Unified Statistical Model Research Articles

Modeling the relationship between listener factors and signal modification: A pooled analysis spanning a decade

The overarching goal of our work is to understand how listeners respond to hearing aid processing and consequently inform individualized hearing aid treatment. Our previous work demonstrated that individual cognitive abilities, age, and hearing loss contribute to variability in response to cumulative signal modifications introduced by hearing aid processing and background noise. Specifically, older individuals with poorer working memory and more hearing loss were more susceptible to signal modifications introduced by hearing aid processing. These relationships were established in independent studies involving systematic manipulations of compression, digital noise reduction, frequency lowering, or microphone directionality. In this study, we present a hierarchical pooled analysis of data collected from six previous studies to develop a unified statistical model of the relationships between response to signal modification and individual listener variables. Across studies, signal modification is quantified using a cepstral correlation metric that accounts for cumulative envelope distortions arising from hearing aid processing and background noise. The statistical model will determine how working memory, age, and degree of hearing loss mediate the relationship between signal modification and speech intelligibility in noise across a large dataset. Both inferential and predictive applications of the combined data and model will be discussed. [Work supported by NIDCD.]

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Polyrate 2023: A computer program for the calculation of chemical reaction rates for polyatomics. New version announcement

Secure Communication Guarantees for Diverse Extended-Reality Applications: A Unified Statistical Security Model

Secure Communication Guarantees for Diverse Extended-Reality Applications: A Unified Statistical Security Model

Mixture of multivariate generalized Gaussians for multi-band texture modeling and representation

We present a unified statistical model for multivariate and multi-modal texture representation. This model is based on the formalism of finite mixtures of multivariate generalized Gaussians (MoMGG) which enables to build a compact and accurate representation of texture images using multi-resolution texture transforms. The MoMGG model enables to describe the joint statistics of subbands in different scales and orientations, as well as between adjacent locations within the same subband, providing a precise description of the texture layout. It can also combine different multi-scale transforms to build a richer and more representative texture signature for image similarity measurement. We tested our model on both traditional texture transforms (e.g., wavelets, contourlets, maximum response filter) and convolution neural networks (CNNs) features (e.g., ResNet, SqueezeNet). Experiments on color-texture image retrieval have demonstrated the performance of our approach comparatively to state-of-the-art methods.

Should phenological information be applied to predict agronomic traits across growth stages of winter wheat?

Most existing agronomic trait models of winter wheat vary across growing seasons, and it is an open question whether a unified statistical model can be developed to predict agronomic traits using a vegetation index (VI) across multiple growing seasons. In this study, we constructed a hierarchical linear model (HLM) to automatically adapt the relationship between VIs and agronomic traits across growing seasons and tested the model’s performance by sensitivity analysis. Results demonstrated that (1) optical VIs give poor performance in predicting AGB and PNC across all growth stages, whereas VIs perform well for LAI, LGB, LNC, and SPAD. (2) The sensitivity indices of the phenological information in the AGB and PNC prediction models were 0.81–0.86 and 0.66–0.73, whereas LAI, LGB, LNC, and SPAD prediction models produced sensitivity indexes of 0.01–0.02, 0.01–0.02, 0.01–0.02, and 0.02–0.08, respectively. (3) The AGB and PNC prediction models considering ZS were more accurate than the prediction models based on VI. Whether or not phenological information is used, there was no difference in model accuracy for LGB, LNC, SPAD, and LAI. This study may provide a guideline for deciding whether phenological correction is required for estimation of agronomic traits across multiple growing seasons.

Bridging the gaps in statistical models of protein alignment.

SummarySequences of proteins evolve by accumulating substitutions together with insertions and deletions (indels) of amino acids. However, it remains a common practice to disconnect substitutions and indels, and infer approximate models for each of them separately, to quantify sequence relationships. Although this approach brings with it computational convenience (which remains its primary motivation), there is a dearth of attempts to unify and model them systematically and together. To overcome this gap, this article demonstrates how a complete statistical model quantifying the evolution of pairs of aligned proteins can be constructed using a time-parameterized substitution matrix and a time-parameterized alignment state machine. Methods to derive all parameters of such a model from any benchmark collection of aligned protein sequences are described here. This has not only allowed us to generate a unified statistical model for each of the nine widely used substitution matrices (PAM, JTT, BLOSUM, JO, WAG, VTML, LG, MIQS and PFASUM), but also resulted in a new unified model, MMLSUM. Our underlying methodology measures the Shannon information content using each model to explain losslessly any given collection of alignments, which has allowed us to quantify the performance of all the above models on six comprehensive alignment benchmarks. Our results show that MMLSUM results in a new and clear overall best performance, followed by PFASUM, VTML, BLOSUM and MIQS, respectively, amongst the top five. We further analyze the statistical properties of MMLSUM model and contrast it with others.Supplementary information Supplementary data are available at Bioinformatics online.

Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling

AbstractAs a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we empirically explore the sampling challenges this approach offers which have to do with the strong correlations and multimodality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in a motorway traffic flow model due to Lighthill, Whitham, and Richards known as LWR. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. To sample from this challenging posterior distribution, we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering.

Hybrid Sparsity Model for Fast Terahertz Imaging.

In order to shorten the long-term image acquisition time of the terahertz time domain spectroscopy imaging system while ensuring the imaging quality, a hybrid sparsity model (HSM) is proposed for fast terahertz imaging in this paper, which incorporates both intrinsic sparsity prior and nonlocal self-similarity constraints in a unified statistical model. In HSM, a weighted exponentiation shift-invariant wavelet transform is introduced to enhance the sparsity of the terahertz image. Simultaneously, the nonlocal self-similarity by means of the three-dimensional sparsity in the transform domain is exploited to ensure high-quality terahertz image reconstruction. Finally, a new split Bregman-based iteration algorithm is developed to solve the terahertz imaging model more efficiently. Experiments are presented to verify the effectiveness of the proposed approach.

An online algorithm for echo cancellation, dereverberation and noise reduction based on a Kalman-EM Method

Many modern smart devices are equipped with a microphone array and a loudspeaker (or are able to connect to one). Acoustic echo cancellation algorithms, specifically their multi-microphone variants, are essential components in such devices. On top of acoustic echos, other commonly encountered interference sources in telecommunication systems are reverberation, which may deteriorate the desired speech quality in acoustic enclosures, specifically if the speaker distance from the array is large, and noise. Although sub-optimal, the common practice in such scenarios is to treat each problem separately. In the current contribution, we address a unified statistical model to simultaneously tackle the three problems. Specifically, we propose a recursive EM (REM) algorithm for solving echo cancellation, dereverberation and noise reduction. The proposed approach is derived in the short-time Fourier transform (STFT) domain, with time-domain filtering approximated by the convolutive transfer function (CTF) model. In the E-step, a Kalman filter is applied to estimate the near-end speaker, based on the noisy and reveberant microphone signals and the echo reference signal. In the M-step, the model parameters, including the acoustic systems, are inferred. Experiments with human speakers were carried out to examine the performance in dynamic scenarios, including a walking speaker and a moving microphone array. The results demonstrate the efficiency of the echo canceller in adverse conditions together with a significant reduction in reverberation and noise. Moreover, the tracking capabilities of the proposed algorithm were shown to outperform baseline methods.

The observation window and the statistical modeling of RTN in time and frequency domain

Charge trapping is studied in the context of random telegraph noise (RTN) and low-frequency noise (1/f noise), aiming unified statistical modeling. Analytical formulations for 1/f noise (frequency domain) and RTN (time domain) have been derived, using a single modeling framework, where model parameters are the same in frequency and time domain. The modeling addresses the time dependent variability in the electrical behavior of MOSFETs, discussing the variability due to a single trap and the ensemble of traps. In the work here presented we detail the role of the observation window, in both time and frequency domain. We discuss how it impacts the variance of drain current (or threshold voltage) measured over time, and the number of observable traps in a given time window or frequency window. Besides analytical modeling, experimental results are presented and discussed.

A unified statistical model for indentation pop-in: Effects of indenter radius and microstructure density on the transition from homogeneous nucleation to heterogeneous nucleation to bulk plasticity

Indentation pop-in, i.e. a sudden displacement burst on the measured load-penetration depth curves, has been known as the onset of elastic-plastic deformation for crystalline materials. Depending on the indenter radius or density of pre-existing dislocation nucleation sources, the evolution of pop-in shear stress can generally be categorized into three deformation stages, i.e. the homogeneous dislocation nucleation stage, heterogeneous dislocation nucleation stage and bulk plasticity stage. For the former, the fluctuation of pop-in stress is dominated by the thermally activated nucleation process. For the middle, a size-dependent pop-in behavior with stress fluctuation is informed over a wide range of indenter radius and microstructure density. For the later, the materials strength is determined by the critical resolved shear stress for the motion of existing dislocations. Here, we find two additional transition stages between the adjacent deformation stages that can be effectively addressed by a novel competition mechanism, and the transition points are affected by the density of dislocation nucleation sites. All these critical features are well characterized by a unified statistical model proposed in this work. Moreover, a mechanistic model with closed-form formulas is developed for the size-dependent pop-in behavior during the heterogeneous dislocation nucleation stage. By comparing both the calibrated and predicted theoretical results with different sets of experimental data, good agreements are achieved that can rationally verify the proposed model. This work presents a theoretical framework to characterize the fundamental pop-in mechanisms, and provides an avenue towards the prediction of transition points distinguishing different plasticity deformation regimes.

A statistical model for predicting size effects on the yield strength in dislocation-mediated crystal plasticity

A unified statistical dislocation-mediated crystal plasticity model is proposed to understand how the sample size affects the yield strength of metals in different crystal systems, namely, single crystals, columnar-grain structured thin films, and polycrystals. The model takes into account the randomness of the pre-existing dislocation network, grain orientation, and grain size to predict the crystal strength as a function of the extrinsic (i.e. sample dimensions) and intrinsic (i.e. microstructural dimensions) length scales. The model is shown to rigorously capture the effect of size across all three crystal systems, i.e. convergence, scatter and overall trend of the strength, and the results are in good agreement with published experimental and simulation results. The developed model provides an accurate and efficient approach to predict the yield strength in metals.

Statistical characterization of the linear attenuation coefficient in polychromatic CT scans.

To provide a unifying statistical model that characterizes the integrated x-ray intensity at the detector after logarithmic transformation and can be extended to the characterization of computed tomography (CT) numbers in the reconstructed image. We study the statistical characteristics of polyenergetic x-ray beams in the detector. Firstly, we consider the characterization of the integrated x-ray intensity at the detector through a probabilistic model (compound Poisson) that describes its statistics. We analyze its properties and derive the probabilistic distribution after the logarithmic transformation analytically. Finally, we propose a more tractable probabilistic distribution with the same features observed in the characterization, the noncentral Gamma (nc-Gamma). This distribution exhibits desirable properties for the statistical characterization across the reconstruction process. We assess the assumptions adopted in the derivation of the statistical models throughout Monte Carlo simulations and validate them with a water phantom and a lung phantom acquired in a Siemens clinical CT scan. We evaluate the statistical similarities between the theoretical distribution and the nc-Gamma using a power analysis with a Kolmogorov-Smirnov test for a 95% confidence level. The Kolmogorov-Smirnov goodness-of-fit test obtained for the Monte Carlo simulation shows an extremely high agreement between the empirical distribution of the post-logarithmic-integrated x-ray intensity and the nc-Gamma. The experimental validation performed with both phantoms confirmed the excellent match between the theoretical distribution, the proposed nc-Gamma, and sample distributions in all situations. We derive an analytical model describing the post-log distribution of the linear attenuation coefficient in the sensor for polychromatic CT scans. We also demonstrate that the nc-Gamma distribution approximates well the theoretical distribution. This distribution also approximates well the CT numbers after reconstruction since it naturally extends across linear operations involved in filtered back projection reconstructions. This probabilistic model may provide the analytical foundation to define new likelihood-based reconstruction methodologies for polychromatic scans.

Varlociraptor: enhancing sensitivity and controlling false discovery rate in somatic indel discovery

Accurate discovery of somatic variants is of central importance in cancer research. However, count statistics on discovered somatic insertions and deletions (indels) indicate that large amounts of discoveries are missed because of the quantification of uncertainties related to gap and alignment ambiguities, twilight zone indels, cancer heterogeneity, sample purity, sampling, and strand bias. We provide a unifying statistical model whose dependency structures enable accurate quantification of all inherent uncertainties in short time. Consequently, false discovery rate (FDR) in somatic indel discovery can now be controlled at utmost accuracy, increasing the amount of true discoveries while safely suppressing the FDR.

A unified statistical model for Málaga distributed optical scattering communications

In this paper, we present a novel analytical model for optical scattering communications over Málaga distributed irradiance fluctuation. The distribution of the received signal is quantified with each scattered optical path following Málaga distribution in the scattering communication links. The model efficiently includes the scattering by the off-axis eddies, in addition to the eddies on the propagation axis over a non-line-of-sight (NLOS) link, thus permitting accurate evaluation of the scattered ultraviolet (UV) communication. It is shown that as the effective number of large-scale cells reduces in the lower atmospheric channel, the probability density function (PDF) of the received signal-to-noise ratio (SNR) spreads widely with large variance and impacts the performance of optical scattering communications. Moreover, based on the derived model, closed-form expressions for the average bit error rate and the outage probability are also presented.

A Unified Statistical Model for Atmospheric Turbulence-Induced Fading in Orbital Angular Momentum Multiplexed FSO Systems

This paper proposes a unified statistical channel model to characterize the atmospheric turbulence induced distortions faced by orbital angular momentum (OAM) in free space optical (FSO) communication systems. In this channel model, the self-channel irradiance of OAM modes as well as crosstalk irradiances between different OAM modes are characterized by a Generalized Gamma distribution (GGD). The latter distribution is shown to provide an excellent match with simulated data for all regimes of atmospheric turbulence. Therefore, it can be used to overcome the computationally complex numerical simulations to model the propagation of OAM modes through atmospheric turbulent FSO channels. The GGD allows obtaining very simple tractable closed-form expressions for a variety of performance metrics. Indeed, the average capacity, the bit-error rate, and the outage probability are derived for FSO systems using single OAM mode transmission with direct detection. Furthermore, we extend our study to FSO systems using OAM mode diversity to improve the performance. By using a maximum ratio combining (MRC) at the receiver, the GGD is also shown to fit the simulated combined received optical powers. Finally, space-time (ST) coding is proposed to provide diversity and multiplexing gains, and the error probability is theoretically derived under the newly proposed generic model.

Developing a Locally Adaptive Spatial Multilevel Logistic Model to Analyze Ecological Effects on Health Using Individual Census Records

Geographical variable distributions often exhibit both macroscale geographic smoothness and microscale discontinuities or local step changes. Nonetheless, accounting for both effects in a unified statistical model is challenging, especially when the data under study involve a multiscale structure and non-Gaussian response variables. This study develops a locally adaptive spatial multilevel logistic model to examine binomial response variables that integrates an innovative locally adaptive spatial econometric model with a multilevel model. It takes into account global spatial autocorrelation, local step changes, and vertical dependence effects arising from the multiscale data structure. Another appealing feature is that the spatial correlation structure, implied by a spatial weights matrix, is learned along with other model parameters via an iterative estimation algorithm, rather than being presumed to be invariant. Bayesian Markov chain Monte Carlo (MCMC) samplers are derived to implement this new spatial multilevel logistic model. A data augmentation approach, drawing on recently devised Pólya-gamma distributions, is adopted to reduce computational burdens of calculating binomial likelihoods with a logit link function. The validity of the developed model is evaluated by a set of simulation experiments, before being applied to analyze self-rated health for the elderly in Shijiazhuang, the capital city of Hebei Province, China. Model estimation results highlight a nuanced geography of self-rated health and identify a range of individual- and area-level correlates of health for the elderly. Key Words: geography of health, local spatial modeling, multilevel models, spatial autocorrelation, spatial econometrics.

Study of Pion Transverse Momentum Distributions in Ultra-Relativistic Heavy Ion Collisions: A USTFM Approach

The mid-rapidity (|y| < 0.5) transverse momentum distributions of identified charged pions produced in different collision systems at different centre-of-mass energies ( $${{\sqrt S }_{{NN}}}$$ ) ranging from RHIC to LHC have been studied using our early proposed unified statistical thermal freeze-out model (USTFM). We have also studied the effect of different collision centralities on the mid-rapidity (|y| < 0.5) production of pions. Our model results are found to be in good agreement with the experimental data. Different thermal freeze-out conditions which include transverse flow, thermal freeze-out temperature, and velocity profile have been extracted by providing the best fit to the experimental data points. We have incorporated the effects of transverse as well as longitudinal flow in this analysis. The effects of heavier decay resonances are also taken into account. Moreover, the strangeness conservation criteria have also been imposed in this analysis of pion distributions. The calculated freeze-out parameters indicates that the freeze-out temperature increases with decreasing centrality, while the transverse flow velocity increases by increase in the centrality of the colliding system.

Unified Statistical Channel Model for Turbulence-Induced Fading in Underwater Wireless Optical Communication Systems

A unified statistical model is proposed to characterize turbulence-induced fading in underwater wireless optical communication (UWOC) channels in the presence of air bubbles and temperature gradient for fresh and salty waters, based on experimental data. In this model, the channel irradiance fluctuations are characterized by the mixture exponential–generalized gamma (EGG) distribution. We use the expectation–maximization algorithm to obtain the maximum likelihood parameter estimation of the new model. Interestingly, the proposed model is shown to provide a perfect fit with the measured data under all channel conditions for both types of water. The major advantage of the new model is that it has a simple mathematical form making it attractive from a performance analysis point of view. Indeed, we show that the application of the EGG model leads to closed-form and analytically tractable expressions for key UWOC system performance metrics such as the outage probability, the average bit-error rate, and the ergodic capacity. To the best of our knowledge, this is the first-ever comprehensive channel model addressing the statistics of optical beam irradiance fluctuations in underwater wireless optical channels due to both air bubbles and temperature gradient.

A spatially varying change points model for monitoring glaucoma progression using visual field data

Glaucoma disease progression, as measured by visual field (VF) data, is often defined by periods of relative stability followed by an abrupt decrease in visual ability at some point in time. Determining the transition point of the disease trajectory to a more severe state is important clinically for disease management and for avoiding irreversible vision loss. Based on this, we present a unified statistical modeling framework that permits prediction of the timing and spatial location of future vision loss and informs clinical decisions regarding disease progression. The developed method incorporates anatomical information to create a biologically plausible data-generating model. We accomplish this by introducing a spatially varying coefficients model that includes spatially varying change points to detect structural shifts in both the mean and variance process of VF data across both space and time. The VF location-specific change point represents the underlying, and potentially censored, timing of true change in disease trajectory while a multivariate spatial boundary detection structure is introduced that accounts for the complex spatial connectivity of the VF and optic disc. We show that our method improves estimation and prediction of multiple aspects of disease management in comparison to existing methods through simulation and real data application. The R package spCP implements the new methodology.