Bayesian Inference Research Articles

Do higher global oil and wheat prices matter for the wheat flour price in Lebanon?

AbstractThis article investigates the effect of global oil and wheat prices, and local price shocks on the real price of wheat flour in Lebanon. We estimate a structural vector autoregressive model with exogenous variables (SVARX) using Bayesian methods. We then compute the impulse response functions and find that global commodity price shocks play a trivial role. Meanwhile, local gasoline price and wheat flour price‐specific shocks trigger large increases in the Lebanese wheat flour price on impact. Furthermore, since 2020, local gasoline price and wheat flour price‐specific shocks have contributed the most to the historical variation in the Lebanese wheat flour price.

Novel Ransomware Detection Exploiting Uncertainty and Calibration Quality Measures Using Deep Learning

Ransomware poses a significant threat by encrypting files or systems demanding a ransom be paid. Early detection is essential to mitigate its impact. This paper presents an Uncertainty-Aware Dynamic Early Stopping (UA-DES) technique for optimizing Deep Belief Networks (DBNs) in ransomware detection. UA-DES leverages Bayesian methods, dropout techniques, and an active learning framework to dynamically adjust the number of epochs during the training of the detection model, preventing overfitting while enhancing model accuracy and reliability. Our solution takes a set of Application Programming Interfaces (APIs), representing ransomware behavior as input we call “UA-DES-DBN”. The method incorporates uncertainty and calibration quality measures, optimizing the training process for better more accurate ransomware detection. Experiments demonstrate the effectiveness of UA-DES-DBN compared to more conventional models. The proposed model improved accuracy from 94% to 98% across various input sizes, surpassing other models. UA-DES-DBN also decreased the false positive rate from 0.18 to 0.10, making it more useful in real-world cybersecurity applications.

62 Implications of factor analyses and Bayesian network learning to develop composite traits of size attributes in developing beef heifers

Abstract Advancements in phenotypic data collection methods provide opportunities to capture complex biological traits more efficiently. Even so, interpreting those phenotypes and using them in selection decisions is challenging in beef cattle production. Objectives of this study were to 1) develop composite phenotype(s) of economic importance in beef heifers given attributes of their body conformation and ultrasound-based measures of reproductive and carcass traits, and 2) identify associated genomic regions under selection using the structure equation modeling (SEM) approach. In this study, we hypothesized that the interplay of factor analysis and Bayesian Network Learning (BNL) approaches would better define the complex composite traits for size and carcass-related traits in beef heifers. Phenotypic data of admixed beef heifers (n = 336) for different reproductive, body conformational, and carcass-associated phenotypic traits (n = 16) were collected. Using exploratory and confirmatory factor analyses, two latent variables explaining 14 phenotypic traits were identified, herein called Body Size (BS; n = 7 traits represented) and Body Composition (BC; n = 7 traits represented). To efficiently model them in genome-wide association studies (GWAS), fixed effects of data collection year, dam age, and primary breed group as well as causal network structure identified through BNL were used within SEM model of GWAS. Body Size was directly or indirectly contributing to BC based on BNL structure. Given the data-driven approach and novelty of the data, BayesCπ model was applied with the sliding window of 1 Mb to avoid noise and linkage disequilibrium implications. Regions capturing large amounts of genetic variance (Posterior Probability of Association, PPA ≥ 0.8) were mapped to their closest gene for enrichment analysis. Twenty-four different genes were identified associated with both composite phenotypes. Functional enrichment analysis of significantly involved pathways (FDR < 0.05) indicated that genes from the HERC family (HERC3, HERC6, and HERC5) were found involved in cellular growth, and those from desmosomes (DC2, and DC3) were involved in morphogenesis like BS. Genes related to energy metabolism like IMPAD1, and PIGY, along with genes associated with traits like muscular development, and other carcass traits (i.e., FAM184B, NCAPG, and LCORL), were also found associated with BS and BC. Heritability ranged from 0.551 ± 0.048 to 0.897 ± 0.145 for BS and BC, respectively. The combined heritability of reproductive and carcass traits (BC) was much greater than the heritability of any related individual trait reported to date and was comparable for individual BS-related traits. Given this, we conclude that the implications of factor analyses with BNL can provide better biological insights for improved genomic selection in beef cattle, even for traits of low heritability.

Mitogenomic Characterization of South African Leopards and the Effect of Past Climatic Events

Revealing phylogeographic structure is important for accurate subspecies delineation and understanding a species’ evolutionary history. In leopards (Panthera pardus), there are currently nine subspecies recognized. On the African continent, only one subspecies occurs (P. p. pardus), although mitochondrial DNA from historical samples suggests the presence of three putative continental clades: (1) West Africa (WA), (2) Central Africa (CA), and (3) Southern Africa (SA). So far, whole genome data did not recover this phylogeographic structure, although leopards in the southern periphery of their distribution range in Africa have not yet been investigated in detail. The Mpumalanga province of South Africa is of particular interest, as here, the CA and the SA clade possibly meet. The aim of this study was to characterize the first mitogenomes of African leopards from Mpumalanga, to help clarifying how South African leopards fit into continental patterns of genetic differentiation. Complete mitogenomes from nine leopards, including a strawberry leopard, were assembled de novo and included in phylogenetic analysis, in combination with 32 publicly available mitogenomes. Bayesian inference and maximum likelihood analyses identified two deeply diverged putative clades within South Africa, which were more genetically distinct than two subspecies in Asia. The clades dated back to 0.76-0.86 million years ago, indicating that they originated during the climatically unstable Mid-Pleistocene, as seen in other large mammals. The Pleistocene refuge theory states that the maintenance of savanna refugia in East and Southern Africa promoted the divergence between populations. As such, leopards may reflect the unique climatic history of southern Africa, which has resulted in eminent and endemic genetic diversity.

Do higher government spending, financial development, and trade reduce income inequality in low‐income countries? A Bayesian perspective

AbstractWe employed the Bayesian method to investigate the impact of government spending, financial development (measured by bank credit), and trade on income inequality reduction in 66 low‐income countries (LICs) across Africa, Asia, America, and Europe from 2000 to 2018. Controlling inflation and unemployment, our results indicate that trade and inflation exacerbate income inequality in LICs, while financial development and government spending have no impact on reducing income inequality in these countries. Furthermore, the findings show that real GDP per capita reduces income inequality in LICs. To ensure the robustness of our results, we also conducted frequentist quantile regression, which yielded consistent findings that financial development, government spending, and trade do not reduce income inequality in LICs. We further discuss the potential channels through which trade, financial development, inflation, and government spending contribute to income inequality in LICs, and provide policy implications based on the empirical evidence.Related ArticlesAdegboye, Alex, Kofo Adegboye, Uwalomwa Uwuigbe, Stephen Ojeka, and Eyitemi Fasanu. 2023. “Taxation, Democracy, and Inequality in Sub‐Saharan Africa: Relevant Linkages for Sustainable Development Goals.” Politics & Policy 51(4): 696–722. https://doi.org/10.1111/polp.12547.Asongu, Simplice, and Nicholas M. Odhiambo. 2023. “The Effect of Inequality on Poverty and Severity of Poverty in Sub‐Saharan Africa: The Role of Financial Development Institutions.” Politics & Policy 51(5): 898–918. https://doi.org/10.1111/polp.12558.Polacko, Matthew. 2023. “Turning Off the Base: Social Democracy's Neoliberal Turn, Income Inequality, and Turnout.” Politics & Policy 51(4): 538–68. https://doi.org/10.1111/polp.12550.

Data-driven Bayesian analysis of marine accidents in the English Channel

The English Channel, renowned for its heavy traffic and challenging conditions, frequently witnesses marine accidents. To understand the causal mechanisms and identify risk factors, this study analyzed 833 accidents from 2017 to 2022, employing a Bayesian network predictive model. Validation using log loss, quadratic loss, and spherical gain metrics confirmed the model’s accuracy. The research elucidates the primary influences on accident occurrence: ship type, tonnage, accident location, and flag state. Ship-related factors surpass environmental ones in significance. Older ships face heightened risks of mechanical failures and collisions, especially in adverse weather with limited visibility. Yachts and fishing vessels are particularly susceptible to fire, explosion, collision, and grounding incidents. The study offers theoretical guidance for management departments to devise prevention strategies and enhance navigation safety in the English Channel.

A novel non-negative Bayesian stacking modeling method for Cancer survival prediction using high-dimensional omics data

BackgroundSurvival prediction using high-dimensional molecular data is a hot topic in the field of genomics and precision medicine, especially for cancer studies. Considering that carcinogenesis has a pathway-based pathogenesis, developing models using such group structures is a closer mimic of disease progression and prognosis. Many approaches can be used to integrate group information; however, most of them are single-model methods, which may account for unstable prediction.MethodsWe introduced a novel survival stacking method that modeled using group structure information to improve the robustness of cancer survival prediction in the context of high-dimensional omics data. With a super learner, survival stacking combines the prediction from multiple sub-models that are independently trained using the features in pre-grouped biological pathways. In addition to a non-negative linear combination of sub-models, we extended the super learner to non-negative Bayesian hierarchical generalized linear model and artificial neural network. We compared the proposed modeling strategy with the widely used survival penalized method Lasso Cox and several group penalized methods, e.g., group Lasso Cox, via simulation study and real-world data application.ResultsThe proposed survival stacking method showed superior and robust performance in terms of discrimination compared with single-model methods in case of high-noise simulated data and real-world data. The non-negative Bayesian stacking method can identify important biological signal pathways and genes that are associated with the prognosis of cancer.ConclusionsThis study proposed a novel survival stacking strategy incorporating biological group information into the cancer prognosis models. Additionally, this study extended the super learner to non-negative Bayesian model and ANN, enriching the combination of sub-models. The proposed Bayesian stacking strategy exhibited favorable properties in the prediction and interpretation of complex survival data, which may aid in discovering cancer targets.

Cost-effectiveness of medication therapy management among Medicare population and across racial/ethnic groups.

Inappropriate medication utilization among older adults is a pressing concern in the United States, owing to its high prevalence and the consequential detrimental impact it engenders. The adverse effects stemming from the inappropriate use of medication may be unequally borne by racial/ethnic minority populations, calling for greater efforts towards promoting equity in healthcare. The study objective was to assess the cost-effectiveness of Medication Therapy Management (MTM) services among Medicare beneficiaries and across racial/ethnic groups. Medicare administrative data from 2016 to 2017 linked to Area Health Resources Files were used to analyze Medicare fee-for-service patients aged 65 or above with continuous Parts A/B/D coverage. The intervention group included new MTM enrollees in 2017; the control group referred to patients who met the general MTM eligible criteria but did not enroll in 2016 or 2017. The 2 groups were matched using a propensity score method. Effectiveness was evaluated as the proportion of appropriate medication utilization based on performance measures developed by the Pharmacy Quality Alliance. Costs were computed as total healthcare costs from Medicare perspective. A multivariable net benefit regressions with a classic linear model and Bayesian analysis were utilized. Net benefit was calculated based on willingness-to-pay thresholds at various multiples of the gross domestic product in 2017. Three-way interaction terms among dummy variables for MTM enrollment, 2017, and racial/ethnic minority groups were incorporated in a difference-in-differences study design. After adjusting for patient characteristics, the findings indicate that MTM receipt was associated with incremental net benefit among each race and ethnicity. For instance, the net benefit of MTM among the non-Hispanic White patients was $2498 (95% confidence interval = $1609, $3386) at a willingness-to-pay value of $59,908. The study found no significant difference in net benefits for MTM services between minority and White patients. The study provides evidence that MTM is a cost-effective tool for managing medication utilization among the Medicare population. However, MTM may not be cost-effective in reducing racial/ethnic disparities in medication utilization in the short term. Further research is needed to understand the long-term cost-effectiveness of MTM on racial/ethnic disparities.

A hybrid quantum ensemble learning model for malicious code detection

Quantum computing as a new computing model with parallel computing capability and high information carrying capacity, has attracted a lot of attention from researchers. Ensemble learning is an effective strategy often used in machine learning to improve the performance of weak classifiers. Currently, the classification performance of quantum classifiers is not satisfactory enough due to factors such as the depth of quantum circuit, quantum noise, and quantum coding method, etc. For this reason, this paper combined the ensemble learning idea and quantum classifiers to design a novel hybrid quantum machine learning model. Firstly, we run the Stacking method in classical machine learning to realize the dimensionality reduction of high-latitude data while ensuring the validity of data features. Secondly, we used the Bagging method and Bayesian hyperparameter optimization method applied to quantum support vector machine (QSVM), quantum K nearest neighbors (QKNN), variational quantum classifier (VQC). Thirdly, the voting method is used to ensemble the predict results of QSVM, QKNN, VQC as the final result. We applied the hybrid quantum ensemble machine learning model to malicious code detection. The experimental results show that the classification precision (accuracy, F1-score) of this model has been improved to 98.9% (94.5%, 94.24%). Combined with the acceleration of quantum computing and the higher precision rate, it can effectively deal with the growing trend of malicious codes, which is of great significance to cyberspace security.

Association of Blood Copper With the Subclinical Carotid Atherosclerosis: An Observational Study.

Copper exposure is reported to be associated with increased risk of stroke. However, the association of copper exposure with subclinical carotid atherosclerosis remains unclear. This observational study included consecutive participants from Xinqiao Hospital between May 2020 and August 2021. Blood metals were measured using inductively coupled plasma mass spectrometry and carotid atherosclerosis was assessed using ultrasound. Modified Poisson regression was performed to evaluate the associations of copper and other metals with subclinical carotid plaque presence. Blood metals were analyzed as categorical according to the quartiles. Multivariable models were adjusted for age, sex, body mass index, education, smoking, drinking, hypertension, diabetes, dyslipidemia, estimated glomerular filtration rate, and coronary artery disease history. Bayesian Kernel Machine Regression was conducted to evaluate the overall association of metal mixture with subclinical carotid plaque presence. One thousand five hundred eighty-five participants were finally enrolled in our study, and carotid plaque was found in 1091 subjects. After adjusting for potential confounders, metal-progressively-adjusted models showed that blood copper was positively associated with subclinical carotid plaque (relative risk according to comparing quartile 4 to quartile 1 was 1.124 [1.021-1.238], relative risk according to per interquartile increment was 1.039 [1.008-1.071]). Blood cadmium and lead were also significantly associated with subclinical carotid plaque. Bayesian Kernel Machine Regression analyses suggested a synergistic effect of copper-cadmium-lead mixture on subclinical carotid plaque presence. Our findings identify copper as a novel risk factor of subclinical carotid atherosclerosis and show the potential synergistic proatherogenic effect of copper, cadmium, and lead mixture.

Bayesian inference of vorticity in unbounded flow from limited pressure measurements

We study the instantaneous inference of an unbounded planar flow from sparse noisy pressure measurements. The true flow field comprises one or more regularized point vortices of various strength and size. We interpret the true flow's measurements with a vortex estimator, also consisting of regularized vortices, and attempt to infer the positions and strengths of this estimator assuming little prior knowledge. The problem often has several possible solutions, many due to a variety of symmetries. To deal with this ill posedness and to quantify the uncertainty, we develop the vortex estimator in a Bayesian setting. We use Markov-chain Monte Carlo and a Gaussian mixture model to sample and categorize the probable vortex states in the posterior distribution, tailoring the prior to avoid spurious solutions. Through experiments with one or more true vortices, we reveal many aspects of the vortex inference problem. With fewer sensors than states, the estimator infers a manifold of equally possible states. Using one more sensor than states ensures that no cases of rank deficiency arise. Uncertainty grows rapidly with distance when a vortex lies outside of the vicinity of the sensors. Vortex size cannot be reliably inferred, but the position and strength of a larger vortex can be estimated with a much smaller one. In estimates of multiple vortices their individual signs are discernible because of the nonlinear coupling in the pressure. When the true vortex state is inferred from an estimator of fewer vortices, the estimate approximately aggregates the true vortices where possible.

Complete mitochondrial genome data and phylogenetic analysis of Papilio macilentus Janson, 1877 (Lepidoptera: Papilionoidea: Papilionidae)

In the present study, the complete mitochondrial genome (mitogenome) of the Papilio macilentus (Lepidoptera: Papilionoidea: Papilionidae) was sequenced by next-generation sequencing method. The mitochondrial genome is a circular DNA molecule of 15,264 bp in size with 80.7% AT content, including 37 genes (13 protein-coding genes, 2 rRNA genes, and 22 tRNA genes), and a long non-coding region (Control region). All protein-coding genes are initiated by ATN codons, and terminated with TAA, TAG, or single T. All tRNAs can be folded into common clover leaf secondary structure, except trn-S1. Phylogenetic analyses based on 13 protein-coding genes and 2 rRNA genes using maximum likelihood and Bayesian inference confirmed that P. macilentus and Papilio memnon are clustered into a clade, and revealed the relationships between Papilionini, Troidini, Teinopaippini and Leptocircini.

A Review of the Bayesian Method in Nuclear Fusion Diagnostic Research

A Review of the Bayesian Method in Nuclear Fusion Diagnostic Research

A zero‐inflated Poisson spatial model with misreporting for wildfire occurrences in southern Italian municipalities

AbstractWe propose a Poisson model for zero‐inflated spatial counts contaminated by measurement error: we accommodate the excess of zeroes in the counts, consider the possible under/over reporting of the response and account for the neighboring structure of spatial areal units. Bayesian inferences are provided by MCMC implementation through the R package NIMBLE. To evaluate the model performance, a simulation study is carried out under configurations that allow for structured and unstructured spatial random effects. The proposed model is applied to investigate the distribution of the counts of wildfire occurrences in the municipal areas of two neighboring Italian regions for the summer season 2021. Fire counts are obtained by processing MODIS satellite data, while several socio‐economic and environmental‐driven potential risk factors are also considered in the model formulation. Data from multiple sources with different spatial support are processed in order to comply with the municipal units. Results suggest the appropriateness of the approach and provide some insights on the features of wildfire occurrences.

Which Drugs are More Effective in Preventing Familial Adenomatous Polyposis Progression Based on Network Meta-Analysis?

Familial adenomatous polyposis (FAP) is an inherited disorder. At present, an increasing number of medications are being employed to treat FAP; however, only a few have been assessed for their efficacy and safety. Therefore, this study aimed to conduct a network meta-analysis to compare the therapeutic outcomes and adverse drug reactions of all FAP-associated medications. Six relevant databases were searched to identify pertinent randomized controlled trials (RCTs), and information on the dosage and frequency of various drugs was extracted. Additionally, data on changes in polyp counts and dimensions, as well as treatment-related adverse reactions for different medications were collected. The Bayesian method was employed to directly or indirectly compare the impact of different treatment regimens on changes in polyp numbers and diameters, and the safety of the drugs was investigated. CXB at 16 mg/kg/day significantly reduced polyp numbers. Celecoxib at 8 mg/kg/day and sulindac (150 mg twice daily) plus erlotinib (75 mg/day) were effective for tolerant FAP patients. Additionally, EPAFFA 2 g daily and sulindac (150 mg twice daily) plus erlotinib (75 mg/day) emerged as the most effective for reducing polyp size. The most effective treatment for reducing the number of colorectal polyps is celecoxib 16 mg/kg/day. On the other hand, a daily dosage of 2 g EPA-FFA demonstrates the best results in terms of decreasing colorectal polyp diameter.

Abstract PO5-09-02: Breast Tissue Proteomic Profile of Breast Cancer in Premenopausal Women and Association with Mammographic Breast Density

Abstract Introduction: Breast cancer incidence is rising in premenopausal, hence, there is a critical need to understand factors underlying premenopausal breast cancer development in order to guide targeted prevention. Mammographic breast density is a strong risk factor for, as well as an intermediate phenotype for premenopausal breast cancer. Yet, the molecular mechanisms underlying the associations of dense breasts with breast cancer are not well understood. Our objectives in this study are to perform proteomic analysis in breast tissues to (i) identify proteins that are associated with breast cancer development in premenopausal women; (ii) determine which of these proteins are also associated with dense breasts. Methods: We performed proteomic analysis on tumor and adjacent normal tissues from 50 premenopausal women with breast cancer who had breast tissue samples archived at the St. Louis Breast Tumor Registry. Samples were analyzed on Orbitrap Eclipse Tribrid coupled with Vanquish Neo LC system (Thermo Fisher Scientific). Database search was performed using MaxQuant and MS1 LFQ intensities were used for further data analysis. We performed multiple imputation using Bayesian Principal Component Analysis and hierarchical clustering analysis using ‘ConsensusClusterPlus’ package in R. Pathway enrichment analysis was performed using Reactome Pathway database. 10 times repeated 5-fold cross validation using Logistic Regression (LR) was performed for model development. Top 10 proteins were selected by variable importance in logistic regression, and recursive feature elimination was performed for feature selection. We corrected for multiple testing by setting the false discovery rate, FDR, p-value < 0.05. Results: After imputing for missing values, we identified 3,571 proteins that were expressed in tumor and normal breast tissues. We selected 1,640 proteins for further analysis using median absolute deviation analysis. In multivariable-adjusted analysis, 451 proteins were up-regulated, and 180 proteins were down-regulated in tumor tissues compared to adjacent normal tissues (FDR < 0.05). 53 of the 451 proteins that were upregulated in tumor tissues were also upregulated in dense breasts. Some of the top proteins that were upregulated in both tumor tissues and dense breasts were AIMP2, ALDH18A1, BZW1, CKAP5, COPG1, ERGIC1, GSPT1, ILF2, IPO7, LRBA, and PSMD12. Mammographic breast density protein clusters were highly correlated with hormone receptor positivity clusters and were enriched in ESR-mediated signaling, IGF1R signaling, NOTCH4, PTEN regulation, and NFkB pathway. Discussion: Using untargeted proteomics, we identified proteomic signatures of breast cancer development in premenopausal women. We further identified protein biomarkers and pathways that are shared between breast tumors and dense breast tissues in premenopausal women. Our novel findings highlight mammographic breast density as a strong intermediate phenotype that can be targeted in breast cancer prevention in premenopausal women. Larger studies are needed to validate our findings. Citation Format: Shaili Tapiavala, Minsoo Son, Graham Colditz, Ah Young Goo, Adetunji Toriola. Breast Tissue Proteomic Profile of Breast Cancer in Premenopausal Women and Association with Mammographic Breast Density [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO5-09-02.

A Review of Fluid Bolus in Critically Ill Patients After Initial Volume Expansion: Bayesian Probability Analysis and Case Studies

A Review of Fluid Bolus in Critically Ill Patients After Initial Volume Expansion: Bayesian Probability Analysis and Case Studies

Application of machine learning for antibiotic resistance in water and wastewater: A systematic review

Antibiotic resistance (AR) is considered one of the greatest global threats in the current century, which can only be overcome if all interconnected areas of humans, animals and the environment are taken into account as part of the One Health concept proposed by the World Health Organization (WHO). Water and wastewater are among the most important environmental media of AR sources, where the phenomena are generally non-linear. Therefore, the aim of this study was to investigate the application of machine learning-based methods (MLMs) to solve AR-induced problems in water and wastewater. For this purpose, most relevant databases were searched in the period between 1987 and 2023 to systematically analyze and categorize the applications. Accordingly, the results showed that out of 12 applications, 11 (91.6%) were for shallow learning and 1 (8.3%) for deep learning. In shallow learning category, n = 6, 50% of the applications were regression and n = 4, 33.3% were classification, mainly using artificial neural networks, decision trees and Bayesian methods for the following objectives: Predicting the survival of antibiotic-resistant bacteria (ARB), determining the order of influencing parameters on AR-based scores, and identifying the major sources of antibiotic resistance genes (ARGs). In addition, only one study (8.3%) was found for clustering and no study for association. Surprisingly, deep learning had been used in only one study (8.3%) to predict ARGs sequences. Therefore, working on the knowledge gaps of AR, especially using clustering, association and deep learning methods, would be a promising option to analyze more aspects of the related problems. However, there is still a long way to go to consider and apply MLMs as unique approaches to study different aspects of AR in water and wastewater.

Estimation and comparison of Weibull-Normal distribution with some other probability models using Bayesian method of estimation

In statistical applications the Normal distribution is adjudged to be the best. Recent studies Terna (2017) using classical method indicated that Weibull-Normal distribution outperformed the Normal distribution. In this study we used the non-classical Bayesian method of estimation to estimate and compare the Weibull-Normal distribution with some other distributions including Normal and Gamma-Normal distributions. This study derived explicit expressions for basic statistical properties such as moments, moment generating function, the characteristic function, reliability analysis and the distribution of order statistics. It looks at estimation of confidence intervals for the parameters of the Weibull-Normal distribution and estimated the parameters of the new distribution using a non-classical approach for the purpose of theoretical comparisons. The two other distributions whose parameters were also estimated by using Bayesian estimation are the normal distribution and gamma distribution as well as the combination Gamma-Normal distribution. Based on the analyses and interpretations of the results obtained it was found that the parameters and other general properties of Normal distribution gives a better fit than other distributions. R-software was used; the models were written as an R code in R program using the rjags library, the distribution parameters were obtained from a Gibbs sampling of a Bayesian Fit for data set I and data set II. The criteria used in R for comparisons were the negative log-likelihood, AIC (Akaike information criterion), CAIC (Consistent Akaike Information Criterion) and BIC (Bayesian information Criterion).

Constraining the properties of Population III galaxies with multi-wavelength observations

Abstract The early Universe, spanning 400,000 to 400 million years after the Big Bang (z ≈ 1100 − 11), has been left largely unexplored as the light from luminous objects is too faint to be observed directly. While new experiments are pushing the redshift limit of direct observations, measurements in the low-frequency radio band promise to probe early star and black hole formation via observations of the hydrogen 21-cm line. In this work we explore synergies between 21-cm data from the HERA and SARAS 3 experiments and observations of the unresolved radio and X-ray backgrounds using multi-wavelength Bayesian analysis. We use the combined data set to constrain properties of Population II and Population III stars as well as early X-ray and radio sources. The joint fit reveals a 68 percentile disfavouring of Population III star formation efficiencies $\gtrsim 5.7~{{\%}}$. We also show how the 21-cm and the X-ray background data synergistically constrain opposite ends of the X-ray efficiency prior distribution to produce a peak in the 1D posterior of the X-ray luminosity per star formation rate. We find (at 68 % confidence) that early galaxies were likely 0.3 to 318 times as X-ray efficient as present-day starburst galaxies. We also show that the functional posteriors from our joint fit rule out global 21-cm signals deeper than ≲ −203 mK and power spectrum amplitudes at k = 0.34 hMpc−1 greater than $\Delta _{21}^2 \gtrsim 946\ \mathrm{mK}^2$ with 3σ confidence.