Bayesian Restricted Likelihood Methods: Conditioning on Insufficient Statistics in Bayesian Regression

Abstract Purpose Sled towing has been shown to be an effective method to enhance the physical qualities in youth athletes. The aim of this study was to evaluate the impact of a 6-week sled towing intervention on muscular strength, speed and power in elite youth soccer players of differing maturity status. Method Seventy-three male elite youth soccer players aged 12–18 years (Pre-Peak Height Velocity [PHV] n = 25; Circa-PHV n = 24; Post-PHV n = 24) from one professional soccer academy participated in this study. Sprint assessments (10 m and 30 m), countermovement jump and isometric mid-thigh pull were undertaken before (T1) and after (T2) a 6-week intervention. The training intervention consisted of 6 weeks (2 × per week, 10 sprints over 20 m distance) of resisted sled towing (linear progression 10%–30% of body mass) during the competitive season. Bayesian regression models analysed differences between T1 and T2 within each maturity group. Results There were minimal changes in strength, speed and power (P = 0.35–0.80) for each maturity group across the 6-week intervention. Where there were changes with greater certainty, they are unlikely to represent real effect due to higher regression to the mean (RTM). Conclusion It appears that a 6-week sled towing training programme with loadings of 10%–30% body mass only maintains physical qualities in elite youth soccer players pre-, circa-, and post-PHV. Further research is required to determine the effectiveness of this training method in long-term athletic development programmes.

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Directional Selection and the Site-Frequency Spectrum

Genetics ◽

10.1093/genetics/159.4.1779 ◽

2001 ◽

Vol 159 (4) ◽

pp. 1779-1788 ◽

Cited By ~ 2

Author(s):

Carlos D Bustamante ◽

John Wakeley ◽

Stanley Sawyer ◽

Daniel L Hartl

Keyword(s):

Maximum Likelihood ◽

High Power ◽

Negative Selection ◽

Likelihood Estimation ◽

Directional Selection ◽

Likelihood Ratio Tests ◽

Maximum Likelihood Estimates ◽

Likelihood Methods ◽

Ancestral States ◽

Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

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Model-independent calibrations of gamma-ray bursts using machine learning

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stab795 ◽

2021 ◽

Vol 503 (3) ◽

pp. 4581-4600

Author(s):

Orlando Luongo ◽

Marco Muccino

Keyword(s):

Machine Learning ◽

Dark Energy ◽

Gamma Ray ◽

Gamma Ray Bursts ◽

Bayesian Regression ◽

Machine Learning Techniques ◽

Acoustic Oscillations ◽

Chi Square ◽

Model Independent ◽

Chi Square Analysis

ABSTRACT We alleviate the circularity problem, whereby gamma-ray bursts are not perfect distance indicators, by means of a new model-independent technique based on Bézier polynomials. We use the well consolidate Amati and Combo correlations. We consider improved calibrated catalogues of mock data from differential Hubble rate points. To get our mock data, we use those machine learning scenarios that well adapt to gamma-ray bursts, discussing in detail how we handle small amounts of data from our machine learning techniques. We explore only three machine learning treatments, i.e. linear regression, neural network, and random forest, emphasizing quantitative statistical motivations behind these choices. Our calibration strategy consists in taking Hubble’s data, creating the mock compilation using machine learning and calibrating the aforementioned correlations through Bézier polynomials with a standard chi-square analysis first and then by means of a hierarchical Bayesian regression procedure. The corresponding catalogues, built up from the two correlations, have been used to constrain dark energy scenarios. We thus employ Markov chain Monte Carlo numerical analyses based on the most recent Pantheon supernova data, baryonic acoustic oscillations, and our gamma-ray burst data. We test the standard ΛCDM model and the Chevallier–Polarski–Linder parametrization. We discuss the recent H0 tension in view of our results. Moreover, we highlight a further severe tension over Ωm and we conclude that a slight evolving dark energy model is possible.

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Dynamic model updating (DMU) approach for statistical learning model building with missing data

BMC Bioinformatics ◽

10.1186/s12859-021-04138-z ◽

2021 ◽

Vol 22 (1) ◽

Author(s):

Rahi Jain ◽

Wei Xu

Keyword(s):

Missing Data ◽

Dynamic Model ◽

Statistical Models ◽

Missing Values ◽

Model Building ◽

Model Updating ◽

Biological Data ◽

Bayesian Regression ◽

Biological Research ◽

Original Dataset

Abstract Background Developing statistical and machine learning methods on studies with missing information is a ubiquitous challenge in real-world biological research. The strategy in literature relies on either removing the samples with missing values like complete case analysis (CCA) or imputing the information in the samples with missing values like predictive mean matching (PMM) such as MICE. Some limitations of these strategies are information loss and closeness of the imputed values with the missing values. Further, in scenarios with piecemeal medical data, these strategies have to wait to complete the data collection process to provide a complete dataset for statistical models. Method and results This study proposes a dynamic model updating (DMU) approach, a different strategy to develop statistical models with missing data. DMU uses only the information available in the dataset to prepare the statistical models. DMU segments the original dataset into small complete datasets. The study uses hierarchical clustering to segment the original dataset into small complete datasets followed by Bayesian regression on each of the small complete datasets. Predictor estimates are updated using the posterior estimates from each dataset. The performance of DMU is evaluated by using both simulated data and real studies and show better results or at par with other approaches like CCA and PMM. Conclusion DMU approach provides an alternative to the existing approaches of information elimination and imputation in processing the datasets with missing values. While the study applied the approach for continuous cross-sectional data, the approach can be applied to longitudinal, categorical and time-to-event biological data.

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