Double reduction estimation and equilibrium tests in natural autopolyploid populations

Many bioinformatics pipelines include tests for equilibrium. Tests for diploids are well studied and widely available, but extending these approaches to autopolyploids is hampered by the presence of double reduction, the co-migration of sister chromatid segments into the same gamete during meiosis. Though a hindrance for equilibrium tests, double reduction rates are quantities of interest in their own right, as they provide insights about the meiotic behavior of autopolyploid organisms. Here, we develop procedures to (i) test for equilibrium while accounting for double reduction, and (ii) estimate double reduction given equilibrium. To do so, we take two approaches: a likelihood approach, and a novel U-statistic minimization approach that we show generalizes the classical equilibrium χ2 test in diploids. For small sample sizes and uncertain genotypes, we further develop a bootstrap procedure based on our U-statistic to test for equilibrium. Finally, we highlight the difficulty in distinguishing between random mating and equilibrium in tetraploids at biallelic loci. Our methods are implemented in the hwep R package on GitHub https://github.com/dcgerard/hwep.

An Iterative Parametric Bootstrap Approach to Evaluating Rater Fit

When analysts evaluate performance assessments, they often use modern measurement theory models to identify raters who frequently give ratings that are different from what would be expected, given the quality of the performance. To detect problematic scoring patterns, two rater fit statistics, the infit and outfit mean square error ( MSE) statistics are routinely used. However, the interpretation of these statistics is not straightforward. A common practice is that researchers employ established rule-of-thumb critical values to interpret infit and outfit MSE statistics. Unfortunately, prior studies have shown that these rule-of-thumb values may not be appropriate in many empirical situations. Parametric bootstrapped critical values for infit and outfit MSE statistics provide a promising alternative approach to identifying item and person misfit in item response theory (IRT) analyses. However, researchers have not examined the performance of this approach for detecting rater misfit. In this study, we illustrate a bootstrap procedure that researchers can use to identify critical values for infit and outfit MSE statistics, and we used a simulation study to assess the false-positive and true-positive rates of these two statistics. We observed that the false-positive rates were highly inflated, and the true-positive rates were relatively low. Thus, we proposed an iterative parametric bootstrap procedure to overcome these limitations. The results indicated that using the iterative procedure to establish 95% critical values of infit and outfit MSE statistics had better-controlled false-positive rates and higher true-positive rates compared to using traditional parametric bootstrap procedure and rule-of-thumb critical values.

Revisiting the functional bootstrap in TFHE

The FHEW cryptosystem introduced the idea that an arbitrary function can be evaluated within the bootstrap procedure as a table lookup. The faster bootstraps of TFHE strengthened this approach, which was later named Functional Bootstrap (Boura et al., CSCML’19). From then on, little effort has been made towards defining efficient ways of using it to implement functions with high precision. In this paper, we introduce two methods to combine multiple functional bootstraps to accelerate the evaluation of reasonably large look-up tables and highly precise functions. We thoroughly analyze and experimentally validate the error propagation in both methods, as well as in the functional bootstrap itself. We leverage the multi-value bootstrap of Carpov et al. (CT-RSA’19) to accelerate (single) lookup table evaluation, and we improve it by lowering the complexity of its error variance growth from quadratic to linear in the value of the output base. Compared to previous literature using TFHE’s functional bootstrap, our methods are up to 2.49 times faster than the lookup table evaluation of Carpov et al. (CT-RSA’19) and up to 3.19 times faster than the 32-bit integer comparison of Bourse et al. (CT-RSA’20). Compared to works using logic gates, we achieved speedups of up to 6.98, 8.74, and 3.55 times over 8-bit implementations of the functions ReLU, Addition, and Maximum, respectively.

Inference on the dynamics of the COVID pandemic from observational data

We describe a time dependent stochastic dynamic model in discrete time for the evolution of the COVID-19 pandemic in various states of USA. The proposed multi-compartment model is expressed through a system of difference equations that describe their temporal dynamics. Various compartments in our model is connected to the social distancing measures and diagnostic testing rates. A nonparametric estimation strategy is employed for obtaining estimates of interpretable temporally static and dynamic epidemiological rate parameters. The confidence bands of the parameters are obtained using a residual bootstrap procedure. A key feature of the methodology is its ability to estimate latent compartments such as the trajectory of the number of asymptomatic but infected individuals which are the key vectors of COVID-19 spread. The nature of the disease dynamics is further quantified by the proposed epidemiological markers, which use estimates of such key latent compartments.

Biomass Estimation of Eaglewood (Aquilaria filaria (Oken) Merr.) in the Karst Ecosystem of West Papua

Eaglewood is Indonesia’s important trade commodity in the form of resins from several infected species of Thymelaeaceae. The basis to determine its international trade quota through CITES is derived from the estimated eaglewood-producing species grown in their habitat. This paper aims to estimate the biomass of eaglewood, Aquilaria filaria, in the karst ecosystem of West Papua. We conducted a plot-based method and calculated the biomass of A. filaria using a diameter-based allometric equation and simulated using a bootstrap procedure. The results showed that 15,500 tons of naturally infected eaglewood are estimated in the karst ecosystem of West Papua.

Bootstrap With Cluster‐Dependence in Two or More Dimensions

We propose a bootstrap procedure for data that may exhibit cluster‐dependence in two or more dimensions. The asymptotic distribution of the sample mean or other statistics may be non‐Gaussian if observations are dependent but uncorrelated within clusters. We show that there exists no procedure for estimating the limiting distribution of the sample mean under two‐way clustering that achieves uniform consistency. However, we propose bootstrap procedures that achieve adaptivity with respect to different uniformity criteria. Important cases and extensions discussed in the paper include regression inference, U‐ and V‐statistics, subgraph counts for network data, and non‐exhaustive samples of matched data.

A Projection Framework for Testing Shape Restrictions That Form Convex Cones

This paper develops a uniformly valid and asymptotically nonconservative test based on projection for a class of shape restrictions. The key insight we exploit is that these restrictions form convex cones, a simple and yet elegant structure that has been barely harnessed in the literature. Based on a monotonicity property afforded by such a geometric structure, we construct a bootstrap procedure that, unlike many studies in nonstandard settings, dispenses with estimation of local parameter spaces, and the critical values are obtained in a way as simple as computing the test statistic. Moreover, by appealing to strong approximations, our framework accommodates nonparametric regression models as well as distributional/density‐related and structural settings. Since the test entails a tuning parameter (due to the nonstandard nature of the problem), we propose a data‐driven choice and prove its validity. Monte Carlo simulations confirm that our test works well.

Testing for asymmetric adjustment in weekly Brazilian inflation

This study analyses the nature of weekly inflation response to shocks in the Brazilian economy by adopting a generalized quantile autoregression model in which the autoregressive parameter is allowed to be quantile-dependent. We test for unit root at different conditional quantiles of the response variable, by characterizing its asymmetric dynamics along the business cycle. The method allows us to estimate the magnitude, sign, and the significance of actual shocks that affect Brazilian inflation. We evaluate the robustness of results by adopting a bootstrap procedure. Concerning previous studies, we find evidence of stronger asymmetric persistence in inflationary dynamics in which an inflationary shock below the average dissipates very fast when compared to an inflationary impulse occurring above the average. Location, size, and the sign of a random shock might be essential for inflation adjustment towards long-run equilibrium. The results do not support the full inertia hypothesis.