155,532 research outputs found
Revisiting the g-null paradox
No full textThe parametric g-formula is an approach to estimating causal effects of
sustained treatment strategies from observational data. An often cited
limitation of the parametric g-formula is the g-null paradox: a phenomenon in
which model misspecification in the parametric g-formula is guaranteed under
the conditions that motivate its use (i.e., when identifiability conditions
hold and measured time-varying confounders are affected by past treatment).
Many users of the parametric g-formula know they must acknowledge the g-null
paradox as a limitation when reporting results but still require clarity on its
meaning and implications. Here we revisit the g-null paradox to clarify its
role in causal inference studies. In doing so, we present analytic examples and
a simulation-based illustration of the bias of parametric g-formula estimates
under the conditions associated with this paradox. Our results highlight the
importance of avoiding overly parsimonious models for the components of the
g-formula when using this method
Publication Bias Against Null Results
No full textStudies suggest a bias against the publication of null (p > .05) results. Instead of significance, we advocate reporting effect sizes and confidence intervals, and using replication studies. If statistical tests are used, power tests should accompany them.publication, bias, null results
The appearance, motion, and disappearance of three-dimensional magnetic null points
No full textN.A.M. acknowledges support from NASA grants NNX11AB61G, NNX12AB25G, and NNX15AF43G; NASA contract NNM07AB07C; and NSF SHINE grants AGS-1156076 and AGS-1358342 to SAO. C.E.P. acknowledges support from the St Andrews 2013 STFC Consolidated grant.While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.Peer reviewe
Linear Operator Inequality and Null Controllability with Vanishing Energy for Unbounded Control Systems
No full textWe consider a linear boundary or point control system on a Hilbert space which is null controllable at some time . To every initial state we associate the minimal ``energy'' needed to transfer to in a time (``energy'' of a control being the square of its norm). Clearly, it decreases with the control time . We shall prove that, under suitable spectral properties of the linear system operator, the minimal energy converges to for $ T\to+\infty
Interpreting null findings from trials of alcohol brief interventions
No full textThe effectiveness of alcohol brief intervention (ABI) has been established by a succession of meta-analyses but, because the effects of ABI are small, null findings from randomized controlled trials are often reported and can sometimes lead to skepticism regarding the benefits of ABI in routine practice. This article first explains why null findings are likely to occur under null hypothesis significance testing (NHST) due to the phenomenon known as ‘the dance of the p-values’. A number of misconceptions about null findings are then described, using as an example the way in which the results of the primary care arm of a recent cluster randomized trial of ABI in England (the SIPS project) have been misunderstood. These misinterpretations include the fallacy of ‘proving the null hypothesis’ that lack of a significant difference between the means of sample groups can be taken as evidence of no difference between their population means, and the possible effects of this and related misunderstandings of the SIPS findings are examined. The mistaken inference that reductions in alcohol consumption seen in control groups from baseline to follow-up are evidence of real effects of control group procedures is then discussed and other possible reasons for such reductions, including regression to the mean, research participation effects, historical trends, and assessment reactivity, are described. From the standpoint of scientific progress, the chief problem about null findings under the conventional NHST approach is that it is not possible to distinguish ‘evidence of absence’ from ‘absence of evidence’. By contrast, under a Bayesian approach, such a distinction is possible and it is explained how this approach could classify ABIs in particular settings or among particular populations as either truly ineffective or as of unknown effectiveness, thus accelerating progress in the field of ABI research
Haar null sets without G δ hulls
No full textLet G be an abelian Polish group, e.g., a separable Banach space. A subset X ⊂ G is called Haar null (in the sense of Christensen) if there exists a Borel set B ⊃ X and a Borel probability measure µ on G such that µ(B + g) = 0 for every g ∈ G. The term shy is also commonly used for Haar null, and co-Haar null sets are often called prevalent. Answering an old question of Mycielski we show that if G is not locally compact then there exists a Borel Haar null set that is not contained in any (Formula presented.) Haar null set. We also show that (Formula presented.) can be replaced by any other class of the Borel hierarchy, which implies that the additivity of the σ-ideal of Haar null sets is ω1. The definition of a generalised Haar null set is obtained by replacing the Borelness of B in the above definition by universal measurability. We give an example of a generalised Haar null set that is not Haar null, more precisely, we construct a coanalytic generalised Haar null set without a Borel Haar null hull. This solves Problem GP from Fremlin’s problem list. Actually, all our results readily generalise to all Polish groups that admit a two-sided invariant metric. © 2015, Hebrew University of Jerusalem
Asymptotic null distributions of stationarity and nonstationarity
No full textThe purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as T " 1. This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.Stable distributions, unit root tests, stationarity tests, asymptotic distributions,local-to-finite variance, size distortion
Current sheet formation and nonideal behavior at three-dimensional magnetic null points
No full textThe nature of the evolution of the magnetic field, and of current sheet formation, at three-dimensional (3D) magnetic null points is investigated. A kinematic example is presented that demonstrates that for certain evolutions of a 3D null (specifically those for which the ratios of the null point eigenvalues are time-dependent), there is no possible choice of boundary conditions that renders the evolution of the field at the null ideal. Resistive magnetohydrodynamics simulations are described that demonstrate that such evolutions are generic. A 3D null is subjected to boundary driving by shearing motions, and it is shown that a current sheet localized at the null is formed. The qualitative and quantitative properties of the current sheet are discussed. Accompanying the sheet development is the growth of a localized parallel electric field, one of the signatures of magnetic reconnection. Finally, the relevance of the results to a recent theory of turbulent reconnection is discussed
Estimation in threshold autoregressive models with a stationary and a unit root regime
No full textThis paper treats estimation in a class of new nonlinear threshold autoregressive models with both a stationary and a unit root regime. Existing literature on nonstationary threshold models have basically focused on models where the nonstationarity can be removed by differencing and/or where the threshold variable is stationary. This is not the case for the process we consider, and nonstandard estimation problems are the result. This paper proposes a parameter estimation method for such nonlinear threshold autoregressive models using the theory of null recurrent Markov chains. Under certain assumptions, we show that the ordinary least squares (OLS) estimators of the parameters involved are asymptotically consistent. Furthermore, it can be shown that the OLS estimator of the coefficient parameter involved in the stationary regime can still be asymptotically normal while the OLS estimator of the coefficient parameter involved in the nonstationary regime has a nonstandard asymptotic distribution. In the limit, the rate of convergence in the stationary regime is asymptotically proportional to n-1/4, whereas it is n-1 in the nonstationary regime. The proposed theory and estimation method are illustrated by both simulated data and a real data example.Autoregressive process; null-recurrent process; semiparametric model; threshold time series; unit root structure.
Optimization Of Off-Null Ellipsometry For Air/Solid Interfaces
No full textThe optimization of off-null ellipsometry is described with emphasis on the improvement of sample thickness sensitivity. Optimal conditions are dependent on azimuth angle settings of the polarizer, compensator, and analyzer in a polarizer-compensator-sample-analyzer ellipsometer arrangement. Numerical simulation utilized offers an approach to present the dependence of the sensitivity on the azimuth angle settings, from which optimal settings corresponding to the best sensitivity are derived. For a series of samples of SiO2 layer (thickness in the range of 1.8-6.5 nm) on silicon substrate, the theory analysis proves that sensitivity at the optimal settings is increased 20 times compared to that at null settings used in most works, and the relationship between intensity and thickness is simplified as a linear type instead of the original nonlinear type, with the relative error reduced to similar to 1/100 at the optimal settings. Furthermore the discussion has been extended toward other factors affecting the sensitivity of the practical system, such as the linear dynamic range of the detector, the signal-to-noise ratio and the intensity from the light source, etc. Experimental results from the investigation Of SiO2 layer on silicon substrate are chosen to verify the optimization. (c) 2007 Optical Society of America
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