scholarly journals Non-dichotomous inference using bootstrapped evidence

2015 ◽  
Author(s):  
D. Sam Schwarzkopf
Keyword(s):  
Experimental Data ◽  
Bayesian Inference ◽  
Null Hypothesis ◽  
Significance Level ◽  
Expected Effect ◽  
Considerable Uncertainty ◽  
Classical Statistics ◽  
Frequentist Statistics ◽  
Wide Range ◽  
Resampling Procedure

The problems with classical frequentist statistics have recently received much attention, yet the enthusiasm of researchers to adopt alternatives like Bayesian inference remains modest. Here I present the bootstrapped evidence test, an objective resampling procedure that takes the precision with which both the experimental and null hypothesis can be estimated into account. Simulations and reanalysis of actual experimental data demonstrate that this test minimizes false positives while maintaining sensitivity. It is equally applicable to a wide range of situations and thus minimizes problems arising from analytical flexibility. Critically, it does not dichotomize the results based on an arbitrary significance level but instead quantifies how well the data support either the alternative or the null hypothesis. It is thus particularly useful in situations with considerable uncertainty about the expected effect size. Because it is non-parametric, it is also robust to severe violations of assumptions made by classical statistics.

scholarly journals Expert Opinions on How to Conduct and Report Bayesian Inference

2018 ◽  
Author(s):  
Balazs Aczel ◽  
Rink Hoekstra ◽  
andrew gelman ◽  
Eric-Jan Wagenmakers ◽  
Irene G. Kluglist ◽  
...  
Keyword(s):  
Bayesian Inference ◽  
Bayesian Methods ◽  
Null Hypothesis ◽  
Social Scientists ◽  
Likelihood Functions ◽  
Expert Opinions ◽  
Wide Range ◽  
Making Choices ◽  
Case Basis ◽  
Behavioural Sciences

Compared to the relatively standard way of conducting null hypothesis significance testing, there seem to be fairly large differences in opinion among experts in Bayesian statistics on how best to conduct Bayesian inference. Employing Bayesian methods involves making choices about prior distributions, likelihood functions, and robustness checks, as well as on how to report, visualize, and interpret the results. This wide range of choices might make it daunting for social scientists to make the transition to conducting Bayesian inference in their own research. In this review, we conducted an expert survey in which nine of the most prominent Bayesian statisticians in the behavioural sciences shared their thinking on seven key choices that need to be made when conducting and reporting Bayesian inference. This paper highlights the areas of their agreements and the arguments behind their disagreements. The results of an iterative survey show experts agree on many more topics than they disagree on. The overall message is that instead of following rituals, researchers should understand the reasoning behind the different positions and make their choices on a case by case basis.

The Use and Misuse of Classical Statistics: A Primer for Social Workers

2021 ◽  
pp. 104973152110082
Author(s):  
Daniel J. Dunleavy ◽  
Jeffrey R. Lacasse
Keyword(s):  
Social Workers ◽  
Null Hypothesis ◽  
Effect Sizes ◽  
Significance Testing ◽  
Null Hypothesis Significance Testing ◽  
P Values ◽  
Research And Practice ◽  
Classical Statistics ◽  
Frequentist Statistics ◽  
Common Misconceptions

In this article, we offer a primer on “classical” frequentist statistics. In doing so, we aim to (1) provide social workers with a nuanced overview of common statistical concepts and tools, (2) clarify ways in which these ideas have oft been misused or misinterpreted in research and practice, and (3) help social workers better understand what frequentist statistics can and cannot offer. We begin broadly, starting with foundational issues in the philosophy of statistics. Then, we outline the Fisherian and Neyman–Pearson approaches to statistical inference and the practice of null hypothesis significance testing. We then discuss key statistical concepts including α, power, p values, effect sizes, and confidence intervals, exploring several common misconceptions about their use and interpretation. We close by considering some limitations of frequentist statistics and by offering an opinionated discussion on how social workers may promote more fruitful, responsible, and thoughtful statistical practice.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

scholarly journals Detecting Heterogeneity of Substitution Along DNA and Protein Sequences

Genetics ◽  
1996 ◽  
Vol 143 (1) ◽  
pp. 589-602 ◽  
Author(s):  
Peter J E Goss ◽  
R C Lewontin
Keyword(s):  
Null Hypothesis ◽  
Nonuniform Distribution ◽  
Critical Values ◽  
Third Order ◽  
Variance Test ◽  
Data Set ◽  
Significance Level ◽  
Uniformly Most Powerful Test ◽  
Interval Lengths ◽  
Uniformly Most Powerful

Abstract Regions of differing constraint, mutation rate or recombination along a sequence of DNA or amino acids lead to a nonuniform distribution of polymorphism within species or fixed differences between species. The power of five tests to reject the null hypothesis of a uniform distribution is studied for four classes of alternate hypothesis. The tests explored are the variance of interval lengths; a modified variance test, which includes covariance between neighboring intervals; the length of the longest interval; the length of the shortest third-order interval; and a composite test. Although there is no uniformly most powerful test over the range of alternate hypotheses tested, the variance and modified variance tests usually have the highest power. Therefore, we recommend that one of these two tests be used to test departure from uniformity in all circumstances. Tables of critical values for the variance and modified variance tests are given. The critical values depend both on the number of events and the number of positions in the sequence. A computer program is available on request that calculates both the critical values for a specified number of events and number of positions as well as the significance level of a given data set.

scholarly journals Experimental analysis and ANN prediction on performances of finned oval-tube heat exchanger under different air inlet angles with limited experimental data

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 968-980
Author(s):  
Xueping Du ◽  
Zhijie Chen ◽  
Qi Meng ◽  
Yang Song
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Correlation Equation ◽  
Tube Heat Exchanger ◽  
Flow Friction ◽  
Air Inlet ◽  
Comparison Results ◽  
Wide Range ◽  
Oval Tube

Abstract A high accuracy of experimental correlations on the heat transfer and flow friction is always expected to calculate the unknown cases according to the limited experimental data from a heat exchanger experiment. However, certain errors will occur during the data processing by the traditional methods to obtain the experimental correlations for the heat transfer and friction. A dimensionless experimental correlation equation including angles is proposed to make the correlation have a wide range of applicability. Then, the artificial neural networks (ANNs) are used to predict the heat transfer and flow friction performances of a finned oval-tube heat exchanger under four different air inlet angles with limited experimental data. The comparison results of ANN prediction with experimental correlations show that the errors from the ANN prediction are smaller than those from the classical correlations. The data of the four air inlet angles fitted separately have higher precisions than those fitted together. It is demonstrated that the ANN approach is more useful than experimental correlations to predict the heat transfer and flow resistance characteristics for unknown cases of heat exchangers. The results can provide theoretical support for the application of the ANN used in the finned oval-tube heat exchanger performance prediction.

scholarly journals Modelling the Inflation and Elastic Instabilities of Rubber-Like Spherical and Cylindrical Shells Using a New Generalised Neo-Hookean Strain Energy Function

2021 ◽  
Author(s):  
Afshin Anssari-Benam ◽  
Andrea Bucchi ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Energy Function ◽  
Limit Point ◽  
Strain Energy ◽  
Cylindrical Shells ◽  
Strain Energy Function ◽  
Model Parameters ◽  
Wide Range ◽  
Cylindrical Tubes ◽  
Gent Model

AbstractThe application of a newly proposed generalised neo-Hookean strain energy function to the inflation of incompressible rubber-like spherical and cylindrical shells is demonstrated in this paper. The pressure ($P$ P ) – inflation ($\lambda $ λ or $v$ v ) relationships are derived and presented for four shells: thin- and thick-walled spherical balloons, and thin- and thick-walled cylindrical tubes. Characteristics of the inflation curves predicted by the model for the four considered shells are analysed and the critical values of the model parameters for exhibiting the limit-point instability are established. The application of the model to extant experimental datasets procured from studies across 19th to 21st century will be demonstrated, showing favourable agreement between the model and the experimental data. The capability of the model to capture the two characteristic instability phenomena in the inflation of rubber-like materials, namely the limit-point and inflation-jump instabilities, will be made evident from both the theoretical analysis and curve-fitting approaches presented in this study. A comparison with the predictions of the Gent model for the considered data is also demonstrated and is shown that our presented model provides improved fits. Given the simplicity of the model, its ability to fit a wide range of experimental data and capture both limit-point and inflation-jump instabilities, we propose the application of our model to the inflation of rubber-like materials.

The Petrogenetic Model, an Extension of Bowen's Petrogenetic Grid

1962 ◽  
Vol 99 (6) ◽  
pp. 558-569 ◽  
Author(s):  
Peter J. Wyllie
Keyword(s):  
Experimental Data ◽  
Constant Pressure ◽  
Three Dimensional ◽  
Pore Fluid ◽  
Fluid Composition ◽  
Solid Reaction ◽  
Petrogenetic Model ◽  
Wide Range ◽  
Opposite Face ◽  
Reaction Surfaces

AbstractBowen's petrogenetic grid is a PT projection containing univariant curves for decarbonation, dehydration, and solid-solid reactions, with vapour pressure (Pf) equal to total pressure (Ps). Analysis of experimental data in the system MgO–CO2–H2O leads to an expansion of this grid. Three of the important variables in metamorphism when Pf = Ps are P, T, and variation of the pore fluid composition between H2O and CO2. These can be illustrated in a three-dimensional petrogenetic model; one face is a PT plane for reactions occurring with pure H2O, and the opposite face is a similar plane for reactions with pure CO2; these are separated by an axis for pore fluid composition varying between H2O and CO2. Superposition of the PT faces of the model provides the petrogenetic grid. The reactions within the model are represented by divariant surfaces, which may meet along univariant lines. For dissociation reactions, the surfaces curve towards lower temperatures as the proportion of non-reacting volatile increases, and solid-solid reaction surfaces are parallel to the vapour composition axis and perpendicular to the PT axes. The relative temperatures of reactions and the lines of intersections of the surfaces can be illustrated in isobaric sections. Isobaric sections are used to illustrate reactions proceeding at constant pressure with (1) pore fluid composition remaining constant during the reaction, with temperature increasing (2) pore fluid composition changing during the reaction, with temperature increasing, and (3) pore fluid changing composition at constant temperature. The petrogenetic model provides a convenient framework for a wide range of experimental data.

Effects of Multiple Impacts and Size Distribution of Particles on Erosion Predictions Using CFD

2007 ◽  
Author(s):  
Yongli Zhang ◽  
Brenton S. McLaury ◽  
Siamack A. Shirzai
Keyword(s):  
Experimental Data ◽  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Target Material ◽  
Average Particle ◽  
Multiple Impacts ◽  
Cfd Simulations ◽  
Erosion Damage ◽  
Wide Range

Erosion equations are usually obtained from experiments by impacting solid particles entrained in a gas or liquid on a target material. The erosion equations are utilized in CFD (Computational Fluid Dynamics) models to predict erosion damage caused by solid particle impingements. Many erosion equations are provided in terms of an erosion ratio. By definition, the erosion ratio is the mass loss of target material divided by the mass of impacting particles. The mass of impacting particles is the summation of (particle mass × number of impacts) of each particle. In erosion experiments conducted to determine erosion equations, some particles may impact the target wall many times and some other particles may not impact the target at all. Therefore, the experimental data may not reflect the actual erosion ratio because the mass of the sand that is used to run the experiments is assumed to be the mass of the impacting particles. CFD and particle trajectory simulations are applied in the present work to study effects of multiple impacts on developing erosion ratio equations. The erosion equation as well as the CFD-based erosion modeling procedure is validated against a variety of experimental data. The results show that the effect of multiple impacts is negligible in air cases. In water cases, however, this effect needs to be accounted for especially for small particles. This makes it impractical to develop erosion ratio equations from experimental data obtained for tests with sand in water or dense gases. Many factors affecting erosion damage are accounted for in various erosion equations. In addition to some well-studied parameters such as particle impacting speed and impacting angle, particle size also plays a significant role in the erosion process. An average particle size is usually used in analyzing experimental data or estimating erosion damage cases of practical interest. In petroleum production applications, however, the size of sand particles that are entrained in produced fluids can vary over a fairly broad range. CFD simulations are also performed to study the effect of particle size distribution. In CFD simulations, particle sizes are normally distributed with the mean equaling the average size of interest and the standard deviation varying over a wide range. Based on CFD simulations, an equation is developed and can be applied to account for the effect of the particle size distribution on erosion prediction for gases and liquids.

Fuel Droplet Evaporation in a Supercritical Environment

2002 ◽  
Vol 124 (4) ◽  
pp. 762-770 ◽  
Author(s):  
G. S. Zhu ◽  
S. K. Aggarwal
Keyword(s):  
Experimental Data ◽  
Phase Equilibrium ◽  
Ambient Pressure ◽  
Droplet Surface ◽  
Fuel Vapor ◽  
Phase Solubility ◽  
Liquid Density ◽  
Ambient Temperatures ◽  
Droplet Vaporization ◽  
Wide Range

This paper reports a numerical investigation of the transcritical droplet vaporization phenomena. The simulation is based on the time-dependent conservation equations for liquid and gas phases, pressure-dependent variable thermophysical properties, and a detailed treatment of liquid-vapor phase equilibrium at the droplet surface. The numerical solution of the two-phase equations employs an arbitrary Eulerian-Lagrangian, explicit-implicit method with a dynamically adaptive mesh. Three different equations of state (EOS), namely the Redlich-Kwong (RK), the Peng-Robinson (PR), and Soave-Redlich-Kwong (SRK) EOS, are employed to represent phase equilibrium at the droplet surface. In addition, two different methods are used to determine the liquid density. Results indicate that the predictions of RK-EOS are significantly different from those obtained by using the RK-EOS and SRK-EOS. For the phase-equilibrium of n-heptane-nitrogen system, the RK-EOS predicts higher liquid-phase solubility of nitrogen, higher fuel vapor concentration, lower critical-mixing-state temperature, and lower enthalpy of vaporization. As a consequence, it significantly overpredicts droplet vaporization rates, and underpredicts droplet lifetimes compared to those predicted by PR and SRK-EOS. In contrast, predictions using the PR-EOS and SRK-EOS show excellent agreement with each other and with experimental data over a wide range of conditions. A detailed investigation of the transcritical droplet vaporization phenomena indicates that at low to moderate ambient temperatures, the droplet lifetime first increases and then decreases as the ambient pressure is increased. At high ambient temperatures, however, the droplet lifetime decreases monotonically with pressure. This behavior is in accord with the reported experimental data.

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