Likelihood Of Data Research Articles

The role of score and information bias in panel data likelihoods

We show why reducing information bias can improve the performance of likelihood based estimators and confidence regions in small samples, and why it seems to matter more for inference than for estimation. The insights in this paper are helpful in explaining several simulation findings in the panel data literature. E.g., we can explain the well documented phenomenon that reducing the score bias alone often reduces the finite sample variance of estimators and improves the coverage of confidence regions in small samples, and why confidence regions based on conditional (on sufficient statistics) likelihoods can have excellent coverage even in very short panels. We can also explain the simulation results in Schumann, Severini, and Tripathi (2021), who find that, in short panels, estimators and confidence regions based on pseudolikelihoods that are simultaneously first-order score and information unbiased perform much better than those based on pseudolikelihoods that are only first-order score unbiased.

Variational inference with vine copulas: an efficient approach for Bayesian computer model calibration

With the advancements of computer architectures, the use of computational models proliferates to solve complex problems in many scientific applications such as nuclear physics and climate research. However, the potential of such models is often hindered because they tend to be computationally expensive and consequently ill-fitting for uncertainty quantification. Furthermore, they are usually not calibrated with real-time observations. We develop a computationally efficient algorithm based on variational Bayes inference (VBI) for calibration of computer models with Gaussian processes. Unfortunately, the standard fast-to-compute gradient estimates based on subsampling are biased under the calibration framework due to the conditionally dependent data which diminishes the efficiency of VBI. In this work, we adopt a pairwise decomposition of the data likelihood using vine copulas that separate the information on dependence structure in data from their marginal distributions and leads to computationally efficient gradient estimates that are unbiased and thus scalable calibration. We provide an empirical evidence for the computational scalability of our methodology together with average case analysis and describe all the necessary details for an efficient implementation of the proposed algorithm. We also demonstrate the opportunities given by our method for practitioners on a real data example through calibration of the Liquid Drop Model of nuclear binding energies.

A flexible and efficient Bayesian implementation of point process models for spatial capture-recapture data.

Spatial capture-recapture (SCR) is now routinely used for estimating abundance and density of wildlife populations. A standard SCR model includes sub-models for the distribution of individual activity centers (ACs) and for individual detections conditional on the locations of these ACs. Both sub-models can be expressed as point processes taking place in continuous space, but there is a lack of accessible and efficient tools to fit such models in a Bayesian paradigm. Here, we describe a set of custom functions and distributions to achieve this. Our work allows for more efficient model fitting with spatial covariates on population density, offers the option to fit SCR models using the semi-complete data likelihood (SCDL) approach instead of data augmentation, and better reflects the spatially continuous detection process in SCR studies that use area searches. In addition, the SCDL approach is more efficient than data augmentation for simple SCR models while losing its advantages for more complicated models that account for spatial variation in either population density or detection. We present the model formulation, test it with simulations, quantify computational efficiency gains, and conclude with a real-life example using non-invasive genetic sampling data for an elusive large carnivore, the wolverine (Gulo gulo) in Norway.

Second Data Release of the COSMOS Lyα Mapping and Tomography Observations: The First 3D Maps of the Detailed Cosmic Web at 2.05 < z < 2.55

We present the second data release of the COSMOS Lyα Mapping And Tomography Observations Survey conducted with the Low Resolution Imaging Spectrometer on the Keck I telescope. This project used Lyα forest absorption in the spectra of faint star-forming galaxies and quasars at z ∼ 2–3 to trace neutral hydrogen in the intergalactic medium. In particular, we use 320 objects over a footprint of ∼0.2 deg2 to reconstruct the absorption field at 2.05 < z < 2.55 at ∼2 h −1 Mpc resolution. We apply a Wiener filtering technique to the observed data to reconstruct three-dimensional (3D) maps of the field over a volume of 4.1 × 105 h −3 Mpc3. In addition to the filtered flux maps, for the first time we infer the underlying dark matter field through a forward-modeling framework from a joint likelihood of galaxy and Lyα forest data, finding clear examples of the detailed cosmic web consisting of cosmic voids, sheets, filaments, and nodes. In addition to traditional figures, we present a number of interactive 3D models to allow exploration of the data and qualitative comparisons to known galaxy surveys. We find that our inferred overdensities are consistent with those found from galaxy fields. We will make all our reduced spectra, extracted Lyα forest pixel data, and reconstructed tomographic maps publicly available upon publication.

The method of forced probabilities: a computation trick for Bayesian model evidence

Bayesian model selection objectively ranks competing models by computing Bayesian Model Evidence (BME) against test data. BME is the likelihood of data to occur under each model, averaged over uncertain parameters. Computing BME can be problematic: exact analytical solutions require strong assumptions; mathematical approximations (information criteria) are often strongly biased; assumption-free numerical methods (like Monte Carlo) are computationally impossible if the data set is large, for example like high-resolution snapshots from experimental movies. To use BME as ranking criterion in such cases, we develop the “Method of Forced Probabilities (MFP)”. MFP swaps the direction of evaluation: instead of comparing thousands of model runs on random model realizations with the observed movie snapshots, we force models to reproduce the data in each time step and record the individual probabilities of the model following these exact transitions. MFP is fast and accurate for models that fulfil the Markov property in time, paired with high-quality data sets that resolve all individual events. We demonstrate our approach on stochastic macro-invasion percolation models that simulate gas migration in porous media, and list additional examples of probable applications. The corresponding experimental movie was obtained from slow gas injection into water-saturated, homogeneous sand in a 25 x 25 x 1 cm acrylic glass tank. Despite the movie not always satisfying the high demands (resolving all individual events), we can apply MFP by suggesting a few workarounds. Results confirm that the proposed method can compute BME in previously unfeasible scenarios, facilitating a ranking among competing model versions for future model improvement.

Population Pharmacokinetics of Inotuzumab Ozogamicin (InO) As Single Agent in Pediatric Relapsed/Refractory Acute Lymphoblastic Leukemia - Results from the ITCC-059 Phase IA and Phase II Trial

INTRODUCTION: This population pharmacokinetics (PopPK) analysis assessed the disposition of InO, a CD22 directed antibody conjugated with calicheamicin, as single agent in pediatric subjects with relapsed/refractory (R/R) B-cell precursor CD22+ acute lymphoblastic leukemia (BCP-ALL). Pooled data from the phase IA and II of the trial ITCC-059 (EudraCT:2016-000227-71) are presented. Clinical results from the Phase IA and Phase II were reported previously (Brivio et al., 2021; Pennesi et al., 2022). The trial was sponsored by Erasmus MC and financed by Pfizer. METHODS: Patients aged 1-18 years, in M2 or M3 marrow status, and either ≥ 2nd relapsed, transplanted after 1st relapse, or with refractory disease were enrolled. In Phase I, InO (fractionated in 3 doses/cycle at day 1, 8 and 15) was initially administered at 1.4 mg/m2/cycle (0.6 + 0.4 + 0.4 mg/m2, dose level 1 (DL1)), then escalated to 1.8 mg/m2 (0.8 + 0.5 + 0.5 mg/m2, DL2). In Phase II, patients received 1.8 mg/m2/cycle of InO, or 1.5 mg/m2/cycle (0.5 + 0.5 + 0.5 mg/m2) once remission was achieved. A maximum of 6 cycles were allowed, except for patients proceeding to transplant, for which maximum 2-3 cycles were recommended. A sparse sampling schedule was applied (on day 1, 8, 15 and 22 (cycle 1) or 28 (cycles 2-3)). The PopPK of InO was developed using nonlinear mixed-effects analysis and combining pediatric data from the trial ITCC-059 with data from 11 trials in 765 adult patients with R/R ALL (n=234) or non-Hodgkin's lymphoma (NHL) (n=531) provided by Pfizer. A prior PopPK model developed for adults (Garrett et al., 2019) was used as a basis for pediatric data. This model had two-compartments with both a linear clearance (CL1) and time-dependent clearance (CLt) that includes a decay coefficient (kdes). Covariates included in that analysis, based on Garret et al., were baseline body surface area (BSA) on CL1, CLt, and volume of distribution in the central compartment; diagnosis (ALL/NHL) and/or bioanalytical assay method on CL1, and the decay coefficient associated with time-dependent clearance (kdes); absence of concomitant rituximab (RITXI) on CL1; and baseline percentage of blasts in the peripheral blood (BLSTPB) as a covariate on kdes of CLt. Simulations were performed to predict InO exposures in both pediatric and adult patients at a fixed dosing regimen of 1.8 mg/m2/cycle. RESULTS: Pharmacokinetic pediatric data were collected from 53 patients (See table 1 for baseline characteristics); 13 treated at DL1, and 40 at DL2; in total 563 serum PK observations were collected. When combined with adult data, the final analysis included a total of 818 patients and 8924 serum PK observations, of which 3394 (38.0%) below the lower limit of quantitation (LLOQ); and hence the M3 method (maximizing the likelihood for data ≥ LLOQ and treating PK data < LLOQ as censored) was selected. Overall, the previous model developed for adults described the pediatric patients’ PK well. Besides the covariates identified in the adult model (BSA, RTX, diagnosis and BLSTPB), the current model also identified the effect of pediatric patients on kdes as a significant covariate. In the final model, InO typical value of CL1 was estimated to be 0.113 L/hr with 40% inter-individual variability (IIV); CL2 was estimated to be 0.384 L/hr with 74% IIV; and central volume of distribution (V1) was estimated to be 6.56 L with 41% IIV. The kdes was estimated to be 0.036 h-1 with 54% IIV. The inter-compartmental CL and peripheral volume of distribution were estimated to be 0.045 L/hr and 4.70 L, respectively. The simulated median Cmax and the accumulated area under the curve (AUC) at end of cycle 1 were 191 ng/mL and 24550 ng.hr/mL; 155 ng/mL and 18200 ng.hr/mL for pediatric and adult patients with ALL, respectively. The simulated median Cmax and accumulated AUC at end of cycle 2 were 284 ng/mL and 117830 ng.hr/mL; 217 ng/mL and 90270 ng.hr/mL for children and adults, respectively. CONCLUSIONS: InO PK is generally comparable between pediatric and adult patients with R/R ALL. This supports the same dosing regimen in these two populations at 1.8 mg/m2/cycle until remission then 1.5 mg/m2/cycle, the same as per our phase I and II trials. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

The multivariate-Tweedie: a self-weighting likelihood for age and length composition data arising from hierarchical sampling designs

Abstract Weighting data appropriately in stock assessment models is necessary to diagnose model mis-specification, estimate uncertainty, and when combining data sets. Age- and length-composition data are often fitted using a multinomial distribution and then reweighted iteratively, and the Dirichlet-multinomial (“DM”) likelihood provides a model-based alternative that estimates an additional parameter and thereby “self-weights” data. However, the DM likelihood requires specifying an input sample size (ninput), which is often unavailable and results are sensitive to ninput. We therefore introduce the multivariate-Tweedie (MVTW) as alternative with three benefits: (1) it can identify both overdispersion (downweighting) or underdispersion (upweighting) relative to the ninput; (2) proportional changes in ninput are exactly offset by parameters; and (3) it arises naturally when expanding data arising from a hierarchical sampling design. We use an age-structured simulation to show that the MVTW (1) can be more precise than the DM in estimating data weights, and (2) can appropriately upweight data when needed. We then use a real-world state-space assessment to show that the MVTW can easily be adapted to other software. We recommend that stock assessments explore the sensitivity to specifying DM, MVTW, and logistic-normal likelihoods, particularly when the DM estimates an effective sample size approaching ninput.

On the equivalence of one-inflated zero-truncated and zero-truncated one-inflated count data likelihoods.

One-inflation in zero-truncated count data has recently found considerable attention. There are currently two views in the literature. In the first approach, the untruncated model is considered as one-inflated whereas in the second approach the truncated model is viewed as one-inflated. Here, we show that both models have identical model spaces as well as identical maximum likelihoods. Consequences of population size estimation are illuminated, and the findings are illustrated at hand of two casestudies.

Parameter estimation for grouped data using EM and MCEM algorithms

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For example, rather than providing the exact measurements of their clients, they may only provide researchers with grouped data, that is, the number of clients falling in each of a set of non-overlapping measurement intervals. The challenge is to estimate the mean and variance structure of the hidden ungrouped data based on the observed grouped data. To tackle this problem, this work considers the exact observed data likelihood and applies the Expectation-Maximization (EM) and Monte Carlo EM (MCEM) algorithms for cases where the hidden data follow a univariate, bivariate, or multivariate normal distribution. Simulation studies are conducted to evaluate the performance of the proposed EM and MCEM algorithms. The well-known Galton data set is considered as an application example.

A Generalized Integration Approach to Association Analysis with Multi-category Outcome: An Application to a Tumor Sequencing Study of Colorectal Cancer and Smoking

Cancer is a heterogeneous disease, and rapid progress in sequencing and -omics technologies has enabled researchers to characterize tumors comprehensively. This has stimulated an intensive interest in studying how risk factors are associated with various tumor heterogeneous features. The Cancer Prevention Study-II (CPS-II) cohort is one of the largest prospective studies, particularly valuable for elucidating associations between cancer and risk factors. In this paper, we investigate the association of smoking with novel colorectal tumor markers obtained from targeted sequencing. However, due to cost and logistic difficulties, only a limited number of tumors can be assayed, which limits our capability for studying these associations. Meanwhile, there are extensive studies for assessing the association of smoking with overall cancer risk and established colorectal tumor markers. Importantly, such summary information is readily available from the literature. By linking this summary information to parameters of interest with proper constraints, we develop a generalized integration approach for polytomous logistic regression model with outcome characterized by tumor features. The proposed approach gains the efficiency through maximizing the joint likelihood of individual-level tumor data and external summary information under the constraints that narrow the parameter searching space. We apply the proposed method to the CPS-II data and identify the association of smoking with colorectal cancer risk differing by the mutational status of APC and RNF43 genes, neither of which is identified by the conventional analysis of CPS-II individual data only. These results help better understand the role of smoking in the etiology of colorectal cancer.

Translation and rotation equivariant normalizing flow (TRENF) for optimal cosmological analysis

ABSTRACT Our Universe is homogeneous and isotropic, and its perturbations obey translation and rotation symmetry. In this work, we develop translation and rotation equivariant normalizing flow (TRENF), a generative normalizing flow (NF) model which explicitly incorporates these symmetries, defining the data likelihood via a sequence of Fourier space-based convolutions and pixel-wise non-linear transforms. TRENF gives direct access to the high dimensional data likelihood p(x|y) as a function of the labels y, such as cosmological parameters. In contrast to traditional analyses based on summary statistics, the NF approach has no loss of information since it preserves the full dimensionality of the data. On Gaussian random fields, the TRENF likelihood agrees well with the analytical expression and saturates the Fisher information content in the labels y. On non-linear cosmological overdensity fields from N-body simulations, TRENF leads to significant improvements in constraining power over the standard power spectrum summary statistic. TRENF is also a generative model of the data, and we show that TRENF samples agree well with the N-body simulations it trained on, and that the inverse mapping of the data agrees well with a Gaussian white noise both visually and on various summary statistics: when this is perfectly achieved the resulting p(x|y) likelihood analysis becomes optimal. Finally, we develop a generalization of this model that can handle effects that break the symmetry of the data, such as the survey mask, which enables likelihood analysis on data without periodic boundaries.

Deep Unsupervised Hashing with Latent Semantic Components

Deep unsupervised hashing has been appreciated in the regime of image retrieval. However, most prior arts failed to detect the semantic components and their relationships behind the images, which makes them lack discriminative power. To make up the defect, we propose a novel Deep Semantic Components Hashing (DSCH), which involves a common sense that an image normally contains a bunch of semantic components with homology and co-occurrence relationships. Based on this prior, DSCH regards the semantic components as latent variables under the Expectation-Maximization framework and designs a two-step iterative algorithm with the objective of maximum likelihood of training data. Firstly, DSCH constructs a semantic component structure by uncovering the fine-grained semantics components of images with a Gaussian Mixture Modal~(GMM), where an image is represented as a mixture of multiple components, and the semantics co-occurrence are exploited. Besides, coarse-grained semantics components, are discovered by considering the homology relationships between fine-grained components, and the hierarchy organization is then constructed. Secondly, DSCH makes the images close to their semantic component centers at both fine-grained and coarse-grained levels, and also makes the images share similar semantic components close to each other. Extensive experiments on three benchmark datasets demonstrate that the proposed hierarchical semantic components indeed facilitate the hashing model to achieve superior performance.

Flow-Based Unconstrained Lip to Speech Generation

Unconstrained lip-to-speech aims to generate corresponding speeches based on silent facial videos with no restriction to head pose or vocabulary. It is desirable to generate intelligible and natural speech with a fast speed in unconstrained settings. Currently, to handle the more complicated scenarios, most existing methods adopt the autoregressive architecture, which is optimized with the MSE loss. Although these methods have achieved promising performance, they are prone to bring issues including high inference latency and mel-spectrogram over-smoothness. To tackle these problems, we propose a novel flow-based non-autoregressive lip-to-speech model (GlowLTS) to break autoregressive constraints and achieve faster inference. Concretely, we adopt a flow-based decoder which is optimized by maximizing the likelihood of the training data and is capable of more natural and fast speech generation. Moreover, we devise a condition module to improve the intelligibility of generated speech. We demonstrate the superiority of our proposed method through objective and subjective evaluation on Lip2Wav-Chemistry-Lectures and Lip2Wav-Chess-Analysis datasets. Our demo video can be found at https://glowlts.github.io/.

Personalized Public Policy Analysis in Social Sciences Using Causal-Graphical Normalizing Flows

Structural Equation/Causal Models (SEMs/SCMs) are widely used in epidemiology and social sciences to identify and analyze the average causal effect (ACE) and conditional ACE (CACE). Traditional causal effect estimation methods such as Inverse Probability Weighting (IPW) and more recently Regression-With-Residuals (RWR) are widely used - as they avoid the challenging task of identifying the SCM parameters - to estimate ACE and CACE. However, much work remains before traditional estimation methods can be used for counterfactual inference, and for the benefit of Personalized Public Policy Analysis (P3A) in the social sciences. While doctors rely on personalized medicine to tailor treatments to patients in laboratory settings (relatively closed systems), P3A draws inspiration from such tailoring but adapts it for open social systems. In this article, we develop a method for counterfactual inference that we name causal-Graphical Normalizing Flow (c-GNF), facilitating P3A. A major advantage of c-GNF is that it suits the open system in which P3A is conducted. First, we show how c-GNF captures the underlying SCM without making any assumption about functional forms. This capturing capability is enabled by the deep neural networks that model the underlying SCM via observational data likelihood maximization using gradient descent. Second, we propose a novel dequantization trick to deal with discrete variables, which is a limitation of normalizing flows in general. Third, we demonstrate in experiments that c-GNF performs on-par with IPW and RWR in terms of bias and variance for estimating the ATE, when the true functional forms are known, and better when they are unknown. Fourth and most importantly, we conduct counterfactual inference with c-GNFs, demonstrating promising empirical performance. Because IPW and RWR, like other traditional methods, lack the capability of counterfactual inference, c-GNFs will likely play a major role in tailoring personalized treatment, facilitating P3A, optimizing social interventions - in contrast to the current `one-size-fits-all' approach of existing methods.

Reward-Reinforced Generative Adversarial Networks for Multi-Agent Systems

Multi-agent systems deliver highly resilient and adaptable solutions for common problems in telecommunications, aerospace, and industrial robotics. However, achieving an optimal global goal remains a persistent obstacle for collaborative multi-agent systems, where learning affects the behaviour of more than one agent. A number of nonlinear function approximation methods have been proposed for solving the Bellman equation, which describe a recursive format of an optimal policy. However, how to leverage the value distribution based on reinforcement learning, and how to improve the efficiency and efficacy of such systems remain a challenge. In this work, we developed a reward-reinforced generative adversarial network to represent the distribution of the value function, replacing the approximation of Bellman updates. We demonstrated our method is resilient and outperforms other conventional reinforcement learning methods. This method is also applied to a practical case study: maximising the number of user connections to autonomous airborne base stations in a mobile communication network. Our method maximises the data likelihood using a cost function under which agents have optimal learned behaviours. This reward-reinforced generative adversarial network can be used as a generic framework for multi-agent learning at the system level.

Mutual information maximization for amortized likelihood inference from sampled trajectories: MINIMALIST.

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence ratio, or equivalently the posterior function. Here we frame the inference task as an estimation of an energy function parametrized with an artificial neural network. We present an intuitive approach, named MINIMALIST, in which the optimal model of the likelihood-to-evidence ratio is found by maximizing the likelihood of simulated data. Within this framework, the connection between the task of simulation-based inference and mutual information maximization is clear, and we show how several known methods of posterior estimation relate to alternative lower bounds to mutual information. These distinct objective functions aim at the same optimal energy form and therefore can be directly benchmarked. We compare their accuracy in the inference of model parameters, focusing on four dynamical systems that encompass common challenges in time series analysis: dynamics driven by multiplicative noise, nonlinear interactions, chaotic behavior, and high-dimensional parameter space.

Machine learning‐accelerated gradient‐based Markov chain Monte Carlo inversion applied to electrical resistivity tomography

ABSTRACTExpensive forward model evaluations and the curse of dimensionality usually hinder applications of Markov chain Monte Carlo algorithms to geophysical inverse problems. Another challenge of these methods is related to the definition of an appropriate proposal distribution that simultaneously should be inexpensive to manipulate and a good approximation of the posterior density. Here we present a gradient‐based Markov chain Monte Carlo inversion algorithm that is applied to cast the electrical resistivity tomography into a probabilistic framework. The sampling is accelerated by exploiting the Hessian and gradient information of the negative log‐posterior to define a proposal that is a local, Gaussian approximation of the target posterior probability. On the one hand, the computing time to run the many forward evaluations needed for both the data likelihood evaluation and the Hessian and gradient computation is decreased by training a residual neural network to predict the forward mapping between the resistivity model and the apparent resistivity value. On the other hand, the curse of dimensionality issue and the computational effort related to the Hessian and gradient manipulation are decreased by compressing data and model spaces through a discrete cosine transform. A non‐parametric distribution is assumed as the prior probability density function. The method is first demonstrated on synthetic data and then applied to field measurements. The outcomes provided by the presented approach are also benchmarked against those obtained when a computationally expensive finite‐element code is employed for forward modelling , with the results of a gradient‐free Markov chain Monte Carlo inversion, and also compared with the predictions of a deterministic inversion. The implemented approach not only guarantees uncertainty assessments and model predictions comparable with those achieved by more standard inversion strategies, but also drastically decreases the computational cost of the probabilistic inversion, making it similar to that of a deterministic inversion.

Optimization and sensitivity analysis of existing deep learning models for pavement surface monitoring using low-quality images

Automated pavement distress detection systems have become increasingly sought after by road agencies to increase the efficiency of field surveys and reduce the likelihood of insufficient road condition data. However, many modern approaches are developed without practical testing using real-world scenarios. This paper addresses this by practically analyzing Deep Learning models to detect pavement distresses using French Secondary road surface images, given the issues of limited available road condition data in those networks. The study specifically explores several experimental and sensitivity-testing strategies using augmentation and hyperparameter case studies to bolster practical model instrumentation and implementation. The tests achieve adequate distress detection performance and provide an understanding of how changing aspects of the workflow influence the actual engineering application, thus taking another step towards low-cost automation of aspects of the pavement management system.

Causality-aware Enhanced Model for Multi-hop Question Answering over Knowledge Graphs

To improve the performance of knowledge graph-based question answering system (KGQA), several approaches have been developed to construct a semantic parser based on entity linking, relation identification and logical/numerical structure identification. However, existing methods arrive at answers only by maximizing the data likelihood only on the sparse or imbalanced explicit relations, ignoring the potentially large number of latent relations. It makes KGQA suffer from a high level of spurious entity relations and missing link challenge. In this paper, we propose a causal filter (CF) model for KGQA (CF-KGQA), which performs causal interference on the relation representation space to reduce the spurious relation representation in a data-driven manner, i.e., the goal of this work is to comprehensively discover disentangled latent factors to alleviate the spurious correlation problem in KGQA. The model comprises a causal pairwise aggregator (AP) and a disentangled latent factor aggregator (AC). The former filters out most spurious entity relations inconsistent to their dense groups’ neighborhood, and generates a causal pairwise matrix among all the candidate relations. The latter learns the latent relation representation via an encoder–decoder on the causal pairwise matrix. It disconnects the latent factor and the causal confounder beneath the knowledge embedding space by causal intervention. To prove the effectiveness and efficiency of the proposed approach, we test CF-KGQA and other state-of-the-art methods on four public real-world datasets. The experiments indicate that our approach outperforms the recent methods and is also less sensitive to the spurious correlation problem, thus demonstrating the robustness of CF-KGQA.

Contrasting the bulk viscous model with the standard $\Lambda$CDM using Bayesian statistics

The causal dissipative model is a plausible choice to explain the late accelerated epoch of the universe. At the same time, \(\Lambda\)CDM is considered the standard model to explain the cosmological data corresponding to the late evolution of the universe. We consider a bulk viscous model in which dissipation is driven by the bulk viscosity \(\zeta =\alpha \rho ^{1/2}\), described using the full causal Israel-Stewart theory. We computed the model parameters using the latest observational data (Pantheon). We contrasted this model with \(\Lambda\)CDM model for the late accelerated phase using the Bayesian inference method. The Bayes factor was obtained by calculating the likelihood for Pantheon data. Suitable prior values were assumed for model parameters to calculate the likelihood. It shows that the evidence for \(\Lambda\)CDM against this viscous model is very strong according to the Jeffreys scale.