Derivation Of Probability Distribution Research Articles

A Bayesian analysis integrating expert beliefs to better understand how new evidence ought to update what we believe: a use case of chiropractic care and acute lumbar disc herniation with early surgery

BackgroundA Bayesian approach may be useful in the study of possible treatment-related rare serious adverse events, particularly when there are strongly held opinions in the absence of good quality previous data. We demonstrate the application of a Bayesian analysis by integrating expert opinions with population-based epidemiologic data to investigate the association between chiropractic care and acute lumbar disc herniation (LDH) with early surgery.MethodsExperts’ opinions were used to derive probability distributions of the incidence rate ratio (IRR) for acute LDH requiring early surgery associated with chiropractic care. A ‘community of priors’ (enthusiastic, neutral, and skeptical) was built by dividing the experts into three groups according to their perceived mean prior IRR. The likelihood was formed from the results of a population-based epidemiologic study comparing the relative incidence of acute LDH with early surgery after chiropractic care versus primary medical care, with sensitive and specific outcome case definitions and surgery occurring within 8- and 12-week time windows after acute LDH. The robustness of results to the community of priors and specific versus sensitive case definitions was assessed.ResultsThe most enthusiastic 25% of experts had a prior IRR of 0.42 (95% credible interval [CrI], 0.03 to 1.27), while the most skeptical 25% of experts had a prior IRR of 1.66 (95% CrI, 0.55 to 4.25). The Bayesian posterior estimates across priors and outcome definitions ranged from an IRR of 0.39 (95% CrI, 0.21 to 0.68) to an IRR of 1.40 (95% CrI, 0.52 to 2.55). With a sensitive definition of the outcome, the analysis produced results that confirmed prior enthusiasts’ beliefs and that were precise enough to shift prior beliefs of skeptics. With a specific definition of the outcome, the results were not strong enough to overcome prior skepticism.ConclusionA Bayesian analysis integrating expert beliefs highlighted the value of eliciting informative priors to better understand how new evidence ought to update prior existing beliefs. Clinical epidemiologists are encouraged to integrate informative and expert opinions representing the end-user community of priors in Bayesian analyses, particularly when there are strongly held opinions in the absence of definitive scientific evidence.

Intelligent detection of underground openings and surrounding disturbed zones

This study aims to develop an intelligent method to detect subsurface anomalies for prediction and mitigation of geologic risks. We trained a convolutional neural network (CNN) model using the seismic data from 6 field cases of regular pipes and irregular cavities and a sliding time window technique to augment the datasets, and tested the CNN model using another 2 field cases. We derived probability distribution as an indicator of anomaly existence and validated high-value and low-value probability distributions corresponding to underground openings and surrounding disturbed zones, respectively. We found that the characteristics of subsurface anomalies determines the effective seismic features and influences the CNN model performance. Finally, we applied the CNN model to investigate a circular-bored tunnel and surrounding disturbed zones. Our results demonstrate that the CNN model is fast and accurate to detect the horizontal locations of subsurface anomalies, while the accuracy of vertical locations depends on the estimation of P-wave velocity. The intelligent method has the potential to identify hidden risks at early stages and to mitigate subsequent geologic hazards.

Multi-view distillation based on multi-modal fusion for few-shot action recognition (CLIP-MDMF)

In recent years, the field of few-shot action recognition (FSAR) has garnered significant attention. Although many methods primarily rely on mono-modal data, there is a growing trend towards utilizing multi-modal data. However, existing FSAR methods often employ simplistic fusion techniques, such as concatenation or comparison, which may not fully leverage the potential of multi-modal information. We aim to explore multi-modal information from different views and subsequently perform multi-view fusion. Based on the textual and visual modality information extracted by the CLIP backbone, we propose an MDMF method that comprehensively utilizes these modalities at two levels. At the first level, we extract visual information from two views: Local Temporal Context and Global Temporal Context. Within each view, we fuse visual features with textual information through concatenation and Cross-Transformer operations. We then employ metric comparison to derive probability distributions for classification under the meta-learning paradigm for each view. At the second level, we fuse the probability distributions from both views to make the final decision. Concurrently, during training, for each query, we calculate the posterior distributions of the textual and visual modalities within each view using text information distance and visual information distance. Based on these distributions, we group query samples with higher view reliability. Subsequently, we enhance the representation of the less reliable view of specific samples through mutual distillation. By delving deep into multi-modal data through a multi-view approach, our few-shot action recognition model demonstrates the potential for achieving higher accuracy and enhanced robustness. Our code is available at the URL: https://github.com/cofly2014/CLIP-MDMF.

A Monte Carlo resampling framework for implementing goodness‐of‐fit tests in spatial capture‐recapture models

Abstract Spatial capture‐recapture (SCR) models provide estimates of animal density from spatially referenced encounter data and has become the most widely adopted approach for estimating density. Despite the rapid growth in the development and application of spatial capture‐recapture methods, approaches for assessing model fit have received very little attention when compared to other classes of hierarchical models in ecology. Here, we develop an approach for testing goodness‐of‐fit (GoF) for frequentist SCR models using Monte Carlo simulations. We derive probability distributions of activity centres from the fitted model. From these, we calculate the expected encounters in the capture history based on the SCR parameter estimates, propagating the uncertainty of the estimates and the activity centre locations via Monte Carlo simulations. Aggregating these test statistics result in count data, allowing us to test fit with Freeman‐Tukey tests. These tests are based on summary statistics of the total encounters of each individual at each trap (FT‐ind‐trap), total encounters of each individual (FT‐individuals) and total encounters at each trap (FT‐traps). We assess the ability of these GoF tests to diagnose lack of fit under a range of assumption violating scenarios. FT‐traps had the strongest response to unmodelled spatial and trap heterogeneity in detection probability (power = 0.53–0.56), while FT‐ind‐traps had the strongest responses to random individual variation in detectability (power = 0.88) and non‐spatial discrete variation in (power = 0.35). The tests, designed to diagnose poor fit in the detection parameters, were insensitive to unmodelled heterogeneity in density (power = <0.001). They also demonstrated low false positive rates (<0.001) when the correct models were fitted; therefore, it is very unlikely that they will provide false indications of poor model fit. We demonstrate that these GoF tests are capable of detecting lack‐of‐fit when unmodelled heterogeneity is present in the detection sub‐model. When used jointly, the combinations of test results are also able to infer the type of lack‐of‐fit in certain cases. Our Monte Carlo sampling methods may be extended to a wider range of GoF tests, thereby providing a platform for developing more GoF methods for SCR.

An approach to seismic damage detection and evaluation in RC bridge piers through vibration data

A timely post-earthquake damage evaluation in existing bridges is fundamental for an efficient emergency management. Structural Health Monitoring (SHM) systems can allow a fast damage assessment; however, a lack of methods for the SHM data interpretation is recognised. The present paper proposes an approach for the probabilistic seismic damage detection and quantification in ductile bridge piers from vibration-based SHM data by comparing time variations of modal properties. To this aim, the selected modal properties are natural frequencies and mode-shapes, expressed in terms of CoMAC and ECoMAC indices. Experimental results of quasi-static cyclic tests and output-only modal identification tests are adopted to calibrate a reliable finite element model able to predict the variations in fundamental modal properties of ductile RC piers due to seismic damage. The calibrated model is used to perform probabilistic analyses to derive probability distributions for the variation of the considered modal-based features of piers at different seismic damage levels. The approach provides fragility models to support a timely assessment of serviceability levels in monitored assets in the immediate aftermath of an earthquake by monitoring the variation of natural frequencies. Conversely, CoMAC and ECoMAC resulted slightly sensitive to seismic damage for the investigated piers portfolio.

Assessing cumulative uncertainties of remote sensing time series and telemetry data in animal-environment studies

ContextRemote sensing time series (hereafter called time series) and telemetry data are widely used to study animal-environment relationships. However, both data sources are subject to uncertainties that can cause erroneous conclusions. To date, only the uncertainty of telemetry data can be estimated, e.g. through movement modelling, while information on the uncertainty of time series is often lacking. Consequently, it remains challenging to assess if and how the results of animal-environment studies are affected by cumulative uncertainties of telemetry and time series data.ObjectivesTo address this gap, we proposed an approach to approximate time series uncertainties. Coupled with movement modelling, this allows to determine whether the results of animal-environment studies are robust to the cumulative uncertainties of time series and telemetry data. We demonstrated the procedure with a study that used time series to distinguish periods of favourable/poor prey accessibility for white storks. Our objective was to test whether the storks’ preference for fields during periods of favourable prey accessibility could be validated despite the uncertainties.MethodsWe estimated the telemetry data uncertainties based on continuous-time movement modelling, and approximated time series uncertainties based on data subsampling. We used Monte Carlo simulations to propagate the uncertainties and to generate several estimates of the stork habitat use and levels of prey accessibility. These data were applied in two habitat selection analyses to derive probability distributions of the analyses results, allowing us to characterise the output uncertainties.ResultsWe found that, after accounting for uncertainty, favourable and poor prey accessibility periods were well discriminated, with storks showing the expected degree of preference/avoidance for them. However, our uncertainty analysis also showed, that compared to croplands, grasslands required more temporal NDVI samples to reliably identify these periods. Furthermore, the NDVI itself did not appear to be a coherent predictor of stork habitat selection when uncertainties were accounted for.ConclusionOur findings highlight the importance of validating results by assessing and quantifying the effect of input data uncertainties in animal-environment studies. To our knowledge, the approach presented is the first to assess the cumulative uncertainty of time series and telemetry data, hopefully raising awareness of the consequences of input data uncertainties for future studies.

Permeable pavement hydraulic optimization by using an analytical-probabilistic model

Abstract On-source storage controls are a sustainable solution for stormwater management in a scenario of continuous urban area growth. Structures that manage storage volumes through infiltration include extra environmental benefits, such as groundwater recharge, evapotranspiration, and pollutant load removal. Permeable pavement systems are among these controls and can easily integrate into dense urban areas, resulting in paved surfaces contributing to stormwater management. The shift toward on-source strategies is encouraged through regulations, policies, incentives, and awareness campaigns, which are substantially increasing their dissemination. Optimizing the design of on-source storage controls with infiltration, such as permeable pavement systems, through robust methodologies can reduce reservoir depth, reducing environmental impact and costs without impact on reliability. The analytical-probabilistic (AP) method using derived probability distribution theory from rainfall event characteristics and the mathematical description of hydrologic processes within the permeable pavement systems provides an analytical equation that can be used as a design tool, proving robustness analogous with continuous simulations. Results obtained with the AP method were compared with traditional event-based methodologies and continuous simulation, assessing the reliability of the proposed method in optimizing permeable pavement systems' reservoir depth.

Supersymmetric higher-derivative models in quantum cosmology

We study the quantum cosmology of supersymmetric, homogeneous and isotropic, higher derivative models. We recall superfield actions obtained in previous works and give classically equivalent actions leading to second order equations for the bosons, and first order for the fermions. Upon quantization, the algebra of fermions leads to a multi-component state, which is annihilated by the Hamiltonian and supersymmetric constraint operators. We obtain asymptotic wave functions of the oscillatory type, whose classical limit corresponds to inflationary evolution, and exact exponential wave functions. We use the latter to derive probability distributions of the initial curvature that are compatible with those obtained using the non-supersymmetric model.

Sequential mutations in exponentially growing populations.

Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with n alterations, and how long will it take for these cells to appear. For exponentially growing populations, these questions have been tackled only in special cases so far. Here, within a multitype branching process framework, we consider a general mutational path where mutations may be advantageous, neutral or deleterious. In the biologically relevant limiting regimes of large times and small mutation rates, we derive probability distributions for the number, and arrival time, of cells with n mutations. Surprisingly, the two quantities respectively follow Mittag-Leffler and logistic distributions regardless of n or the mutations' selective effects. Our results provide a rapid method to assess how altering the fundamental division, death, and mutation rates impacts the arrival time, and number, of mutant cells. We highlight consequences for mutation rate inference in fluctuation assays.

Probability Distribution of Transient Response of an Electric Circuit

In this work, we explore the transient response of an electric circuit using probabilistic analysis when the precise value of the characteristic parameter of a circuit element is not known and is instead constrained to a range of values. To accomplish this, a combination of probability theory and traditional circuit analysis techniques is employed. In this approach, the circuit element’s parameter is treated as a random variable, and probability methods are used to derive the probability distribution of the voltage or current across it. To demonstrate this approach, we apply it to a resistor capacitor (RC) circuit, where the capacitance parameter of the capacitor is regarded as a random variable. We derive probability distributions for the transient voltage across the capacitor and the voltage at the output terminals to illustrate the method’s effectiveness.

An improved sequential importance sampling method for reliability assessment of renewable power systems with energy storage

Due to the temporal coupling constraints of energy storage, the reliability of modern renewable power systems can no longer be assessed by non-sequential methods. However, the existing sequential methods cannot be combined with variance reduction methods as easily as the non-sequential ones. Hence, the power system reliability assessment is faced with incredible computational burden. In this paper, we propose an improved sequential importance sampling method to accelerate the computation of power system reliability indices. The proposed method is composed of two stages, namely the pre-simulation and main simulation stages. In the pre-simulation stage, we design a customized probability distribution parameter optimization process for load curves in the cross entropy based importance sampling method. In the main simulation stage, the derived probability distribution parameters in the pre-simulation stage are converted and further used to carry out a sequential Monte Carlo sampling process to efficiently estimate the reliability indices of renewable power systems with energy storage. The proposed method is validated by numerical tests performed on the modified IEEE-RTS 79 and IEEE-RTS 96 test systems, both of which are integrated with three wind farms, one photovoltaic station and one battery energy storage power station. Results show that the proposed method is much faster than existing sequential importance sampling methods in both test systems because of exploiting the acceleration potential of the load. Therefore, the proposed method can be used to assess the reliability of the renewable power systems with more energy storage devices in the future.

Construction of a Probabilistic Model Describing Deterioration of Pumping Wells and Its Verification Using Actual Data

A probabilistic model is newly proposed for describing random deterioration of pumping wells, in consideration of application to efficient management of pumping wells using a concept of asset management procedure. First, introducing a health index for quantifying specific capacity, we formulate a differential equation describing mean deterioration of the helth index. Next, it is extended to a random differential equation, in which a Gaussian white noise is introduced for representing intensive fluctuation around the mean deterioration behavior, so that intensively random variation of the health index can be well reproduced. A probability distribution of the health index is then derived in an analytical form. Finally, the obtained probability distribution is compared with actual data of the health index for active eight pumping wells in Joyo area, Kyoto prefecture, Japan. It is clarified that the scatter of health index of actual pumping wells is quite well reproduced by the theoretically derived probability distribution from the newly proposed probabilistic model.

Quantitative Resilience-Based Assessment Framework Using EAGLE-I Power Outage Data

Catastrophic impacts to power systems caused by extreme weather events have significantly increased during the last decade. These events highlight the need to develop approaches to assess the resilience of power systems against extreme events; however, the availability of data that capture power system performance during and after disruptive events is scarce. This paper proposes an assessment framework to evaluate the performance aspects of the power grid during extreme outage events using the Environment for Analysis of Geo-Located Energy Information (EAGLE-I) data. EAGLE-I data include information related to the number of impacted customers, the duration, and the location of power outages in the United States. Statistical analyses were conducted to extract resilience-based outage data and derive probability distribution functions of their impact and recovery characteristics. A list of extreme events is identified based on population-based threshold values. Metrics from other power outage assessments were used to measure the characteristics of each event, including the impact rate and duration, the recovery rate and duration, and the impact level. A probability distribution function is obtained for each metric. The proposed framework is conducted for each state across the United States. The obtained results provide a probabilistic representation of state-level outage behaviors, which can be applied as a framework to evaluate various resilience enhancement techniques.

Antenna Array Topologies for mmWave Massive MIMO Systems: Spectral Efficiency Analysis

This article investigates the achievable spectral efficiency (SE) of millimeter wave massive multiple-input multiple-output systems with three different array topologies deployed at the base station (BS), namely uniform rectangular array (URA), uniform linear array (ULA) or uniform circular array (UCA). To be practical, both small scale fading and large scale path loss, and shadowing effects are considered in the analysis. A 3D channel model taking both the azimuth and elevation domains into account is adopted for the analysis of the URA and UCA topologies. Considering randomly distributed users in the cell, we firstly deduce the distribution functions of the distances between the users and the BS, and the azimuth and elevation angles of departure, respectively. Based on the derived probability distribution, tight approximations on the achievable SE with maximum ration transmission under the three antenna array topologies are derived. Analytical results show that under all the three topologies, the total achievable SE increases with the number of BS antennas, but decreases with the radius of cell and decay exponent. Moreover, it converges to a saturated value in the high SNR regime and a large inter-element spacing. It is also found that the UCA configuration has a superior achievable SE than the URA and ULA cases, and thus is the best choice for mmWave massive MIMO systems in terms of the achievable SE.

Assessment of the residential Finnish wolf population combines DNA captures, citizen observations and mortality data using a Bayesian state-space model

Assessment of the Finnish wolf population relies on multiple sources of information. This paper describes how Bayesian inference is used to pool the information contained in different data sets (point observations, non-invasive genetics, known mortalities) for the estimation of the number of territories occupied by family packs and pairs. The output of the assessment model is a joint probability distribution, which describes current knowledge about the number of wolves within each territory. The joint distribution can be used to derive probability distributions for the total number of wolves in all territories and for the pack status within each territory. Most of the data set comprises of both voluntary-provided point observations and DNA samples provided by volunteers and research personnel. The new method reduces the role of expert judgement in the assessment process, providing increased transparency and repeatability.

LoS MIMO transmission for LEO satellite communication systems

To provide global service with low latency, the broadband low earth orbits (LEO) satellite constellation based communication systems have become one of the focuses in academic and industry. To allow for wideband access for user links, the feeder link of LEO satellite is correspondingly required to support high throughput data communications. To this end, we propose to apply line-of-sight (LoS) multiple-input multiple-output (MIMO) transmission for the feeder link to achieve spatial multiplexing by optimizing the antenna arrangement. Unlike the LoS MIMO applications for static scenarios, the movement of LEO satellites make it impractical to adjust the optimal antenna separation for all possible satellite positions. To address this issue, we propose to design the antenna placement to maximize the ergodic channel capacity during the visible region of the ground station. We first derive the closed-form probability distribution of the satellite trajectory in visible region. Based on which the ergodic channel capacity can be then calculated numerically. The antenna placement can be further optimized to maximize the ergodic channel capacity. Numerical results verify the derived probability distribution of the satellite trajectory, and show that the proposed LoS MIMO scheme can significantly increase the ergodic channel capacity compared with the existing SISO one.

Modeling distance uncertainties in two-dimensional space

Distances are functions of spatial positions, therefore distance uncertainties should be resulted from transmission of spatial position uncertainties via the functional relationships accordingly. How to model the transmission precisely, a challenging problem in GIScience, has increasingly drawn attentions during the past several decades. Aiming at the limitations of presently available solutions to the problem, this article derived probability distribution functions and corresponding density functions of distance uncertainties in two-dimensional space related to one or two uncertain endpoints respectively, under the premise that real positions, corresponding with the observed position of an uncertain point, follow the kernel function within its error circle. The density functions were employed to explore the diffusing law of uncertainty information from point positions to distances, which opened up a new way for thoroughly solving problems of measuring distance uncertainties. It turns out that the proposed methods in this article are more efficient, robust than the corresponding Monte Carlo ones, which verifies their effectiveness and advantages.

On the Hydrosphere Stability of TESS Targets: Applications to 700 d, 256 b, and 203 b

A main determinant of the habitability of exoplanets is the presence of stable liquid surface water. In an era of abundant possible targets, the potential to find a habitable world remains a driving force in prioritization. We present here a data-forward method to investigate the likelihood of a stable hydrosphere on the timescales of the formation of life, 1 Gyr, and beyond. As our primary application, we use this method to examine the potential hydrospheres of TESS objects of interest 700 d, 256 b (LHS 1140 b), and 203 b. We first present our selection criteria, which are based on an implementation of the Earth Similarity Index, as well as the results of an initial investigation into the desiccation of the targets, which reveals that TOI 203 b is almost certainly desiccated based on TESS observations. We then describe the characterization of the remaining targets and their host stars from 2MASS, Gaia, and TESS data and the derivation of sampled probability distributions for their parameters. Following this, we describe our process of simulating the desiccation of the targets’ hydrospheres using the Virtual Planet Simulator, VPlanet, with inputs directly linked to the previously derived probability distributions. We find that 50.86% of the likely cases for TOI 700 d are desiccated, and no modeled cases for TOI 256 b are without water. In addition, we calculate the remaining water inventory for the targets, the percentage of cases that are continuing to lose water, and the rate at which these cases are losing water.

Detailed models of interacting short-period massive binary stars

Context. The majority of massive stars are part of binary systems. In about a quarter of these, the companions are so close that mass transfer occurs while they undergo core hydrogen burning, first on the thermal and then on the nuclear timescale. The nuclear timescale mass transfer leads to observational counterparts: the semi-detached so-called massive Algol binaries. These systems may provide urgently needed tests of the physics of mass transfer. However, comprehensive model predictions for these systems are sparse. Aims. We use a large grid of detailed evolutionary models of short-period massive binaries and follow-up population synthesis calculations to derive probability distributions of the observable properties of massive Algols and their descendants. Methods. Our results are based on ∼10 000 binary model sequences calculated with the stellar evolution code MESA, using a metallicity suitable for the Large Magellanic Cloud (LMC), covering initial donor masses between 10 M⊙ and 40 M⊙ and initial orbital periods above 1.4 d. These models include internal differential rotation and magnetic angular momentum transport, non-conservative mass and angular momentum transfer between the binary components, and time-dependent tidal coupling. Results. Our models imply ∼30, or ∼3% of the ∼1000, core hydrogen burning O-star binaries in the LMC to be currently in the semi-detached phase. Our donor models are up to 25 times more luminous than single stars of an identical mass and effective temperature, which agrees with the observed Algols. A comparison of our models with the observed orbital periods and mass ratios implies rather conservative mass transfer in some systems, while a very inefficient one in others. This is generally well reproduced by our spin-dependent mass transfer algorithm, except for the lowest considered masses. The observations reflect the slow increase of the surface nitrogen enrichment of the donors during the semi-detached phase all the way to CNO equilibrium. We also investigate the properties of our models after core hydrogen depletion of the donor star, when these models correspond to Wolf-Rayet or helium+OB star binaries. Conclusions. A dedicated spectroscopic survey of massive Algol systems may allow to derive the dependence of the efficiency of thermal timescale mass transfer on the binary parameters, as well as the efficiency of semiconvective mixing in the stellar interior. This would be a crucial step towards reliable binary models up to the formation of supernovae and compact objects.

Outage Probability of Intelligent Reflecting Surface Assisted Full Duplex Two-Way Communications

In this letter, we study the outage probability (OP) of intelligent reflecting surface (IRS) assisted full duplex two-way (TW) communication systems, which characterizes the performance of overcoming the transmitted data loss caused by long deep fades. To this end, we first derive the probability distribution of the cascaded end-to-end equivalent channel with an arbitrarily given IRS beamformer. Our analysis shows that deriving such probability distribution in the considered case is more challenging than the case with the phase-matched IRS beamformer. Then, with the derived probability distribution of the equivalent channel, we obtain the closed-form expression of the OP. It theoretically shows that the number of reflecting elements has a conspicuous effect on the improvement of the system reliability. Extensive numerical results verify the correctness of the derived results and confirm the superiority of the considered IRS assisted TW communication system comparing to the one-way counterpart.