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1

Conigliani, Caterina, and Anthony O'hagan. "Sensitivity of the fractional Bayes factor to prior distributions." Canadian Journal of Statistics 28, no. 2 (2000): 343–52. http://dx.doi.org/10.2307/3315983.

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2

De Santis, Fulvio, and Fulvio Spezzaferri. "Consistent fractional Bayes factor for nested normal linear models." Journal of Statistical Planning and Inference 97, no. 2 (2001): 305–21. http://dx.doi.org/10.1016/s0378-3758(00)00240-8.

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3

Ariza-Hernandez, Francisco J., Jorge Sanchez-Ortiz, Martin P. Arciga-Alejandre, and Luis X. Vivas-Cruz. "Bayesian Analysis for a Fractional Population Growth Model." Journal of Applied Mathematics 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/9654506.

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We implement the Bayesian statistical inversion theory to obtain the solution for an inverse problem of growth data, using a fractional population growth model. We estimate the parameters in the model and we make a comparison between this model and an exponential one, based on an approximation of Bayes factor. A simulation study is carried out to show the performance of the estimators and the Bayes factor. Finally, we present a real data example to illustrate the effectiveness of the method proposed here and the pertinence of using a fractional model.
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Dittrich, Dino, Roger Th A. J. Leenders, and Joris Mulder. "Network Autocorrelation Modeling: A Bayes Factor Approach for Testing (Multiple) Precise and Interval Hypotheses." Sociological Methods & Research 48, no. 3 (2017): 642–76. http://dx.doi.org/10.1177/0049124117729712.

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Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing procedures that do not have these limitations. We propose Bayes factors based on an empirical and a uniform prior for the network effect, respectively, first. Next, we develop a fractional Bayes factor where a default prior is automatically constructed. Sim
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5

de Santis, Fulvio, and Fulvio Spezzaferri. "Methods for Default and Robust Bayesian Model Comparison: The Fractional Bayes Factor Approach." International Statistical Review / Revue Internationale de Statistique 67, no. 3 (1999): 267. http://dx.doi.org/10.2307/1403706.

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6

Santis, Fulvio, and Fulvio Spezzaferri. "Methods for Default and Robust Bayesian Model Comparison: the Fractional Bayes Factor Approach." International Statistical Review 67, no. 3 (1999): 267–86. http://dx.doi.org/10.1111/j.1751-5823.1999.tb00449.x.

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7

Mashayekhi, Somayeh, and Peter Beerli. "Fractional coalescent." Proceedings of the National Academy of Sciences 116, no. 13 (2019): 6244–49. http://dx.doi.org/10.1073/pnas.1810239116.

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An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values ofα<1lead to an increase of short time intervals, but occasionally allow for very long time intervals. Whenα=1, the f-coalescent and the Kingman’s n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that
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8

Kaiser, Andrew R., Nihan S. Pol, Maura A. McLaughlin, et al. "Disentangling Multiple Stochastic Gravitational Wave Background Sources in PTA Data Sets." Astrophysical Journal 938, no. 2 (2022): 115. http://dx.doi.org/10.3847/1538-4357/ac86cc.

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Abstract With strong evidence of a common-spectrum stochastic process in the most recent data sets from the NANOGrav Collaboration, the European Pulsar Timing Array (PTA), Parkes PTA, and the International PTA, it is crucial to assess the effects of the several astrophysical and cosmological sources that could contribute to the stochastic gravitational wave background (GWB). Using the same data set creation and injection techniques as in Pol et al., we assess the separability of multiple GWBs by creating single and multiple GWB source data sets. We search for these injected sources using Bayes
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9

O'Hagan, Anthony. "Fractional Bayes Factors for Model Comparison." Journal of the Royal Statistical Society: Series B (Methodological) 57, no. 1 (1995): 99–118. http://dx.doi.org/10.1111/j.2517-6161.1995.tb02017.x.

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10

O’Hagan, A. "Properties of intrinsic and fractional Bayes factors." Test 6, no. 1 (1997): 101–18. http://dx.doi.org/10.1007/bf02564428.

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11

Vijayaragunathan, R., and M. R. Srinivasan. "Comparisons of Bayes factors for 𝟐𝟒 full, fractional, and reduced factorial designs." International Journal of ADVANCED AND APPLIED SCIENCES 9, no. 9 (2022): 158–67. http://dx.doi.org/10.21833/ijaas.2022.09.020.

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The effect of factors in full and fractional factorial designs is being studied ubiquitously in all fields of science and engineering. At times, researchers would want to gather additional information than the fractional factorial design provided, there is no restriction to conducting more experimental runs. In this study, we propose a reduced fractional factorial design consisting of all significant factors. This paper illustrates the effectiveness of factors through real data application and simulation by comparing the full factorial, reduced factorial, and fractional factorial designs. The
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12

Vijayaragunathan, R., and M. R. Srinivasan. "Comparisons of Bayes factors for 𝟐𝟒 full, fractional, and reduced factorial designs." International Journal of ADVANCED AND APPLIED SCIENCES 9, no. 9 (2022): 158–67. http://dx.doi.org/10.21833/ijaas.2022.09.020.

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The effect of factors in full and fractional factorial designs is being studied ubiquitously in all fields of science and engineering. At times, researchers would want to gather additional information than the fractional factorial design provided, there is no restriction to conducting more experimental runs. In this study, we propose a reduced fractional factorial design consisting of all significant factors. This paper illustrates the effectiveness of factors through real data application and simulation by comparing the full factorial, reduced factorial, and fractional factorial designs. The
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13

Gu, Xin, Joris Mulder, and Herbert Hoijtink. "Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses." British Journal of Mathematical and Statistical Psychology 71, no. 2 (2017): 229–61. http://dx.doi.org/10.1111/bmsp.12110.

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14

Yang, Xihua. "Deriving RUSLE cover factor from time-series fractional vegetation cover for hillslope erosion modelling in New South Wales." Soil Research 52, no. 3 (2014): 253. http://dx.doi.org/10.1071/sr13297.

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Soil loss due to water erosion, in particular hillslope erosion, can be estimated using predictive models such as the Revised Universal Soil Loss Equation (RUSLE). One of the important and dynamic elements in the RUSLE model is the cover and management factor (C-factor), which represents effects of vegetation canopy and ground cover in reducing soil loss. This study explores the potential for using fractional vegetation cover, rather than traditional green vegetation indices (e.g. NDVI), to estimate C-factor and consequently hillslope erosion hazard across New South Wales (NSW), Australia. Val
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15

Martínez, Carlos Alberto, Kshitij Khare, Arunava Banerjee, and Mauricio A. Elzo. "Joint genome-wide prediction in several populations accounting for randomness of genotypes: A hierarchical Bayes approach. II: Multivariate spike and slab priors for marker effects and derivation of approximate Bayes and fractional Bayes factors for the complete family of models." Journal of Theoretical Biology 417 (March 2017): 131–41. http://dx.doi.org/10.1016/j.jtbi.2016.12.022.

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16

Mohapatra, Sushmita, Kei-Long Cheung, Mickaël Hiligsmann, and Nana Anokye. "Most Important Factors for Deciding Rehabilitation Provision for Severe Stroke Survivors Post Hospital Discharge: A Study Protocol for a Best–Worst Scaling Experiment." Methods and Protocols 4, no. 2 (2021): 27. http://dx.doi.org/10.3390/mps4020027.

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Efficient decision-making is crucial to ensure adequate rehabilitation with optimal use of healthcare resources. Establishing the factors associated with making decisions concerning rehabilitation provision is important to guide clinical staff towards person-centred decisions for rehabilitation after severe stroke. In this study we conduct a best–worst scaling (BWS) experiment to identify the most important factors and their relative weight of importance for deciding the type of ongoing rehabilitation services a person with severe stroke might receive post hospital discharge. Fractional, effic
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17

Filippova, A.Yu., I.A. Gubar, and V.V Rudakova. "Prediction of course and progression of nonalcoholic fatty liver disease in patients with obesity and pathology of the biliary tract with the help of mathematical modeling." Medicni perspektivi 22, no. 4 (2017): 74–80. https://doi.org/10.26641/2307-0404.2017.4.117674.

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Determination of the most important functional parameters of the liver, lipid peroxidation (LPO) and antioxidant protection (AOP) markers of endogenous intoxication and indicators of connective-tissue metabolism in patients with non-alcoholic fatty liver disease (NAFLD) associated with obesity and pathology of the biliary tract and development of criteria for predicting the likelihood of the transformation of non-alcoholic steatosis (NAHS) to non-alcoholic steatohepatitis (NASH) using mathematical modeling was performed. The data of patients with different clinical stages of NAFLD in combinati
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18

Fu, Qianrao, Mirjam Moerbeek, and Herbert Hoijtink. "Sample size determination for Bayesian ANOVAs with informative hypotheses." Frontiers in Psychology 13 (November 22, 2022). http://dx.doi.org/10.3389/fpsyg.2022.947768.

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Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Baye
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19

Fu, Qianrao, Herbert Hoijtink, and Mirjam Moerbeek. "Sample-size determination for the Bayesian t test and Welch’s test using the approximate adjusted fractional Bayes factor." Behavior Research Methods, July 6, 2020. http://dx.doi.org/10.3758/s13428-020-01408-1.

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20

Cao, Xuan, Lili Ding, and Tesfaye B. Mersha. "Joint variable selection and network modeling for detecting eQTLs." Statistical Applications in Genetics and Molecular Biology 19, no. 1 (2020). http://dx.doi.org/10.1515/sagmb-2019-0032.

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AbstractIn this study, we conduct a comparison of three most recent statistical methods for joint variable selection and covariance estimation with application of detecting expression quantitative trait loci (eQTL) and gene network estimation, and introduce a new hierarchical Bayesian method to be included in the comparison. Unlike the traditional univariate regression approach in eQTL, all four methods correlate phenotypes and genotypes by multivariate regression models that incorporate the dependence information among phenotypes, and use Bayesian multiplicity adjustment to avoid multiple tes
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21

Tan, Qin, You Wu, and Lang Liu. "Constraining string cosmology with the gravitational-wave background using the NANOGrav 15-year data set." European Physical Journal C 85, no. 3 (2025). https://doi.org/10.1140/epjc/s10052-025-13998-1.

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Abstract Multiple pulsar timing array (PTA) collaborations, including the European PTA in partnership with the Indian PTA, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), the Parkes PTA, and the Chinese PTA have recently reported strong evidence for a signal at nanohertz, potentially the first detection of the stochastic gravitational-wave background (SGWB). We investigate whether the NANOGrav signal is consistent with the SGWB predicted by string cosmology models. By performing Bayesian parameter estimation on the NANOGrav 15-year data set, we constrain the key pa
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22

Plavén-Sigray, Pontus, Pauliina Ikonen Victorsson, Alexander Santillo, et al. "Thalamic dopamine D2-receptor availability in schizophrenia: a study on antipsychotic-naive patients with first-episode psychosis and a meta-analysis." Molecular Psychiatry, November 10, 2021. http://dx.doi.org/10.1038/s41380-021-01349-x.

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AbstractPharmacological and genetic evidence support a role for an involvement of the dopamine D2-receptor (D2-R) in the pathophysiology of schizophrenia. Previous molecular imaging studies have suggested lower levels of D2-R in thalamus, but results are inconclusive. The objective of the present study was to use improved methodology to compare D2-R density in whole thalamus and thalamic subregions between first-episode psychosis patients and healthy controls. Differences in thalamocortical connectivity was explored based on the D2-R results. 19 antipsychotic-naive first-episode psychosis pati
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23

Kim, Minchul, Inpyeong Hwang, Jung Hyun Park, et al. "Comparative analysis of glymphatic system alterations in multiple sclerosis and neuromyelitis optica spectrum disorder using MRI indices from diffusion tensor imaging." Human Brain Mapping 45, no. 5 (2024). http://dx.doi.org/10.1002/hbm.26680.

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AbstractObjectiveThe glymphatic system is a glial‐based perivascular network that promotes brain metabolic waste clearance. Glymphatic system dysfunction has been observed in both multiple sclerosis (MS) and neuromyelitis optica spectrum disorder (NMOSD), indicating the role of neuroinflammation in the glymphatic system. However, little is known about how the two diseases differently affect the human glymphatic system. The present study aims to evaluate the diffusion MRI‐based measures of the glymphatic system by contrasting MS and NMOSD.MethodsThis prospective study included 63 patients with
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24

Nakanishi, N., K. Kaikita, M. Ishii, Y. Oimatsu, T. Mitsuse, and K. Tsujita. "P2563Effects of rivaroxaban on cardiac remodeling after experimental myocardial infarction in mice." European Heart Journal 40, Supplement_1 (2019). http://dx.doi.org/10.1093/eurheartj/ehz748.0891.

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Abstract Background Rivaroxaban, a direct activated factor X (FXa) inhibitor, has been established for prevention and treatment of arterial and venous thrombosis. Although FXa plays an important role in thrombosis, FXa also involves in inflammation via the protease-activated receptor (PAR)-1 and PAR-2 pathway. We assessed the hypothesis that rivaroxaban might protect cardiac remodeling after myocardial infarction (MI) in mice. Methods MI was induced in wild-type mice by permanent ligation of the left anterior descending coronary artery. At 1 day after MI, mice were randomly assigned to the riv
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PARK, JIHYUN, RICHARD BEARE, LYNN ANG, et al. "1275-P: Association of Metabolic Risk Factors with Brain Health Outcomes in Persons with Type 1 Diabetes." Diabetes 74, Supplement_1 (2025). https://doi.org/10.2337/db25-1275-p.

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Introduction and Objective: Exploring the impact of metabolic risk factors on brain health outcomes in individuals with type 1 diabetes (T1D) Methods: We performed a cross-sectional study of adults with T1D. Cognition was assessed using the NIH Toolbox Cognitive Battery composite score (NIHTB-CB), adjusting for age, sex, race, ethnicity, and education level. A subset of participants also completed functional and structural magnetic resonance imaging (MRI) sequences. MRI-metrics included mean cortical thickness, cerebral blood flow, gray matter volume, white matter volume, subcortical grey matt
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