AR exogenous input model, and adaptive neuro fuzzy inference system model, are applied to update raw deterministic inflow forecasts of the Three Gorges Reservoir on the Yangtze River, China with lead times of 1d, 2d, and 3d. Results show that the conditional probability model provides a reasonable and reliable forecast interval. The updating models both enhance the forecast accuracy and improve the reliability of probabilistic forecasts. The conditional probability model based on copula functions is a useful tool to describe and quantify forecast uncertainty, and using an updating model is an effective measure to improve the accuracy and reliability of probabilistic forecast.

Controlled Synthesis of Hyperbranched Poly (ester)s From Biorenewable Monomers for the Delivery of Therapeutic Agents

A series of hyperbranched poly(ester)s (HBPEs) has been prepared from renewable bio monomers using the Macosko-Miller conditional probability model (appropriate for monomers containing functional groups of unequal reactivity) to select ratios of reactants (ratios of reactive functional groups) to permit high monomer conversion without gelation and to assure the presence of specific reactive end groups.

Conditional probability-based ensemble learning for indoor landmark localization

Indoor location awareness enables many location-based services, such as smart homes or smart offices. The huge amount of sensor data collected by nowadays’ smartphones provides a solid basis for applying advanced machine learning algorithms to derive the correlation between indoor locations and sensor measurements. The combination of multiple sensor measurements, such as the Received Signal Strength of surrounding Wi-Fi access points and magnetic fields, is assumed to be unique in many locations, which can be derived to accurately predict smartphones’ indoor locations. In this work, we propose a novel ensemble learning method to provide room level indoor localization in smart buildings. The proposal is based on a conditional probability model, which combines prediction results of multiple individual machine learning predictors using conditional probability concepts to predict class labels. We have implemented the system on Android smartphones and conducted extensive experiments in real-world office-like environments. The experiment results show that the proposed ensemble predictor outperforms individual and ensemble voting-based machine learning algorithms. It achieves the best indoor landmark localization accuracy of nearly 97% in office-like environments. This work provides a coarse-grained indoor room recognition, which can be envisioned as a basis for accurate indoor positioning.

Improving causal determination

Holistic expert judgments about causality are widely used in regulatory risk assessments, with causal determination categories being used to summarize huge amounts of complex evidence and to help inform and drive major regulatory decisions. The causal determination categories used typically cover a relatively narrow range (e.g., from “causal relationship,” “likely to be a causal relationship,” or “suggestive of a causal relationship” to “inadequate to infer a causal relationship” and “not likely to be a causal relationship”). Other categories, such as “not a causal relationship” or “likely to not be a causal relationship,” are omitted entirely. We note fundamental limitations of such procedures. A few categories cannot encode most of the wide variations in evidence about risks and causal exposure-response relationships found in both theory and practice. “Causal relationship” is usually left undefined, and may be interpreted very differently by different people. Whether it refers to direct, indirect, or total causal effects is seldom specified. We propose that causal partial dependence plots of predicted risk against exposure, calculated from conditional probability tables (CPTs) or models that satisfy an empirically testable condition of invariant causal prediction (ICP) across studies, can provide much more useful and clearly defined information to decision-makers. This alternative framework treats causal relationships, and evidence about them, as continuous and quantitative rather than categorical and qualitative. This is not only advantageous for clarity and realism, but it encourages better use of data and scientific method, including applying independently verifiable tests to inform conclusions about how and whether changes in exposures would change individual and population health risks.

Application of the GIS-Based Probabilistic Models for Mapping the Flood Susceptibility in Bansloi Sub-basin of Ganga-Bhagirathi River and Their Comparison

Flood is one of the devastating environmental hazards, causes massive economic breakdown and enormous loss of life, and destructs the houses in the affected areas. The present work intends to prepare the spatial flood susceptibility maps (FSMs) applying the probabilistic models, viz, frequency ratio (FR), weights of evidence (WoE), Shannon’s entropy (SE), conditional probability (CP), and certainty factor (CF) and find out the most effective model among them. A supervised neural network technique, i.e., learning vector quantization (LVQ) algorithm, has been employed to trace the involvement of conditioning factors for flood occurrences. For this work, twelve morphological, hydrological, and lithological flood conditioning factors, i.e., elevation, slope steepness, drainage density, distance from the river, plan curvature, topographical wetness index, stream power index, rainfall, normalized difference vegetation index, normalized difference water index, lithology, and land use/land cover, have been employed in the geographic information system (GIS) environment. Weights of each class of each factor have been computed through the four models except Shannon’s entropy, as it defines only factor weights. Finally, FSMs of each model are showing 9.61% (FR), 11.69% (WoE), 9.47% (SE), 11.17% (CF), and 10.99% (CP) areas of the basin under the most susceptible zone, respectively. The performances of the models have been evaluated using receiver operating characteristics (ROC) and seven statistical diagnostic tests. The results confirm that the CF and CP models are more adaptable than others. This flood-susceptible map can be used for flood management planning to prevent and lessen anticipated losses.

Multi-outcome longitudinal small area estimation – a case study

ABSTRACTA recent paper [Thibaudeau, Slud, and Gottschalck (2017). Modeling log-linear conditional probabilities for estimation in surveys. The Annals of Applied Statistics, 11, 680–697] proposed a ‘hybrid’ method of survey estimation combining coarsely cross-classified design-based survey-weighted totals in a population with loglinear or generalised-linear model-based conditional probabilities for cells in a finer cross-classification. The models were compared in weighted and unweighted forms on data from the US Survey of Income and Program Participation (SIPP), a large national longitudinal survey. The hybrid method was elaborated in a book-chapter [Thibaudeau, Slud, & Cheng (2019). Small-area estimation of cross-classified gross flows using longitudinal survey data. In P. Lynn (Ed.), Methodology of longitudinal surveys II. Wiley] about estimating gross flows in (two-period) longitudinal surveys, by considering fixed versus mixed effect versions of the conditional-probability models and allowing for 3 or more outcomes in the later-period categories used to define gross flows within generalised logistic regression models. The methodology provided for point and interval small-area estimation, specifically area-level two-period labour-status gross-flow estimation, illustrated on a US Current Population Survey (CPS) dataset of survey respondents in two successive months in 16 states. In the current paper, that data analysis is expanded in two ways: (i) by analysing the CPS dataset in greater detail, incorporating multiple random effects (slopes as well as intercepts), using predictive as well as likelihood metrics for model quality, and (ii) by showing how Bayesian computation (MCMC) provides insights concerning fixed- versus mixed-effect model predictions. The findings from fixed-effect analyses with state effects, from corresponding models with state random effects, and fom Bayes analysis of posteriors for the fixed state-effects with other model coefficients fixed, all confirm each other and support a model with normal random state effects, independent across states.

A Hybrid Metaheuristic of Integrating Estimation of Distribution Algorithm with Tabu Search for the Max-Mean Dispersion Problem

This paper presents a hybrid metaheuristic that combines estimation of distribution algorithm with tabu search (EDA-TS) for solving the max-mean dispersion problem. The proposed EDA-TS algorithm essentially alternates between an EDA procedure for search diversification and a tabu search procedure for search intensification. The designed EDA procedure maintains an elite set of high quality solutions, based on which a conditional preference probability model is built for generating new diversified solutions. The tabu search procedure uses a fast 1-flip move operator for solution improvement. Experimental results on benchmark instances with variables ranging from 500 to 5000 disclose that our EDA-TS algorithm competes favorably with state-of-the-art algorithms in the literature. Additional analysis on the parameter sensitivity and the merit of the EDA procedure as well as the search balance between intensification and diversification sheds light on the effectiveness of the algorithm.

A Copula-Based Conditional Probabilistic Forecast Model for Wind Power Ramps

Efficient management of wind ramping characteristics can significantly reduce wind integration costs for balancing authorities. By considering the stochastic dependence of wind power ramp (WPR) features, this paper develops a conditional probabilistic WPR forecast (cp-WPRF) model based on copula theory. The WPRs dataset is constructed by extracting ramps from a large dataset of historical wind power. Each WPR feature (e.g., rate, magnitude, duration, and start-time) is separately forecasted by considering the coupling effects among different ramp features. To accurately model the marginal distributions with a copula, a Gaussian mixture model is adopted to characterize the WPR uncertainty and features. The Canonical maximum likelihood method is used to estimate parameters of the multivariable copula. The optimal copula model is chosen based on the Bayesian information criterion from each copula family. Finally, the best conditions based cp-WPRF model is determined by predictive interval based evaluation metrics. Numerical simulations on publicly available wind power data show that the developed copula-based cp-WPRF model can predict WPRs with a high level of reliability and sharpness.

Approximating the Partially Coherent Additive White Gaussian Noise Channel in Polar Coordinates

We consider the partially coherent additive white Gaussian noise channel (PCAWGN) in optical communications and review the derivation of the exact channel conditional probability model in a closed-form solution in polar coordinates. In addition, we derive a reduced-complexity approximation by replacing the Rician and Tikhonov distributions describing amplitude and phase components, respectively, with their Gaussian approximation under certain assumptions of high SNR and low phase noise or jitter . Our proposal significantly reduces the hardware complexity by removing the modified Bessel functions involved in the exact solution. Furthermore, we compare the proposed approximation with a different metric previously found in the literature and observe that for maximum-likelihood hard symbol decision, both models are in perfect agreement with the optimal detector. However, our model not only reduces the required number of multiplications from 12 to 8 and additions from 9 to 3 (per computed symbol) but also reduces the information loss by at least one and up to several orders of magnitude with respect to the previously published metric when used to compute the channel achievable information rate (AIR). In all the simulation cases, we use QAM constellations of orders 4, 8, 16, and 32 as test input symbol sets.

Regularized topic-aware latent influence propagation in dynamic relational networks

On social networks, investigating how the influence is propagated is crucial in understanding the network evolution and the social impact of different topics. In previous study, the influence propagation is either modeled based on the static network structure, or the infection between two connected users is recovered from some given event cascades. Unfortunately, existing solutions are incapable of identifying the user susceptibility delivered by user generated content. In this paper, we propose RegInfoIbp, a general regularized learning framework for modeling topic-aware influence propagation in dynamic network structures. Specifically, the observed time-sequential user topic preference and user adjacency information are factorized by the prior information reflected by a user-influential bipartite relation graph. The influence propagation is approximated with a nonparametric regularized Bayesian matrix factorization model with tractable polynomial complexity. and the influential users are identified by several sampling algorithms with slightly different approximation qualities. To further model dynamic temporal evolution, we construct Markov conditional probabilistic model on the compact latent feature representation. By integrating both topic and structure information into the regularized non-parametric probabilistic learning process, RegInfoIbp is more efficient and accurate in discovering the key factors in the content and influential users in dynamic network structure. Extensive experiments demonstrate that RegInfoIbp better adapts to real data, and achieves better approximation in influence propagation over existing approaches.

On the Failure Probability of Offshore Wind Turbines in the China Coastal Waters Due to Typhoons: A Case Study Using the OC4-DeepCwind Semisubmersible

The paper introduces a set of modeling methods to predict the failure probability of offshore wind turbines in the China coastal waters. In detail, a series of full-set three-dimensional meteorology simulations are conducted using the Weather Research and Forecast model to provide the extreme wind fields, while the extreme wave fields are predicted according to the conditional probability model. After the extreme wind and wave fields are prepared, the ultimate loads on the three critical parts of an OC4-DeepCwind semisubmersible wind turbine are simulated using the fatigue, aerodynamics, structures, and turbulence code, which in turn leads to the prediction of the failure probability. It has been found that the OC4-DeepCwind semisubmersible constructed in the Taiwan Strait has higher chance to fail under typhoon conditions than in other parts of the China coastal waters, showing a maximum failure probability of 0.6. In addition, the failure probabilities in the South and East China Sea are in the range of 0.3–0.45. The probability densities of the ultimate loads show, in some cases, a bimodal shape, which indicates that the loads as well as the failure probability are not in a simple linear relationship with the extreme wind speeds and wave heights/periods.

Analyzing High‐Frequency Soil Respiration Using a Probabilistic Model in a Semiarid, Mediterranean Climate

AbstractHigh‐frequency (subhourly) changes in soil respiration (Rs), a critical component of the carbon cycle, are not well documented in semiarid ecosystems. We investigate the response of Rs to subhourly soil temperature (Tsoil) and soil volumetric water content (VWC) variation in a semiarid ecosystem across a year of highly variable weather. We propose a probabilistic model to estimate the likelihood of Rs exceeding its annual mean (1.2 μmol CO2/m2s), conditioned on different Tsoil and VWC values. The results show that Rs follows a Gaussian‐like pattern as Tsoil increases, where it follows an upward trend until ~18 °C, and then begins to decline. Rs remains constant at Tsoil beyond ~27 °C. Using our novel conditional probability model, we show both the increasing and decreasing response of Rs to rising Tsoil through two ranges (14–17 and 20–23 °C) where Rs observations show opposing responses. We demonstrate that an increase in Tsoil from 14 to 17 °C causes a rise in Rs by a factor of 1.4 relative to the mean. The proposed model also describes how Rs reduces as Tsoil continues to increase above ~18 °C. Considering VWC and Tsoil into the proposed model, we show that when Tsoil is low (e.g., 17 °C), a rise in VWC yields a decrease of Rs by a factor of 3.6. However, when Tsoil is high (e.g., 23 °C), Rs increases with increasing VWC by a factor of 2.5. Overall, the probabilistic model enables us to detect and characterize changes in Rs distribution in response to different environmental variables and thresholds.