Confidence Intervals After Variance Stabilization May Go Head-to-Head with Exact Confidence Intervals: A New Class of Illustrations

We begin with an overview on variance stabilizing transformations (VST) along with three classical examples for completeness: the arcsine, square-root and Fisher's z-transformations (Examples 1–3). Then, we construct three new examples (Examples 4–6) of VST-based and central limit theorem (CLT)’based large-sample confidence interval methodologies. These are special examples in the sense that in each situation, we also have an exact confidence interval procedure for the parameter of interest. Tables 1–3 obtained exclusively under Examples 4–6 via exact calculations show that the VST-based (a) large-sample confidence interval methodology wins over the CLT-based large-sample confidence interval methodology, (b) confidence intervals’ exact coverage probabilities are better than or nearly same as those associated with the exact confidence intervals and (c) intervals are never wider (in the log-scale) than the CLT-based intervals across the board. A possibility of such a surprising behaviour of the VST-based confidence intervals over the exact intervals was not on our radar when we began this investigation. Indeed the VST-based inference methodologies may do extremely well, much more so than the existing literature reveals as evidenced by the new Examples 4–6. AMS subject classifications: 62E20; 62F25; 62F12

Investigating seasonality, policy intervention and forecasting in the Indian gold futures market: a comparison based on modeling non-constant variance using two different methods

This study focuses on the Indian gold futures market where primary participants hold sentimental value for the underlying asset and are globally ranked number two in terms of the largest private holdings in the physical form. The trade of gold futures relates to seasons, festivity, and government policy. So, the paper will discuss seasonality and intervention in the analysis. Due to non-constant variance, we will also use the standard variance stabilization transformation method and the ARIMA/GARCH modelling method to compare the forecast performance on the gold futures prices. The results from the analysis show that while the standard variance transformation method may provide better point forecast values, the ARIMA/GARCH modelling method provides much shorter forecast intervals. The empirical results of this study which rationalise the effect of seasonality in the Indian bullion derivative market have not been reported in literature.

Comparison of the Performance of the SANN, SARIMA and ARIMA Models for Forecasting Quarterly GDP of Nigeria

This research aimed at modelling and forecasting the quarterly GDP of Nigeria using the Seasonal Artificial Neural Network (SANN), SARIMA and Box-Jenkins models as well as comparing their predictive performance. The three models mentioned earlier were successfully fitted to the data set. Tentative architecture for the SANN was suggested by varying the number of neurons in the hidden layer while that of the input and output layer remained constant at 4. It was observed that the best architecture was when the hidden layer had 10 neurons and thus SANN (4-10-4) was chosen as the best. In fitting the ARIMA/SARIMA models, the Augmented Dickey Fuller (ADF) test was used to check for stationarity. Variance stabilization and Stationarity were achieved after logarithm transformation and first regular differencing. The ARIMA/SARIMA model with lowest AIC, BIC and HQIC values was chosen as the best amongst the competing models and fitted to the data. The adequacy of the fitted models was confirmed observing the correlogram of the residuals and the Ljung-Box Chi-Squared test result. The SANN model performed better than the SARIMA and ARIMA models as it had a Mean Squared Error value of 0.004 while SARIMA and ARIMA had mean squared errors of 0.527 and 0.705 respectively. It was concluded that the SANN which is a non-linear model be used in modelling the quarterly GDP of Nigeria. Hybrid models which combine the strength of individual models are recommended for further research.

Demystifying “drop-outs” in single cell UMI data

Analysis of scRNA-seq data has been challenging particularly because of excessive zeros observed in UMI counts. Prevalent opinions are that many of the detected zeros are “drop-outs” that occur during experiments and that those zeros should be accounted for through procedures such as normalization, variance stabilization, and imputation. Here, we extensively analyze publicly available UMI datasets and challenge the existing scRNA-seq workflows. Our results strongly suggest that resolving cell-type heterogeneity should be the foremost step of the scRNA-seq analysis pipeline because once cell-type heterogeneity is resolved, “drop-outs” disappear. Additionally, we show that the simplest parametric count model, Poisson, is sufficient to fully leverage the biological information contained in the UMI data, thus offering a more optimistic view of the data analysis. However, if the cell-type heterogeneity is not appropriately taken into account, pre-processing such as normalization or imputation becomes inappropriate and can introduce unwanted noise. Inspired by these analyses, we propose a zero inflation test that can select gene features contributing to cell-type heterogeneity. We integrate feature selection and clustering into iterative pre-processing in our novel, efficient, and straightforward framework for UMI analysis, HIPPO (Heterogeneity Inspired Pre-Processing tOol). HIPPO leads to downstream analysis with much better interpretability than alternatives in our comparative studies.

Data transformations for statistical assessment of quantitative imaging biomarkers: Application to lung nodule volumetry

Variance stabilization is an important step in the statistical assessment of quantitative imaging biomarkers. The objective of this study is to compare the Log and the Box–Cox transformations for variance stabilization in the context of assessing the performance of a particular quantitative imaging biomarker, the estimation of lung nodule volume from computed tomography images. First, a model is developed to generate and characterize repeated measurements typically observed in computed tomography lung nodule volume estimation. Given this model, we derive the parameter of the Box–Cox transformation that stabilizes the variance of the measurements across lung nodule volumes. Second, simulated, phantom, and clinical datasets are used to compare the Log and the Box–Cox transformations. Two metrics are used for quantifying the stability of the measurements across the transformed lung nodule volumes: the coefficient of variation for the standard deviation and the repeatability coefficient. The results for simulated, phantom, and clinical datasets show that the Box–Cox transformation generally had better variance stabilization performance compared to the Log transformation for lung nodule volume estimates from computed tomography scans.

VSS: Variance-stabilized signals for sequencing-based genomic signals

MotivationA sequencing-based genomic assay such as ChIP-seq outputs a real-valued signal for each position in the genome that measures the strength of activity at that position. Most genomic signals lack the property of variance stabilization. That is, a difference between 100 and 200 reads usually has a very different statistical importance from a difference between 1,100 and 1,200 reads. A statistical model such as a negative binomial distribution can account for this pattern, but learning these models is computationally challenging. Therefore, many applications—including imputation and segmentation and genome annotation (SAGA)—instead use Gaussian models and use a transformation such as log or inverse hyperbolic sine (asinh) to stabilize variance.ResultsWe show here that existing transformations do not fully stabilize variance in genomic data sets. To solve this issue, we propose VSS, a method that produces variance-stabilized signals for sequencingbased genomic signals. VSS learns the empirical relationship between the mean and variance of a given signal data set and produces transformed signals that normalize for this dependence. We show that VSS successfully stabilizes variance and that doing so improves downstream applications such as SAGA. VSS will eliminate the need for downstream methods to implement complex mean-variance relationship models, and will enable genomic signals to be easily understood by [email protected]://github.com/faezeh-bayat/Variance-stabilized-units-for-sequencing-based-genomic-signals.