Bayesian Inference Methods Research Articles

Holistic characterization of an under-expanded high-enthalpy jet under uncertainty

Elaborate methodologies have been developed to study the thermo-chemical response of materials in high-enthalpy flows. To reach the high magnitudes of heat flux encountered in some hypersonic applications, one can resort to supersonic jets. They involve several physical effects, such as detached shocks ahead of probes. Because of these features, characterizing supersonic flows is a challenging task, especially when one accounts for experimental and modeling uncertainties. Building on the development of stochastic approaches, we propose a holistic methodology to determine the quantities of interest in an optimal manner for an under-expanded high-enthalpy jet, using both experimental measurements and high-fidelity flow simulations. Given the high computational cost of the high-fidelity simulations needed to describe the flow, we built an adaptive/multi-fidelity surrogate model to replace the estimation of the costly computer solver. A Bayesian inference method then allowed for characterizing an experiment carried out in the von Karman Institute's Plasmatron facility, for which no robust methodology currently exists. We show that the reservoir pressure and temperature and the nitrogen catalytic recombination coefficient of the copper probes can be accurately determined from the available measurements. Contrarily, the test conditions do not allow us to estimate the oxygen catalytic recombination coefficient. Finally, the characterized uncertainties are propagated through the numerical solver, yielding an uncertainty-based high-fidelity representation of the hypersonic flow's structure variability.

Advancing Bayesian Inference: Fitting Type I Half-logistic Nadarajah-Haghighi Distribution and its Comparison with Related Distributions for Censored Survival Data

In recent years, the field of Bayesian modeling of generalized distributions has garnered substantial attention. This surge in interest can be attributed to the remarkable strides made in computational capabilities and the enhanced accessibility of sophisticated software tools. This study aims to apply Bayesian inference methods to the Type I Half-logistic Nadarajah- Haghighi model and compares it with the Exponential model and the Type I Half-logistic Exponential model. These distributions are analyzed and fitted to censored survival data using the probabilistic programming language STAN. To incorporate censored mechanisms within the STAN framework, customized codes are developed. The models are then compared using fully Bayesian model selection methods.. KEYWORDS :Censored data, Nadarajah-Haghighi distribution, Type I half-logistic family, LOOIC, WAIC, STAN.

Bayesian inference methodology to characterize the dust emissivity at far-infrared and submillimeter frequencies

ABSTRACT We present a Bayesian inference method to characterize the dust emission properties using the well-known dust-${\rm H\,{\small I}}$ correlation in the diffuse interstellar medium at Planck frequencies $\nu \ge 217$ GHz. We use the Galactic ${\rm H\,{\small I}}$ map from the Galactic All-Sky Survey (GASS) as a template to trace the Galactic dust emission. We jointly infer the pixel-dependent dust emissivity and the zero level present in the Planck intensity maps. We use the Hamiltonian Monte Carlo technique to sample the high-dimensional parameter space ($D \sim 10^3$). We demonstrate that the methodology leads to unbiased recovery of dust emissivity per pixel and the zero level when applied to realistic Planck sky simulations over a 6300 $\rm {deg}^2$ area around the Southern Galactic pole. As an application on data, we analyse the Planck intensity map at 353 GHz to jointly infer the pixel-dependent dust emissivity at $N_{\rm side}=32$ resolution (1.8° pixel size) and the global offset. We find that the spatially varying dust emissivity has a mean of 0.031 MJy sr$^{-1}$$(10^{20} \, \mathrm{cm^{-2}})^{-1}$ and $1\sigma$ standard deviation of 0.007 MJy sr$^{-1}$$(10^{20} \, \mathrm{cm^{-2}})^{-1}$. The mean dust emissivity increases monotonically with increasing mean ${\rm H\,{\small I}}$ column density. We find that the inferred global offset is consistent with the expected level of cosmic infrared background (CIB) monopole added to the Planck data at 353 GHz. This method is useful in studying the line-of-sight variations of dust spectral energy distribution in the multiphase interstellar medium.

Multiple evidence reveals a new species of Neocucurbitaria (Cucurbitariaceae, Pleosporales) from China

Xanthoceras sorbifolium (yellowhorn) is an endemic edible oil crop in China. A novel Neocucurbitaria species associated with dead stems of yellowhorn in Jilin Province (northeast China) is described and illustrated. It is characterized by stromata with 1–5 locules and a subhyaline pycnidial wall under the inner layer. Full morphological details and a comparison with closely related species are also provided. The new species differs from the closely related species N. ribicola, N. rhamni, N. rhamnicola and N. rhamnioides by its distinct conidiogenous cells and conidia. Phylogenetic analysis (maximum likelihood and Bayesian inference method) of combined ITS, LSU, rpb2, tef1-α and tub2 sequence data reveal that two strains of the fungus differ from all other species of Neocucurbitaria (Cucurbitariaceae). Therefore, we introduce N. subribicola as a new species, and this is the first report of the asexual morph of Neocucurbitaria in China

Generalized fiducial inference for the generalized logistic distribution: Censored and uncensored cases

. This article primarily considers the statistical inference of the scale parameter, shape parameter, and reliability of the generalized logistic distribution in both censored and uncensored cases. For the progressively Type-II censored and complete samples, the frequentist method is utilized to construct asymptotic confidence intervals, and the Bayesian inference method is employed for constructing the point estimators as well as posterior credible intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Furthermore, the non parametric generalized fiducial method is introduced to estimate the survival function. Simulation results demonstrate that the generalized fiducial method consistently outperforms other methods in terms of mean square error, average length, and empirical coverage. Finally, two real datasets are used to illustrate the proposed methods.

RETRACTED: Phylogenomic data exploration with increased sampling provides new insights into the higher-level relationships of butterflies and moths (Lepidoptera)

A robust and stable phylogenetic framework is a fundamental goal of evolutionary biology. As the third largest insect order in the world following Coleoptera and Diptera, Lepidoptera (butterflies and moths) play a central role in almost every terrestrial ecosystem as indicators of environmental change and serve as important models for biologists exploring questions related to ecology and evolutionary biology. However, for such a charismatic insect group, the higher-level phylogenetic relationships among its superfamilies are still poorly resolved. Compared to earlier phylogenomic studies, we increased taxon sampling among Lepidoptera (37 superfamilies and 68 families containing 263 taxa) and acquired a series of large amino-acid datasets from 69,680 to 400,330 for phylogenomic reconstructions. Using these datasets, we explored the effect of different taxon sampling with significant increases in the number of included genes on tree topology by considering a series of systematic errors using maximum-likelihood (ML) and Bayesian inference (BI) methods. Moreover, we also tested the effectiveness in topology robustness among the three ML-based models. The results showed that taxon sampling is an important determinant in tree robustness of accurate lepidopteran phylogenetic estimation. Long-branch attraction (LBA) caused by site-wise heterogeneity is a significant source of bias giving rise to unstable positions of ditrysian groups in phylogenomic reconstruction. Phylogenetic inference showed the most comprehensive framework to reveal the relationships among lepidopteran superfamilies, and presented some newly relationships with strong supports (Papilionoidea was sister to Gelechioidea and Immoidea was sister to Galacticoidea, respectively), but limited by taxon sampling, the relationships within the species-rich and relatively rapid radiation Ditrysia and especially Apoditrysia remain poorly resolved, which need to increase taxon sampling for further phylogenomic reconstruction. The present study demonstrates that taxon sampling is an important determinant for an accurate lepidopteran tree of life and provides some essential insights for future lepidopteran phylogenomic studies.

Phylogenetic Analysis of Rare and Endangered Tulipa Species (Liliaceae) of Kazakhstan Based on Universal Barcoding Markers.

In Kazakhstan, the genus Tulipa is represented by 35 species, 18 of which are listed in the Red Data Book of Kazakhstan and protected by the state. Recent studies of tulip specimens from regions bordering Kazakhstan emphasize the significance of species inventory and report the discovery of several hybrids. In this study, eight tulip species were identified based on morphological characteristics and using DNA barcoding methods. Molecular genetic markers, including nrDNA (ITS) and cpDNA markers (rbcL, matK), of the studied species were sequenced and analyzed using the Bayesian inference and maximum likelihood phylogenetic analysis methods. Our work demonstrates that DNA barcodes based on the ITS, rbcL, and matK marker regions have successful practical applicability, with ITS being the most informative at the intragenic level. However, for distinguishing closely related taxa, the most effective approach would be to use a combined dataset of sequences from multiple DNA markers. The results showed discrepancies in the placement of several taxa (T. kaufmanniana, T. patens), likely due to introgression and natural spontaneous hybridization. The molecular phylogenetic analysis suggests the existence of a previously undescribed hybrid between T. patens and T. alberti. Further detailed population studies are needed to validate this hypothesis.

A New Species of Scymnus (Coleoptera, Coccinellidae) from Pakistan with Mitochondrial Genome and Its Phylogenetic Implications.

In this study, a new species of the subgenus Pullus belonging to the Scymnus genus from Pakistan, Scymnus (Pullus) cardi sp. nov., was described and illustrated, with information on its distribution, host plants, and prey. Additionally, the completed mitochondrial genome (mitogenome) of the new species using high-throughput sequencing technology was obtained. The genome contains the typical 37 genes (13 protein-coding genes, two ribosomal RNAs, and 22 transfer RNAs) and a non-coding control region, and is arranged in the same order as that of the putative ancestor of beetles. The AT content of the mitogenome is approximately 85.1%, with AT skew and GC skew of 0.05 and -0.43, respectively. The calculated values of relative synonymous codon usage (RSCU) determine that the codon UUA (L) has the highest frequency. Furthermore, we explored the phylogenetic relationship among 59 representatives of the Coccinellidae using Bayesian inference and maximum likelihood methods, the results of which strongly support the monophyly of Coccinellinae. The phylogenetic results positioned Scymnus (Pullus) cardi in a well-supported clade with Scymnus (Pullus) loewii and Scymnus (Pullus) rubricaudus within the genus Scymnus and the tribe Scymnini. The mitochondrial sequence of S. (P.) cardi will contribute to the mitochondrial genome database and provide helpful information for the identification and phylogeny of Coccinellidae.

Bayesian inference for the onset time and epidemiological characteristics of emerging infectious diseases.

Emerging infectious diseases pose a significant threat to global public health. Timely detection and response are crucial in mitigating the spread of such epidemics. Inferring the onset time and epidemiological characteristics is vital for accelerating early interventions, but accurately predicting these parameters in the early stages remains challenging. We introduce a Bayesian inference method to fit epidemic models to time series data based on state-space modeling, employing a stochastic Susceptible-Exposed-Infectious-Removed (SEIR) model for transmission dynamics analysis. Our approach uses the particle Markov chain Monte Carlo (PMCMC) method to estimate key epidemiological parameters, including the onset time, the transmission rate, and the recovery rate. The PMCMC algorithm integrates the advantageous aspects of both MCMC and particle filtering methodologies to yield a computationally feasible and effective means of approximating the likelihood function, especially when it is computationally intractable. To validate the proposed method, we conduct case studies on COVID-19 outbreaks in Wuhan, Shanghai and Nanjing, China, respectively. Using early-stage case reports, the PMCMC algorithm accurately predicted the onset time, key epidemiological parameters, and the basic reproduction number. These findings are consistent with empirical studies and the literature. This study presents a robust Bayesian inference method for the timely investigation of emerging infectious diseases. By accurately estimating the onset time and essential epidemiological parameters, our approach is versatile and efficient, extending its utility beyond COVID-19.

Bayesian Inference Based on Monte Carlo Technique for Multiplier of Performance Shaping Factor

Abstract The Human Error Probabilities (HEP) can be estimated using multipliers that correspond to the level of Performance Shaping Factors (PSFs) in the Human Reliability Analysis (HRA). This paper focuses on the adjustment of multipliers through Bayesian inference based on Monte Carlo techniques using the experimental results from simulators. Markov Chain Monte Carlo (MCMC) and Bayesian Monte Carlo (BMC) are used as Bayesian inference methods based on Monte Carlo techniques. MCMC is utilized to obtain the posterior distribution of the multipliers. BMC is used for the estimation of the moments of the posterior distribution such as the mean and variance. The results obtained by MCMC and that by BMC well agree with the reference results. As a case study, the data assimilation was performed using the results of the simulator experiment of Halden reactor. The results show that the multiplier changes by the result of a particular scenario and HEP of another scenario that uses the same multiplier also changes by data assimilation. Also, in the case study, the correlation between multipliers is obtained by the data assimilation and the correlation contributes to the reduction of uncertainty of HEP.

The rearrangement features and phylogenetic signals of mitochondrial genomes of gall midge subfamily Cecidomyiinae (Diptera: Cecidomyiidae) with first complete mitogenome of an economically important mango gall midge pest, Procontarina fructiculi from Guangxi, China

ABSTRACT In this study, we obtained the first complete mitochondrial genome of Procontarina fructiculi, an important mango gall midge pest from Guangxi, China. The mitogenome of P. fructiculi was sequenced and annotated for the first time, and compared with all the published and annotated data of Cecidomyiidae species to summarise the gall midge organisation and rearrangement features of mitochondrial genomes with phylogenetic analysis. The comparison of gall midge mitochondrial genome structure shows that the rearrangement of the mitochondrial gene structure is very common, and most rearrangements are embodied in rearrangement in the order of tRNAs. The phylogenetic results based on the maximum likelihood (ML) and Bayesian inference (BI) methods both highly supported the monophyly of Cecidomyiinae. Cecidomyiinae can be divided into two distinct clades (except Cecidomyiidae sp. 3): A: (Mayetiola destructor + Rhopalomyia pomum) and B: (Asphondylia rosetta + ((Procontarinia fructiculi + Orseolia oryzae) + ((Cecidomyiidae sp. 1 + Aphidoletes aphidimyza) + Cecidomyiidae sp. 2))). Based on the above results, some phylogenetic signals in rearrangement have been found in the mitochondrial genome structure of Cecidomyiinae for the first time.

Morphological and molecular identification for four new wood-inhabiting species of Trechispora (Basidiomycota) from China.

Four new wood-inhabiting fungi, Trechisporaalbofarinosa, T.bisterigmata, T.pileata and T.wenshanensisspp. nov., are proposed based on a combination of morphological features and molecular evidence. Trechisporaalbofarinosa is characterized by the farinose basidiomata with flocculence hymenial surface, a monomitic hyphal system with clamped generative hyphae, and ellipsoid, warted basidiospores. Trechisporabisterigmata is characterized by the membranous basidiomata with odontioid hymenial surface, rhizomorphic sterile margin, barrelled basidia and subglobose to broad ellipsoid, smooth basidiospores. Trechisporapileata is characterized by the laterally contracted base, solitary or imbricate basidiomata, fan shaped pileus, radially striate-covered surface with appressed scales, odontioid hymenophore surface, and subglobose to broad ellipsoid, thin-walled, smooth basidiospores. Trechisporawenshanensis is characterized by a cottony basidiomata with a smooth hymenial surface, and ellipsoid, thin-walled, warted basidiospores. Sequences of ITS and LSU marker of the studied samples were generated, and phylogenetic analyses were performed with the maximum likelihood, maximum parsimony, and Bayesian inference methods. The phylogenetic tree inferred from the ITS+nLSU sequences highlighted that four new species were grouped into the genus Trechispora.

Common Methods for Phylogenetic Tree Construction and Their Implementation in R.

A phylogenetic tree can reflect the evolutionary relationships between species or gene families, and they play a critical role in modern biological research. In this review, we summarize common methods for constructing phylogenetic trees, including distance methods, maximum parsimony, maximum likelihood, Bayesian inference, and tree-integration methods (supermatrix and supertree). Here we discuss the advantages, shortcomings, and applications of each method and offer relevant codes to construct phylogenetic trees from molecular data using packages and algorithms in R. This review aims to provide comprehensive guidance and reference for researchers seeking to construct phylogenetic trees while also promoting further development and innovation in this field. By offering a clear and concise overview of the different methods available, we hope to enable researchers to select the most appropriate approach for their specific research questions and datasets.

Information content of JWST spectra of WASP-39b

The era of James Webb Space Telescope (JWST) transmission spectroscopy of exoplanetary atmospheres commenced with the study of the Saturn-mass gas giant WASP-39b as part of the Early Release Science (ERS) program. WASP-39b was observed using several different JWST instrument modes (NIRCam, NIRISS, NIRSpec G395H and NIRSpec PRISM) and the spectra were published in a series of papers by the ERS team. The current study examines the information content of these spectra measured using the different instrument modes, focusing on the complexity of the temperature-pressure profiles and number of chemical species warranted by the data. We examine if the molecules H2O CO CO2 K H2S CH4 and SO2 are detected in each of the instrument modes. Two Bayesian inference methods are used to perform atmospheric retrievals: the standard nested sampling method, as well as the supervised machine learning method of the random forest (trained on a model grid). For nested sampling, Bayesian model comparison is used as a guide to identify the set of models with the required complexity to explain the data. Generally, non-isothermal transit chords are needed to fit the transmission spectra of WASP-39b, although the complexity of the temperature-pressure profile required is mode-dependent. The minimal set of chemical species needed to fit a spectrum is mode-dependent as well, and also depends on whether grey or non-grey clouds are assumed. When a non-grey cloud model is used to fit the NIRSpec G395H spectrum, it generates a spectral continuum that compensates for the water opacity. The same compensation is absent when fitting the non-grey cloud model to the NIRSpec PRISM spectrum (which has broader wavelength coverage), suggesting that it is spurious. The interplay between the cloud spectral continuum and the water opacity determines if sulphur dioxide is needed to fit either spectrum. The inferred elemental abundances of carbon and oxygen and the carbon-to-oxygen (C/O) ratios are all mode- and model-dependent, and should be interpreted with caution. Bayesian model comparison does not always offer a clear path forward for favouring specific retrieval models (e.g. grey versus non-grey clouds) and thus for enabling unambiguous interpretations of exoplanet spectra.

Molecular evidence provides new insights into the evolutionary origin of an ancient traditional Chinese medicine, the domesticated "Baizhi".

"Baizhi" is a famous herbal medicine in China, and it includes four landraces named as 'Hangbaizhi', 'Chuanbaizhi', 'Qibaizhi', and 'Yubaizhi'. Long-term artificial selection had caused serious degradation of these germplasms. Determining the wild progenitor of the landraces would be benefit for their breed improvements. Previous studies have suggested Angelica dahurica var. dahurica, A. dahurica var. formosana, or A. porphyrocaulis as potential candidates, but the conclusion remains uncertain, and their phylogenetic relationships are still in controversy. In this study, the genetic variation and phylogenetic analyses of these species and four landraces were conducted on the basis of both the nrITS and plastome datasets. Genetic variation analysis showed that all 8 population of four landraces shared only one ITS haplotype, meanwhile extremely low variation occurred within 6 population at plastid genome level. Both datasets supported the four landraces might be originated from a single wild germplasm. Phylogenetic analyses with both datasets revealed largely consistent topology using Bayesian inference and Maximum likelihood methods. Samples of the four landraces and all wild A. dahurica var. dahurica formed a highly supported monophyletic clade, and then sister to the monophyly clade comprised by samples of A. porphyrocaulis, while four landraces were clustered into one clade, which further clustered with a mixed branches of A. porphyrocaulis and A. dahurica var. dahurica to form sister branches for plastid genomes. Furthermore, the monophyletic A. dahurica var. formosana was far distant from the A. dahurica var. dahurica-"Baizhi" clade in Angelica phylogeny. Such inferences was also supported by the evolutionary patterns of nrITS haplotype network and K2P genetic distances. The outcomes indicated A. dahurica var. dahurica is most likely the original plant of "Baizhi". Considering of phylogenetic inference and evolutionary history, the species-level status of A. dahurica var. formosana should be accepted, and the taxonomic level and phylgenetic position of A. porphyrocaulis should be further confirmed. This study preliminarily determined the wild progenitor of "Baizhi" and clarified the phylogenetic relationships among A. dahurica var. dahurica, A.dahurica var. formosana and A. porphyrocaulis, which will provide scientific guidance for wild resources protections and improvement of "Baizhi".

Inferring failure coupling strength in complex networks through generative models

ABSTRACT The failure propagation process has always been a research hotspot in the field of complex system reliability. Most of the research studies focus on the inference of network structure, ignoring one of the most critical parameters for network reliability, failure coupling strength. Here, we develop a generative model describing the failure process to infer the failure coupling strength. Using this model, we generate the node failure sequences under different coupling strength and analyze the spatial properties of failure propagation. We find the failed nodes tend to appear near the previously failed nodes with increasing coupling strength. Based on our generative model, we propose a Bayesian inference method to infer the failure coupling strength from observed system instantaneous failure state data. We find the inferred values are close to the true values for small failure coupling strength. As failure coupling strength increases, error comes from the limits of failure propagation spatial data. We apply this Bayesian inference method to actual biological networks and infer the network failure coupling strength. Our proposed Bayesian inference method helps analyze the hidden failure mechanism from actual scenarios.

The complete chloroplast genome of Oxytropis ochrocephala Bunge 1874 (Fabaceae) and its phylogenetic analysis

This study presents the first-ever complete chloroplast (cp) genome sequence of Oxytropis ochrocephala Bunge 1874, a member of the Fabaceae family. The cp genome spans 126,996 base pairs and includes 109 genes, comprising 76 protein-coding genes, 29 tRNA genes, and four rRNA genes. Notably, the genome lacks an inverted repeat (IR) region. Additionally, we constructed phylogenetic trees for 34 species within Trib. Galegeae, employing both maximum likelihood (ML) and Bayesian inference (BI) methods. These analyses robustly support the monophyly of the Oxytropis species, evidenced by high bootstrap values (BP = 100) and posterior probabilities (PP = 1). Within this clade, O. ochrocephala exhibits a sister relationship with other Oxytropis species. Our findings provide valuable insights into the genetic makeup and evolutionary relationships of O. ochrocephala within the Galegeae tribe.

Transforms-Based Bayesian Tensor Completion Method for Network Traffic Measurement Data Recovery

Network traffic measurement is regarded as the bedrock of next-generation network systems. Its purpose is to monitor the network traffic and provide data support for traffic engineering. For this reason, monitoring traffic data from a network-wide perspective is particularly important. However, the proliferation of network services has led to the explosive growth of network traffic, which has brought significant challenges to the measure of network-wide traffic. Therefore, how to infer network-wide traffic from partial traffic data is extremely important. In this article, a transforms-based Bayesian tensor completion (TBTC) method is proposed to infer network traffic data. First, the heterogeneous network traffic data with missing entries are organized into observation tensors according to temporal dimensions and other attributes. Second, the sparse hierarchical prior is used to induce lateral slices sparsity of factor tensors, which makes the tubal rank of the observation tensor can be estimated. Further, a variational Bayesian inference method is developed for model learning, and an efficient updating method is presented. Finally, two cases of the linear transforms-based tensor completion model are implemented in the experiments. Experimental results on two real-world network traffic datasets validate that the proposed method can efficiently and accurately recover network traffic data.

Revolutionizing prostate cancer diagnosis: Unleashing the potential of an optimized deep belief network for accurate Gleason grading in histological images

PC (Prostate Cancer) is the second highest cause of death due to cancer in men globally. Proper detection and treatment are critical for halting or controlling the growth and spread of cancer cells within the human organism. However, evaluating these sorts of images is difficult and time-consuming, requiring histopathological image recognition as the most reliable method for treating PC because of its distinct visual characteristics. Risk evaluation and treatment planning rely heavily on histological image-based Gleason grading of prostate tumors. This work introduces an innovative approach to histological image analysis for prostate cancer diagnosis and Gleason grading. The Elephant Herding Optimization-based Hyper-parameter Convolutional Deep Belief Network (CDBN-EHO) is presented alongside a grading network head-optimized deep belief network technique for multi-task prediction. Leveraging an effective Bayesian inference method, fully linked Conditional Random Field (CRF) techniques are utilized for segmentation, with pairwise boundary capacities determined by a linear mixture of Gaussian kernels. The multi-task approach aims to enhance performance by incorporating contextual information, leading to breakthrough results in the identification of epithelial cells and the grading of Gleason scores. The objective of this study is to demonstrate the effectiveness of the optimized deep belief network technique in improving diagnostic accuracy and efficiency for prostate cancer diagnosis and Gleason grading in histological images.

Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions

We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops . Our method is built on a denotational semantics represented by probability generating functions , which resolves semantic intricacies induced by intertwining discrete probabilistic loops with conditioning (for encoding posterior observations). We implement our method in a tool called Prodigy; it augments existing computer algebra systems with the theory of generating functions for the (semi-)automatic inference and quantitative verification of conditioned probabilistic programs. Experimental results show that Prodigy can handle various infinite-state loopy programs and exhibits comparable performance to state-of-the-art exact inference tools over loop-free benchmarks.