Prior-predictive value from fast-growth simulations: error analysis and bias estimation.

This paper presents an innovative in-field coarse bias estimation (CBE) method for stationary intermediate-grade inertial measurement units (IMUs), which is based on the existence of normality and orthogonality errors in the attitude matrix supplied by the traditional three-axis attitude determination stationary coarse alignment (CA) stage. Differently from the currently existing in-field bias estimation formulations, the proposed CBE method is conceived to be conducted in stationary conditions, jointly with the CA, and it allows the down accelerometer bias and the north and down angular rate sensor biases to be adequately estimated. As a main contribution of this paper, we demonstrate that the proposed CBE method is able to greatly accelerate the estimation process of the aforementioned biases, contributing, hence, to shorten the IMU setup time. A comprehensive error analysis is presented, and the conclusions are twofold: 1) the proposed CBE method is valid regardless of the IMU orientation and 2) its estimation accuracy is mainly constrained by the north accelerometer bias and the position location uncertainty, which are, in general, very reduced. Results from simulated and experimental test confirm the adequacy of the outlined verifications, also attesting the superiority of the proposed CBE method in situations where, due to time constraints, stationary fine alignment procedures are not allowed to be carried out.

Bayesian data analysis (BDA) is today used by a multitude of research disciplines. These disciplines use BDA as a way to embrace uncertainty by using multilevel models and making use of all available information at hand. In this chapter, we first introduce the reader to BDA and then provide an example from empirical software engineering, where we also deal with a common issue in our field, i.e., missing data. The example we make use of presents the steps done when conducting state-of-the-art statistical analysis. First, we need to understand the problem we want to solve. Second, we conduct causal analysis. Third, we analyze non-identifiability. Fourth, we conduct missing data analysis. Finally, we do a sensitivity analysis of priors. All this before we design our statistical model. Once we have a model, we present several diagnostics one can use to conduct sanity checks. We hope that through these examples, the reader will see the advantages of using BDA. This way, we hope Bayesian statistics will become more prevalent in our field, thus partly avoiding the reproducibility crisis we have seen in other disciplines.

"Zero waste" is the eternal pursuit of goals of global manufacturing. But the 2D error analysis has not yet comprehensive and accurate analysis and prediction of product quality information. Comprehensive 3D error analysis and judgments can be obtained through the high-precision 3D data acquisition on part and standard error of alignment for 3D data. According to the error information, the deformation of the part can be measured, traced and predicted, thus to reduce waste generation. 3D error analysis and deformation prediction system is proposed in this article, it has higher reliability and a certain role for the correct evaluation of processing conditions and comprehensive understanding of the process of evaluating the whole production process.

Bayesian Data Analysis (BDA) offers a consistent framework for integrating prior knowledge with empirical data, which is particularly beneficial in fields with complex datasets or substantial prior information, such as management and organizational sciences. This paper presents a comprehensive literature review assessing the adoption and implications of BDA in this domain from 2001 to 2022. The review provides the first comprehensive examination of how BDA is applied in these fields, with a special focus on the clarity of these applications, including the specification and disclosure of prior distributions. A critical finding from the review is the widespread shortfall in transparency, particularly in the justification and reporting of prior distributions. Notably, the analysis shows that a substantial 33\% of the reviewed papers fail to adequately disclose their prior distributions. These issues could undermine the reliability of research findings and hinder the broader adoption of Bayesian methods. To address these challenges, researchers, reviewers, and editors should adopt and promote standardized reporting guidelines for BDA in organizational research, aiming to improve the reproducibility and trustworthiness of the results.

Land surface temperature retrieval from MSG1-SEVIRI data

Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics have traditionally dominated empirical data analysis, and certainly remain prevalent in empirical software engineering. This situation is unfortunate because frequentist statistics suffer from a number of shortcomings---such as lack of flexibility and results that are unintuitive and hard to interpret---that curtail their effectiveness when dealing with the heterogeneous data that is increasingly available for empirical analysis of software engineering practice. In this paper, we pinpoint these shortcomings, and present Bayesian data analysis techniques that provide tangible benefits---as they can provide clearer results that are simultaneously robust and nuanced. After a short, high-level introduction to the basic tools of Bayesian statistics, we present the reanalysis of two empirical studies on the effectiveness of automatically generated tests and the performance of programming languages. By contrasting the original frequentist analyses with our new Bayesian analyses, we demonstrate the concrete advantages of the latter. To conclude we advocate a more prominent role for Bayesian statistical techniques in empirical software engineering research and practice.

Doing Bayesian data analysis in the classroom: An experience based review of John K. Kruschke’s “Doing Bayesian Data Analysis: A Tutorial with R and BUGS”2011

BackgroundTau aggregates in Alzheimer’s disease (AD) induce loss of synapses and neurons, leading to cognitive impairment. Predicting tau and neurodegeneration temporal evolution could be used for prognostication and for assessing results of therapeutic trials. Tau PET and MRI volumetry are reliable markers of disease stage, but cost and radiation protection considerations limit research measurement frequency, lowering the accuracy of disease progression modeling. Here, we evaluate, using Bayesian analysis, whether models based on limited numbers of observations can be refined to better predict the temporal trajectory of pathology.MethodImaging data comes from subjects (113; 68 females; 18 AD dementia, 23 MCI and 72 cognitively normal) of the TRIAD cohort (McGill University) who have been evaluated at least twice ( 1 year interval) with both tau PET ([18F]MK‐6240) and structural MRI. Four probability models were evaluated: 1‐ a basic one, assuming that all data points come from 1 data distribution; 2‐ one where subjects' observations are clustered within anatomical ROIs, where an independent distribution is hypothesized; 3‐ data is clustered within known physiological networks, each networks’ distribution parameters having their own specific values ; 4‐ a model assuming that subjects’ observations are described by a distribution of voxel parameters dictated by both the ROI and network(s) in which they lay. Bayesian data analysis was used to compare the predictive accuracy of those models for progression at 1 year from baseline of tau PET and MRI data.ResultModel 4 was the most accurate model for both tau and cortical thickness prediction. We therefore used it to perform posterior predictions across hemispheres, showing that the prediction curves of the left and right hemispheres for the pericalcarine cortex differ. We also noticed a decreasing trend in the CN tau curve for the left hemisphere as the rate of cortical thinning increases. In contrast, there is an increasing trend in the AD tau curve as the rate of cortical thinning increases.ConclusionThe model that incorporated both ROI‐level and network‐level information was the best predictor of progression, and such an approach can reveal underappreciated properties of the disease (i.e., laterality).

One of the first things one learns in a basic psychology or statistics course is that you cannot prove the null hypothesis that there is no difference between two conditions such as a patient group and a normal control group. This remains true. However now, thanks to ongoing progress by a special group of devoted methodologists, even when the result of an inferential test is p > .05, it is now possible to rigorously and quantitatively conclude that (a) the null hypothesis is actually unlikely, and (b) that the alternative hypothesis of an actual difference between treatment and control is more probable than the null. Alternatively, it is also possible to conclude quantitatively that the null hypothesis is much more likely than the alternative. Without Bayesian statistics, we couldn't say anything if a simple inferential analysis like a t-test yielded p > .05. The present, mostly non-quantitative article describes free resources and illustrative procedures for doing Bayesian analysis, with t-test and ANOVA examples.

Context. Manual unit test creation is a cognitively intensive and time-consuming activity, prompting researchers and practitioners to increasingly adopt automated testing tools. Recent advancements in language models have expanded automation possibilities, including unit test generation, yet these models raise substantial sustainability concerns due to their energy consumption compared to conventional, specialized tools. Goal. Our research investigates whether the energy overhead associated with employing a small language model (SLM) for unit test generation is justified compared to a conventional, lightweight testing tool. We compare and analyze the energy consumption incurred during test suite generation, as well as the fault-finding effectiveness of the resulting test suites, for an SLM (Phi-3.1 Mini 128k) and Pynguin, a purpose-built tool for unit test generation. Method.We posed two research questions: (i) What is the difference in energy usage between Phi and Pynguin during the generation of unit test suites for Python programs?; and (ii) To what extent do unit test suites generated by Phi and Pynguin differ in their fault-finding effectiveness? To rigorously address the first research question, we employed Bayesian Data Analysis (BDA). For the second research question, we conducted a complementary empirical analysis using descriptive statistics. Results. Our Bayesian analysis provides robust evidence indicating that Phi consistently consumes significantly more energy than Pynguin during test suite generation. Conclusions. These findings underscore significant sustainability concerns associated with employing even SLMs for routine Software Engineering tasks such as unit test generation. The results challenge the assumption of universal energy efficiency benefits from smaller-scale models and emphasize the necessity for careful energy consumption evaluations in the adoption of automated software testing approaches.

We analyze the convergence rate of a simplified version of a popular Gibbs sampling method used for statistical discovery of gene regulatory binding motifs in DNA sequences. This sampler satisfies a very strong form of ergodicity (uniform). However, we show that, due to multimodality of the posterior distribution, the rate of convergence often decreases exponentially as a function of the length of the DNA sequence. Specifically, we show that this occurs whenever there is more than one true repeating pattern in the data. In practice there are typically multiple such patterns in biological data, the goal being to detect the most well-conserved and frequently-occurring of these. Our findings match empirical results, in which the motif-discovery Gibbs sampler has exhibited such poor convergence that it is used only for finding modes of the posterior distribution (candidate motifs) rather than for obtaining samples from that distribution. Ours are some of the first meaningful bounds on the convergence rate of a Markov chain method for sampling from a multimodal posterior distribution, as a function of statistical quantities like the number of observations.

Comprehensive error analysis of ultra-wideband direct conversion receivers

Optimal power flow solution via noise-resilient quantum interior-point methods

Bayesian model checking, comparison and selection with emphasis on outlier detection for geotechnical reliability-based design

We present a second‐order ensemble method based on a blended three‐step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier–Stokes equations. Compared with the only existing second‐order ensemble method that combines the two‐step BDF timestepping scheme and a special explicit second‐order Adams–Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 34–61, 2017