scholarly journals Streamlined solutions to multilevel sparse matrix problems

2020 ◽  
Vol 62 ◽  
pp. 18-41
Author(s):  
Tui H. Nolan ◽  
Matt P. Wand
Keyword(s):  
Sparse Matrix ◽  
Level Structure ◽  
Mean Field ◽  
Multilevel Modelling ◽  
Standard Errors ◽  
Variational Bayesian Inference ◽  
The Common ◽  
Level 1 ◽  
Matrix Problems ◽  
Common Situation

We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects. doi: 10.1017/S1446181120000061

scholarly journals STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS

2020 ◽  
Vol 62 (1) ◽  
pp. 18-41 ◽  
Author(s):  
TUI H. NOLAN ◽  
MATT P. WAND
Keyword(s):  
Sparse Matrix ◽  
Level Structure ◽  
Mean Field ◽  
Multilevel Modelling ◽  
Standard Errors ◽  
Variational Bayesian Inference ◽  
The Common ◽  
Level 1 ◽  
Matrix Problems ◽  
Common Situation

We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects.

Ḥadith ‘Āishah fī Man’i al-Nisā’ Min al-Masājid; Niqāsh ‘Ulamā’ Bangladesh Ḥaulahu

2020 ◽  
Vol 9 (1) ◽  
pp. 97-115
Author(s):  
Syed Mahmudul Hasan
Keyword(s):  
Analytical Method ◽  
Inductive Method ◽  
The Common ◽  
The Difference ◽  
Common Situation

The Narration of Aisyah (May Allah be pleased with her), is the main focus of the controversy among Bangladeshi scholars on the issue of women's prayer in the mosque. The reason for the dispute is that a group of them issued the ruling based on the phenomenon of the text, and the others explained the ruling of Hadith according to the common situation in the society. If the circumstances change, the ruling will change along with it, because the originality of the issue is permissible, that is proven from other texts. This research adopts an inductive method to survey the Prophetic hadiths that talk about the prayer of women in the Mosque in terms of permissibility and prohibition and analytical method to analyze the difference in opinion of Bangladeshi scholars related to this issue. The research finds that the ruling of Shari’ah is a process that is continuous and permanent. But in necessity and emergency, it has the notion of flexibility and explanation. In the issue of women’s presence in the mosque, they should be allowed if they abide by the suggestions of Prophet (s) and should not if they don’t. So, Prohibition is not from the prophet (s), but it is from their obedience to the ruling.

scholarly journals Fast and Robust Orientation of Cryo-Electron Microscopy Images

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Guoliang Xu ◽  
Xia Wang ◽  
Ming Li ◽  
Zhucui Jing
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Image Plane ◽  
Real Space ◽  
Computation Method ◽  
Common Line ◽  
The Matrix ◽  
Common Lines ◽  
The Common ◽  
Dimensional Object

AbstractWe present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.

scholarly journals Regression Discontinuity and Heteroskedasticity Robust Standard Errors: Evidence from a Fixed-Bandwidth Approximation

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Otávio Bartalotti
Keyword(s):  
Bias Correction ◽  
Asymptotic Theory ◽  
Regression Discontinuity ◽  
Traditional Approach ◽  
Standard Errors ◽  
Test Coverage ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Theoretical Results ◽  
Robust Standard Errors

AbstractIn regression discontinuity designs (RD), for a given bandwidth, researchers can estimate standard errors based on different variance formulas obtained under different asymptotic frameworks. In the traditional approach the bandwidth shrinks to zero as sample size increases; alternatively, the bandwidth could be treated as fixed. The main theoretical results for RD rely on the former, while most applications in the literature treat the estimates as parametric, implementing the usual heteroskedasticity-robust standard errors. This paper develops the “fixed-bandwidth” alternative asymptotic theory for RD designs, which sheds light on the connection between both approaches. I provide alternative formulas (approximations) for the bias and variance of common RD estimators, and conditions under which both approximations are equivalent. Simulations document the improvements in test coverage that fixed-bandwidth approximations achieve relative to traditional approximations, especially when there is local heteroskedasticity. Feasible estimators of fixed-bandwidth standard errors are easy to implement and are akin to treating RD estimators aslocallyparametric, validating the common empirical practice of using heteroskedasticity-robust standard errors in RD settings. Bias mitigation approaches are discussed and a novel bootstrap higher-order bias correction procedure based on the fixed bandwidth asymptotics is suggested.

scholarly journals PEDAGOGICAL PRACTICE AS A KEY TO REAL PEDAGOGUE’S SUCCESS SOLUTION

2013 ◽  
Vol 6 (1) ◽  
pp. 4-5
Author(s):  
Vincentas Lamanauskas
Keyword(s):  
Education System ◽  
Scientific Research ◽  
Scientific Conference ◽  
Pedagogical Practice ◽  
Psychological Preparation ◽  
University Studies ◽  
State Pedagogical ◽  
The Common ◽  
Organizational Mechanisms ◽  
Common Situation

Pedagogical practice preparing future teachers is, undoubtedly, one of the most important elements of university studies. However, up to now pedagogical practice remains a very problematic sphere. Pedagogical activity, on the whole, is complicated, diverse and manifold. After all, it is an activity requiring creativity, high intellect and good psychological preparation. A student doing pedagogical practice, inevitably encounters various hardships -both specialty/professional and psychological. During the practice many different kinds of pedagogical situations are revealed. Various scientific research studies, carried out in the last few years, show the common situation – students-practitioners lack psychological preparation in communication with students, adjusting to a new environment, understanding them and so on. Actually, pedagogical practice theoretical and practical questions were discussed in the international scientific conference which took place between 1- 5 July, 2013 in Yerevan (Armenia). The conference under the theme „Modernization of Continuous Practice and Implementation of Organizational Mechanisms in the Higher Pedagogical Education System“ was organised by Armenian State Pedagogical University named after Khachatur Abovyan.

scholarly journals Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200688
Author(s):  
Valerio Lucarini ◽  
Grigorios A. Pavliotis ◽  
Niccolò Zagli
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Linear Response ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Transitions ◽  
Autocorrelation Time ◽  
The Common ◽  
Fokker Planck Equations ◽  
Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

scholarly journals Inference in Regression Discontinuity Designs with a Discrete Running Variable

2018 ◽  
Vol 108 (8) ◽  
pp. 2277-2304 ◽  
Author(s):  
Michal Kolesár ◽  
Christoph Rothe
Keyword(s):  
Confidence Intervals ◽  
Conditional Expectation ◽  
Regression Discontinuity ◽  
Model Misspecification ◽  
Standard Errors ◽  
Moderate Number ◽  
Regression Discontinuity Designs ◽  
The Common ◽  
Present Simulation ◽  
Theoretical Results

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable as a means to make inference robust to model misspecification (Lee and Card 2008). We derive theoretical results and present simulation and empirical evidence showing that these CIs do not guard against model misspecification, and that they have poor coverage properties. We therefore recommend against using these CIs in practice. We instead propose two alternative CIs with guaranteed coverage properties under easily interpretable restrictions on the conditional expectation function. (JEL C13, C51, J13, J31, J64, J65)

Estimates of the size of winter flocks of the Pied Currawong, Strepera graculina (Shaw) from mark -recapture data - a new approach

1968 ◽  
Vol 16 (1) ◽  
pp. 27 ◽  
Author(s):  
JL Readshaw
Keyword(s):  
Population Size ◽  
Emigration And Immigration ◽  
New Method ◽  
Random Numbers ◽  
Sampling Effort ◽  
Mark Recapture ◽  
New Approach ◽  
The Common ◽  
Winter Flocks ◽  
Common Situation

Banding records were used to estimate the size of non-breeding winter flocks of the pied currawong, Strepera graculina, at Albury, N.S.W., during 1964 and 1965. A new method of analysing mark-recapture data is compared with conventional methods, and it is shown that the flocks contained between 500 and 1000 birds in both years. In 1964, the new method provided information on emigration and immigration that was not apparent when the data were treated in the conventional way. The new approach considers the common situation in which a population (flock) is sampled continuously by catching one member (bird) at a time, marking (banding) it, and returning it to the population. For closed populations, the population size was estimated by a method involving cumulative catch and recapture data. Subsequently, this method was successfully tested by simulating the sampling of 20 "populations" of 10,000 random numbers with a computer. The method also provided a simple way of controlling sampling effort based on recapture data to obtain any desired precision in the estimation of population size.

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