scholarly journals An analysis of Bayesian estimates for missing higher orders in perturbative calculations

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Claude Duhr ◽  
Alexander Huss ◽  
Aleksas Mazeliauskas ◽  
Robert Szafron
Keyword(s):  
Ad Hoc ◽  
Probability Distributions ◽  
Model Parameters ◽  
Collider Phenomenology ◽  
Bayesian Approaches ◽  
Standard Scale ◽  
Variation Approach ◽  
New Public ◽  
Specific Scale ◽  
Scale Variation

Abstract With current high precision collider data, the reliable estimation of theoretical uncertainties due to missing higher orders (MHOs) in perturbation theory has become a pressing issue for collider phenomenology. Traditionally, the size of the MHOs is estimated through scale variation, a simple but ad hoc method without probabilistic interpretation. Bayesian approaches provide a compelling alternative to estimate the size of the MHOs, but it is not clear how to interpret the perturbative scales, like the factorisation and renormalisation scales, in a Bayesian framework. Recently, it was proposed that the scales can be incorporated as hidden parameters into a Bayesian model. In this paper, we thoroughly scrutinise Bayesian approaches to MHO estimation and systematically study the performance of different models on an extensive set of high-order calculations. We extend the framework in two significant ways. First, we define a new model that allows for asymmetric probability distributions. Second, we introduce a prescription to incorporate information on perturbative scales without interpreting them as hidden model parameters. We clarify how the two scale prescriptions bias the result towards specific scale choice, and we discuss and compare different Bayesian MHO estimates among themselves and to the traditional scale variation approach. Finally, we provide a practical prescription of how existing perturbative results at the standard scale variation points can be converted to 68%/95% credibility intervals in the Bayesian approach using the new public code MiHO.

scholarly journals Joint inversion of proxy system models to reconstruct paleoenvironmental time series from heterogeneous data

2020 ◽  
Vol 16 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Gabriel J. Bowen ◽  
Brenden Fischer-Femal ◽  
Gert-Jan Reichart ◽  
Appy Sluijs ◽  
Caroline H. Lear
Keyword(s):  
Time Series ◽  
Ad Hoc ◽  
Joint Inversion ◽  
Environmental Variable ◽  
Heterogeneous Data ◽  
Published Data ◽  
Model Parameters ◽  
Qualitative Comparison ◽  
Bayesian Hierarchical ◽  
Proxy Reconstructions

Abstract. Paleoclimatic and paleoenvironmental reconstructions are fundamentally uncertain because no proxy is a direct record of a single environmental variable of interest; all proxies are indirect and sensitive to multiple forcing factors. One productive approach to reducing proxy uncertainty is the integration of information from multiple proxy systems with complementary, overlapping sensitivity. Mostly, such analyses are conducted in an ad hoc fashion, either through qualitative comparison to assess the similarity of single-proxy reconstructions or through step-wise quantitative interpretations where one proxy is used to constrain a variable relevant to the interpretation of a second proxy. Here we propose the integration of multiple proxies via the joint inversion of proxy system and paleoenvironmental time series models in a Bayesian hierarchical framework. The “Joint Proxy Inversion” (JPI) method provides a statistically robust approach to producing self-consistent interpretations of multi-proxy datasets, allowing full and simultaneous assessment of all proxy and model uncertainties to obtain quantitative estimates of past environmental conditions. Other benefits of the method include the ability to use independent information on climate and environmental systems to inform the interpretation of proxy data, to fully leverage information from unevenly and differently sampled proxy records, and to obtain refined estimates of proxy model parameters that are conditioned on paleo-archive data. Application of JPI to the marine Mg∕Ca and δ18O proxy systems at two distinct timescales demonstrates many of the key properties, benefits, and sensitivities of the method, and it produces new, statistically grounded reconstructions of Neogene ocean temperature and chemistry from previously published data. We suggest that JPI is a universally applicable method that can be implemented using proxy models of wide-ranging complexity to generate more robust, quantitative understanding of past climatic and environmental change.

Use of a stochastic model of a calving distribution for beef cows for formulating optimal natural mating strategies

1997 ◽  
Vol 64 (3) ◽  
pp. 413-421 ◽  
Author(s):  
A. B. Pleasants
Keyword(s):  
Probability Distributions ◽  
Live Weight ◽  
Beef Cows ◽  
Mating Strategies ◽  
Conception Rate ◽  
Model Parameters ◽  
Gestation Length ◽  
Mating Period ◽  
Frequency Distributions ◽  
The Cost

AbstractA model of a birthdate distribution for a herd of beef cows is constructed using the probability distributions of the variables that affect reproduction in the cow — anoestrous interval, oestrous cycle length, conception to each oestrus, gestation length, period of mating and the prior calving frequency distribution. The model is general and can be reparamaterized to deal with issues such as intervention to synchronize oestrous cycles among cows in the herd by changing the form of the relevant probability distributions.The model is applied to the question of what time to begin mating in a herd of beef cows. The average calf live weight at day 200, herd conception rate and proportion of cows calving before the planned start of calving were calculated from the model output. The model parameters given by the anoestrous period, conception rate to each oestrus and the regression between prior calving date and anoestrous period, were varied in a factorial design to investigate a range of circumstances found on a farm. Prior calving distributions were generated by random sampling from eight actual calving frequency distributions.Generally starling mating earlier produced an advantage in terms of extra calf live weight and herd conception rate. However, the proportion of the herd calving earlier than expected increased with early mating. Thus, the feasibility of early mating depends on the cost to the farmer of dealing with early calving cows as well as the advantage of heavier older calves.Altering the fixed parameters in the model (variances and covariances, prior calving distributions, mating period) to accommodate the circumstances of herds run under different conditions may produce different results. Model structure allows easy alteration of these parameters and also the introduction of different probability distributions for some variables. This might be necessary to model oestrous synchronization and artificial insemination, issues not considered in this paper.

scholarly journals Geometric potentials from deep learning improve prediction of CDR H3 loop structures

2020 ◽  
Vol 36 (Supplement_1) ◽  
pp. i268-i275 ◽  
Author(s):  
Jeffrey A Ruffolo ◽  
Carlos Guerra ◽  
Sai Pooja Mahajan ◽  
Jeremias Sulam ◽  
Jeffrey J Gray
Keyword(s):  
Deep Neural Networks ◽  
De Novo ◽  
Probability Distributions ◽  
Supplementary Information ◽  
Model Parameters ◽  
Loop Structure ◽  
Variable Loops ◽  
Chain Sequence ◽  
Antibody Structure ◽  
Complementarity Determining Region

Abstract Motivation Antibody structure is largely conserved, except for a complementarity-determining region featuring six variable loops. Five of these loops adopt canonical folds which can typically be predicted with existing methods, while the remaining loop (CDR H3) remains a challenge due to its highly diverse set of observed conformations. In recent years, deep neural networks have proven to be effective at capturing the complex patterns of protein structure. This work proposes DeepH3, a deep residual neural network that learns to predict inter-residue distances and orientations from antibody heavy and light chain sequence. The output of DeepH3 is a set of probability distributions over distances and orientation angles between pairs of residues. These distributions are converted to geometric potentials and used to discriminate between decoy structures produced by RosettaAntibody and predict new CDR H3 loop structures de novo. Results When evaluated on the Rosetta antibody benchmark dataset of 49 targets, DeepH3-predicted potentials identified better, same and worse structures [measured by root-mean-squared distance (RMSD) from the experimental CDR H3 loop structure] than the standard Rosetta energy function for 33, 6 and 10 targets, respectively, and improved the average RMSD of predictions by 32.1% (1.4 Å). Analysis of individual geometric potentials revealed that inter-residue orientations were more effective than inter-residue distances for discriminating near-native CDR H3 loops. When applied to de novo prediction of CDR H3 loop structures, DeepH3 achieves an average RMSD of 2.2 ± 1.1 Å on the Rosetta antibody benchmark. Availability and Implementation DeepH3 source code and pre-trained model parameters are freely available at https://github.com/Graylab/deepH3-distances-orientations. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Parameter Optimization of the 3PG Model Based on Sensitivity Analysis and a Bayesian Method

Forests ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1369
Author(s):  
Chenjian Liu ◽  
Xiaoman Zheng ◽  
Yin Ren
Keyword(s):  
Sensitivity Analysis ◽  
Parameter Optimization ◽  
Bayesian Method ◽  
Growth Models ◽  
Probability Distributions ◽  
Model Parameters ◽  
Simulation Accuracy ◽  
Sensitivity Analysis Method ◽  
Improved Model ◽  
Posterior Estimation

Sensitivity analysis and parameter optimization of stand models can improve their efficiency and accuracy, and increase their applicability. In this study, the sensitivity analysis, screening, and optimization of 63 model parameters of the Physiological Principles in Predicting Growth (3PG) model were performed by combining a sensitivity analysis method and the Markov chain Monte Carlo (MCMC) method of Bayesian posterior estimation theory. Additionally, a nine-year observational dataset of Chinese fir trees felled in the Shunchang Forest Farm, Nanping, was used to analyze, screen, and optimize the 63 model parameters of the 3PG model. The results showed the following: (1) The parameters that are most sensitive to stand stocking and diameter at breast height (DBH) are nWs(power in stem mass vs. diameter relationship), aWs(constant in stem mass vs. diameter relationship), alphaCx(maximum canopy quantum efficiency), k(extinction coefficient for PAR absorption by canopy), pRx(maximum fraction of NPP to roots), pRn(minimum fraction of NPP to roots), and CoeffCond(defines stomatal response to VPD); (2) MCMC can be used to optimize the parameters of the 3PG model, in which the posterior probability distributions of nWs, aWs, alphaCx, pRx, pRn, and CoeffCond conform to approximately normal or skewed distributions, and the peak value is prominent; and (3) compared with the accuracy before sensitivity analysis and a Bayesian method, the biomass simulation accuracy of the stand model was increased by 13.92%, and all indicators show that the accuracy of the improved model is superior. This method can be used to calibrate the parameters and analyze the uncertainty of multi-parameter complex stand growth models, which are important for the improvement of parameter estimation and simulation accuracy.

Probabilistic High-Cycle Fatigue Risk Assessment of an Integrally Bladed Rotor

2011 ◽  
Author(s):  
Benjamin D. Hall ◽  
Lauren Gray
Keyword(s):  
Risk Assessment ◽  
Monte Carlo ◽  
High Cycle Fatigue ◽  
Probability Distributions ◽  
Direct Monte Carlo Simulation ◽  
Model Parameters ◽  
Cycle Fatigue ◽  
Turbine Engine ◽  
Engineering Models ◽  
Mcmc Simulation

A fully probabilistic high-cycle fatigue (HCF) risk assessment methodology for application to turbine engine blades is described. The assessment uses the Bayesian paradigm of probability theory in which probability distributions are used to encode states of knowledge. Multi-level (or hierarchical) models are employed to capture engineering knowledge of the factors important for assessing HCF risk. This structure allows us to use standard probability distributions to adequately represent uncertainties in model parameters. The model accounts for engine-to-engine, run-to-run, and blade-to-blade variability as well as uncertainty in material capability, usage (flight conditions, time at resonance), and steady and vibratory stresses. Markov chain Monte Carlo (MCMC) simulation is used to fit observed data to the engineering models, then direct Monte Carlo simulation is used to assess the HCF risk.

Feasible stock trajectories: a flexible and efficient sequential estimator for use in fisheries management procedures

2012 ◽  
Vol 69 (1) ◽  
pp. 161-177 ◽  
Author(s):  
Nokome Bentley ◽  
Adam D. Langley
Keyword(s):  
Fisheries Management ◽  
Probability Distributions ◽  
Sequential Estimation ◽  
Alternative Methods ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Likelihood Functions ◽  
Management Procedure ◽  
Management Procedures ◽  
Stock Recruitment

We describe a sequential estimation approach designed to be used as part of a fisheries management procedure; it is computationally efficient and able to be applied to varying types, and extents, of data. The estimator maintains a pool of stock trajectories, each having a unique combination of model parameters (e.g., stock–recruitment steepness) sampled from prior probability distributions. Each year, for each trajectory, the values of variables (e.g., current biomass) are updated and tested against specified constraints. Constraints further determine the feasibility of the trajectories by defining likelihood functions for model variables, or combinations of variables, in particular years. Trajectories that fail to meet one or more of the constraints are discarded from the pool and replaced by new trajectories. Each year, stochastic forward projections of the trajectories in the pool are used to determine an optimal catch level. The flexibility and accuracy of the estimator is evaluated using the fishery for snapper, Pagrus auratus , off northern New Zealand as a case study. The sequential nature of the algorithm suggests alternative methods of presentation for understanding and explaining the fisheries estimation process. We provide recommendations for both the evaluation and operation of management procedures that employ the estimator.

scholarly journals Results of a tuberculin skin testing survey in Albania

2014 ◽  
Vol 8 (03) ◽  
pp. 310-314 ◽  
Author(s):  
Hasan Hafizi ◽  
Anila Aliko ◽  
Elda Sharra ◽  
Albana Fico ◽  
Giovanni Battista Migliori ◽  
...  
Keyword(s):  
Ad Hoc ◽  
Skin Testing ◽  
Cluster Sampling ◽  
Tuberculin Skin Testing ◽  
Tuberculosis Transmission ◽  
New Public Health ◽  
New Public ◽  
Latent Tb ◽  
Latent Tb Infection ◽  
Public Health Strategies

Introduction: Tuberculosis affected about 8.5 million patients in 2011. Numerous efforts are needed to reduce the pool of individuals with latent TB infection (LTBI). The aim of the study was to describe a tuberculin skin testing (TST) survey carried out in Albania to estimate the LTBI burden; furthermore, knowledge of TB was evaluated through an ad hoc questionnaire. Methodology: A TST survey was performed in three geographical districts of Albania: Tirana-Kamez, Vlora, and Dibra. Cluster sampling was carried out of young Albanian students. In addition, the same students were given a questionnaire to assess their knowledge, attitudes, and any misconceptions about TB. The mean (standard deviation) age of the individuals, according to their educational level, was the following: grade five, 11.03 (0.18) years; grade six, 12.02 (0.17) years; and grade seven, 13.02 (0.16) years. Results: The TST induration size was read in 4,648 students. About 5.0% showed a reaction >5 mm, with a significant variability in the districts selected (12.1% in the district of Dibra). An induration diameter >15 mm was found mainly in those areas with high TB incidence (i.e., Tirana-Kamez and Dibra). About 13% of the students had no knowledge of TB. Conclusion: LTBI prevalent cases are estimated to be low in Albania, although there are areas where the TB management should be improved to reduce the probability of Mycobacterium tuberculosis transmission. The level of knowledge about TB disease is inadequate and new public health strategies should be implemented, focusing on educational TV programs.

scholarly journals Forecasting Development of COVID-19 Epidemic in European Union Using Entropy-Randomized Approach

2021 ◽  
Vol 20 (5) ◽  
pp. 1010-1033
Author(s):  
Yuri Popkov ◽  
Yuri Dubnov ◽  
Alexey Popkov
Keyword(s):  
European Union ◽  
Least Squares Method ◽  
Probability Distributions ◽  
Real Data ◽  
Logistic Growth ◽  
Model Parameters ◽  
The European Union ◽  
Infected People ◽  
Testing Dataset ◽  
The Mean

The paper is devoted to the forecasting of the COVID-19 epidemic by the novel method of randomized machine learning. This method is based on the idea of estimation of probability distributions of model parameters and noises on real data. Entropy-optimal distributions correspond to the state of maximum uncertainty which allows the resulting forecasts to be used as forecasts of the most "negative" scenario of the process under study. The resulting estimates of parameters and noises, which are probability distributions, must be generated, thus obtaining an ensemble of trajectories that considered to be analyzed by statistical methods. In this work, for the purposes of such an analysis, the mean and median trajectories over the ensemble are calculated, as well as the trajectory corresponding to the mean over distribution values of the model parameters. The proposed approach is used to predict the total number of infected people using a three-parameter logistic growth model. The conducted experiment is based on real COVID-19 epidemic data in several countries of the European Union. The main goal of the experiment is to demonstrate an entropy-randomized approach for predicting the epidemic process based on real data near the peak. The significant uncertainty contained in the available real data is modeled by an additive noise within 30%, which is used both at the training and predicting stages. To tune the hyperparameters of the model, the scheme is used to configure them according to a testing dataset with subsequent retraining of the model. It is shown that with the same datasets, the proposed approach makes it possible to predict the development of the epidemic more efficiently in comparison with the standard approach based on the least-squares method.

scholarly journals Abraded Glass Strength: An Ad Hoc Fitting Protocol Based on the Change of Variable Theorem

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Camilla Ferretti ◽  
Piero Ganugi ◽  
Gabriele Pisano ◽  
Francesco Zammori
Keyword(s):  
Experimental Data ◽  
Ad Hoc ◽  
Probability Distributions ◽  
Glass Strength ◽  
Innovative Method ◽  
Change Of Variable ◽  
Random Nature ◽  
Over Time ◽  
Variable Theorem ◽  
Glass Properties

This work tackles the problem of finding a suitable statistical model to describe relevant glass properties, such as the strength under tensile stress. As known, glass is a brittle material, whose strength is strictly related to the presence of microcracks on its surface. The main issue is that the number of cracks, their size, and orientation are of random nature, and they may even change over time, due to abrasion phenomena. Consequently, glass strength should be statistically treated, but unfortunately none of the known probability distributions properly fit experimental data, when measured on abraded and/or aged glass panes. Owing to these issues, this paper proposes an innovative method to analyze the statistical properties of glass. The method takes advantage of the change of variable theorem and uses an ad-hoc transforming function to properly account for the distortion, on the original probability distribution of the glass strength, induced by the abrasion process. The adopted transforming function is based on micromechanical theory, and it provides an optimal fit of the experimental data.

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