Selection models with monotone weight functions in meta analysis

Publication bias, the fact that studies identified for inclusion in a meta analysis do not represent all studies on the topic of interest, is commonly recognized as a threat to the validity of the results of a meta analysis. One way to explicitly model publication bias is via selection models or weighted probability distributions. We adopt the nonparametric approach initially introduced by Dear (1992) but impose that the weight function $w$ is monotonely non-increasing as a function of the $p$-value. Since in meta analysis one typically only has few studies or "observations", regularization of the estimation problem seems sensible. In addition, virtually all parametric weight functions proposed so far in the literature are in fact decreasing. We discuss how to estimate a decreasing weight function in the above model and illustrate the new methodology on two well-known examples. The new approach potentially offers more insight in the selection process than other methods and is more flexible than parametric approaches. Some basic properties of the log-likelihood function and computation of a $p$-value quantifying the evidence against the null hypothesis of a constant weight function are indicated. In addition, we provide an approximate selection bias adjusted profile likelihood confidence interval for the treatment effect. The corresponding software and the datasets used to illustrate it are provided as the R package selectMeta. This enables full reproducibility of the results in this paper.Comment: 15 pages, 2 figures. Some minor changes according to reviewer comment

Automatic Differentiation Variational Inference

Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving algorithms for new models can be both mathematically and computationally challenging, which makes it difficult to efficiently cycle through the steps. To this end, we develop automatic differentiation variational inference (ADVI). Using our method, the scientist only provides a probabilistic model and a dataset, nothing else. ADVI automatically derives an efficient variational inference algorithm, freeing the scientist to refine and explore many models. ADVI supports a broad class of models-no conjugacy assumptions are required. We study ADVI across ten different models and apply it to a dataset with millions of observations. ADVI is integrated into Stan, a probabilistic programming system; it is available for immediate use

Wing and body motion during flight initiation in Drosophila revealed by automated visual tracking

The fruit fly Drosophila melanogaster is a widely used model organism in studies of genetics, developmental biology and biomechanics. One limitation for exploiting Drosophila as a model system for behavioral neurobiology is that measuring body kinematics during behavior is labor intensive and subjective. In order to quantify flight kinematics during different types of maneuvers, we have developed a visual tracking system that estimates the posture of the fly from multiple calibrated cameras. An accurate geometric fly model is designed using unit quaternions to capture complex body and wing rotations, which are automatically fitted to the images in each time frame. Our approach works across a range of flight behaviors, while also being robust to common environmental clutter. The tracking system is used in this paper to compare wing and body motion during both voluntary and escape take-offs. Using our automated algorithms, we are able to measure stroke amplitude, geometric angle of attack and other parameters important to a mechanistic understanding of flapping flight. When compared with manual tracking methods, the algorithm estimates body position within 4.4±1.3% of the body length, while body orientation is measured within 6.5±1.9 deg. (roll), 3.2±1.3 deg. (pitch) and 3.4±1.6 deg. (yaw) on average across six videos. Similarly, stroke amplitude and deviation are estimated within 3.3 deg. and 2.1 deg., while angle of attack is typically measured within 8.8 deg. comparing against a human digitizer. Using our automated tracker, we analyzed a total of eight voluntary and two escape take-offs. These sequences show that Drosophila melanogaster do not utilize clap and fling during take-off and are able to modify their wing kinematics from one wingstroke to the next. Our approach should enable biomechanists and ethologists to process much larger datasets than possible at present and, therefore, accelerate insight into the mechanisms of free-flight maneuvers of flying insects

Linear evolution of sandwave packets

We investigate how a local topographic disturbance of a flat seabed may become morphodynamically active, according to the linear instability mechanism which gives rise to sandwave formation. The seabed evolution follows from a Fourier integral, which can generally not be evaluated in closed form. As numerical integration is rather cumbersome and not transparent, we propose an analytical way to approximate the solution. This method, using properties of the fastest growing mode only, turns out to be quick, insightful, and to perform well. It shows how a local disturbance develops gradually into a sandwave packet, the area of which increases roughly linearly with time. The elevation at the packet¿s center ultimately tends to increase, but this may be preceded by an initial stage of decrease, depending on the spatial extent of the initial disturbance. In the case of tidal asymmetry, the individual sandwaves in the packet migrate at the migration speed of the fastest growing mode, whereas the envelope moves at the group speed. Finally, we apply the theory to trenches and pits and show where results differ from an earlier study in which sandwave dynamics have been ignored

The devil is in the detail: hints for practical optimisation

Finding the minimum of an objective function, such as a least squares or negative log-likelihood function, with respect to the unknown model parameters is a problem often encountered in econometrics. Consequently, students of econometrics and applied econometricians are usually well-grounded in the broad differences between the numerical procedures employed to solve these problems. Often, however, relatively little time is given to understanding the practical subtleties of implementing these schemes when faced with illbehaved problems. This paper addresses some of the details involved in practical optimisation, such as dealing with constraints on the parameters, specifying starting values, termination criteria and analytical gradients, and illustrates some of the general ideas with several instructive examples