Data_Sheet_1.docx

The Einstein Telescope is a third-generation gravitational wave detector which is expected to be an order of magnitude more sensitive than the current detectors. While the current detectors enabled various measurements which were first of their kind (such as the strong field test of general relativity, an independent measurement of the Hubble constant, probing the dense nuclear matter inside the neutron stars, and many more), the proposed third-generation detectors may not only bring about unprecedented accuracy and precision to these measurements but also enable new first-of-their-kind measurements which may be outside the reach of current detectors (the detection of primordial black holes or phase transitions in the neutron star matter, for example). While the improvement in the sensitivity is desirable, it also makes it more difficult to extract physics-related insights from data. Of particular concern are transient, instrumental noise sources (also known as glitches) overlapping with the gravitational wave signal(s). For the third-generation detectors, we expect many more glitches to overlap with the signals compared to the current scenario, making it crucial to develop a methodology which can reliably “de-glitch” the data without corrupting the underlying signal. To address this challenge, we develop a novel framework which can accurately remove glitches overlapping with gravitational wave signals. The framework is unique to the triangular geometry of the Einstein Telescope, i.e., it cannot be realised for other proposed geometries such as the two distant, mis-aligned L-shaped detectors. Exploiting the triangular geometry, our framework outperforms the traditional methodology of de-glitching the signals used for L-shaped detector networks, showcasing a clear edge of the triangle geometry over the geometries. In this context, our work stands to play an important role in the design studies related to the Einstein Telescope, underway at the time of writing of this thesis. Bayesian parameter inference plays a key role in the measurements of the source parameters (such as masses, spins, sky-location, and distance) of a gravitational wave signal. Increasing costs of Bayesian parameter inference is another challenge posed by the improved sensitivity of the detectors. To address this challenge, we develop a relative-binning based framework to reduce the cost of Bayesian inferences. We benchmark our methodology on a large number of real as well as simulated signals for the current and next generation detectors. We also test the validity of our rapid inference framework on overlapping signals and lensed gravitational wave signals. In addition, we perform simulation to demonstrate how gravitational lensing can help constrain gravitational wave propagation beyond general relativity.

Hypothesis tests

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage of the TRV approach is that it can be easily extended to a multiple step‐stress model as well as for different lifetime distributions. In this paper, it is assumed that the lifetime of the experimental units at each stress level follows Weibull distribution with the same shape parameter and different scale parameters. Further, we have introduced different tempering co‐efficient for different causes of failures. The maximum likelihood estimators and the associated asymptotic confidence intervals are obtained based on Type‐II censored observations. Further, we have considered the Bayesian inference of the unknown model parameters based on a fairly general class prior distributions. An extensive simulation study is performed to examine the performances of the proposed method, and the analysis of a real data set has been provided to show how the method can be used in practice. We have compared the TRV model with some of the other existing models, and the TRV model provides a better fit in terms of information theoretic criteria. We have also provided some optimality criteria, to determine the optimal stress change time and some sensitivity analyses have been performed. Most of the methods can be extended for other lifetime distributions also.

Quiescent solar prominence fine structures are typically modelled as density enhancements, called threads, which occupy a fraction of a longer magnetic flux tube. The profile of the mass density along the magnetic field is however unknown and several arbitrary alternatives are employed in prominence wave studies. We present a comparison of theoretical models for the field-aligned density along prominence fine structures. We consider Lorentzian, Gaussian, and parabolic profiles. We compare their theoretical predictions for the period ratio between the fundamental transverse kink mode and the first overtone to obtain estimates for the ratio of densities between the central part of the tube and its foot-points and to assess which one would better explain observed period ratio data. Bayesian parameter inference and model comparison techniques are developed and applied. Parameter inference requires the computation of the posterior distribution for the density gradient parameter conditional on the observable period ratio. Model comparison involves the computation of the marginal likelihood as a function of the period ratio to obtain the plausibility of each density model and the computation of Bayes Factors to quantify the relative evidence for each model, given a period ratio observation. A Lorentzian density profile, with plasma density concentrated around the centre of the tube seems to offer the most plausible inversion result. A Gaussian profile would require unrealistically large values of the density gradient parameter and a parabolic density distribution does not enable us to obtain well constrained posterior probability distributions. However, our model comparison results indicate that the evidence points to the Gaussian and parabolic profiles for period ratios in between 2 and 3, while the Lorentzian profile is preferred for larger period ratio values.

Analyses of satellite‐derived chlorophyll data indicate that the phase of rapid phytoplankton population growth in the North Atlantic (the “spring bloom”) is actually initiated in the winter rather than the spring, contradicting Sverdrup's critical depth hypothesis. An alternative disturbance‐recovery hypothesis (DRH) has been proposed to explain this discrepancy, in which the rapid deepening of the mixed layer reduces zooplankton grazing rates sufficiently to initiate the bloom. We use Bayesian parameter inference on a simple Nutrient‐Phytoplankton‐Zooplankton (NPZ) model to investigate the DRH and also investigate how well the model can capture the multiyear and spatial dynamics of phytoplankton concentrations and population growth rates. Every parameter in our NPZ model was inferred as a probability distribution given empirical constraints, which provides a more objective method to identify a model parameterization given available empirical evidence, rather than fixing or tuning individual parameter values. Our model explains around 75% of variation in the seasonal dynamics of phytoplankton concentrations, 30% of variation in their population rates of change, and correctly predicts the phases of population growth and decline. Our parameter‐inferred model supports the DRH, revealing the sustained reduction of grazing due to mixed‐layer deepening as the driving mechanism behind bloom initiation, with the relaxation of nutrient limitation being another contributory mechanism. Our results also show that the continuation of the bloom is caused in part by the maintenance of phytoplankton concentrations below a level that can support positive zooplankton population growth. Our approach could be employed to formally assess alternative hypotheses for bloom formation.

Although forecasts of future events are simply uncertain, predicting is one of the most important aspects of future planning. Accurate rice price predictions tend to be helpful for wholesalers, producers, and farmers to develop plans and strategies to reduce the risks that can be faced. Structural time series models are the most plausible alternative for long-term forecasting. This paper proposes an alternate method for modeling average rice prices using structural time series along with Bayesian parameter inference via Hamiltonian Monte Carlo (HMC). The model has been built using the monthly average wholesale rice price from January 2010 to December 2019. For working out both structural time series and HMC, the TensorFlow Probability Library was used. Linear trend, seasonal, and autoregressive components were combined as an additive model to the structural time model. The proposed Hamiltonian parameter produces an optimal acceptance rate. Their trace plot was used to diagnose the convergence of their chain. One of the predictive accuracy of models was assessed using the mean absolute percent error (MAPE). Through both single and multiple chain iterations, the prediction accuracy of a year-ahead is highly accurate, with MAPE less than 2%. Long-term iteration draws during Hamiltonian Monte Carlo should be considered when attempting to achieve more convergence.

An offline methodology is applied to estimate parameters of a subgrid-scale non-orographic gravity-wave scheme using observations from constant-level balloons. The approach integrates the Ensemble Kalman Filter (EnKF) with an iterative parameter estimation method based on the expectationmaximization (EM) algorithm. The meteorological fields required for the parameterization offline are taken from the ERA5 reanalysis, corresponding to the instantaneous meteorological conditions found underneath the Strateole-2 balloon observations made in the lower tropical stratosphere from November 2019 to February 2021 and October 2021 to January 2022. Compared to a direct approach that minimizes a cost function and uses Bayesian inference of parameters, our analysis demonstrates that the EnKF/EM method effectively characterizes the launching amplitudes and altitudes of the parameterized gravity waves and while quantifying their associated uncertainties. Furthermore, we illustrate how the method can help improving a scheme, specifically the results indicate that introducing a background wave activity renders the convective wave parameterization more realistic.

Geodetic data covering different phases of the earthquake cycle provide a great opportunity to improve our understanding of the processes and parameters governing the dynamics at subduction margins. However, quantifying the individual contributions of physical processes such as viscoelastic relaxation, afterslip, and (re)locking throughout the earthquake cycle remains challenging. Moreover, it is relevant to account for these processes within a rheological framework that is consistent over the entire earthquake cycle. We address this using Bayesian inference in the form of an ensemble smoother, a Monte Carlo approach that represents the probability density distribution of model states with a finite number of realizations, to estimate geodynamic model parameters. Prior estimates of the imperfect physical model are combined with the likelihood of noisy observations to estimate the posterior probability density distribution of model parameters.   We construct a 2D finite element seismic cycle model with a power-law rheology in the mantle. A priori information, such as a realistic temperature field and a coseismic slip distribution, is integrated into the model. Model pre-stresses are initialized during repeated earthquake cycles wherein the accumulated slip deficit is released entirely. We tailor the last earthquake to match the observed co-seismic slip of the 2011 Tohoku earthquake. The heterogeneous rheology structure is derived from the temperature field and experimental flow laws. Additionally, we simulate afterslip using a thin, low-viscosity shear zone with a Newtonian rheology. We focus on constraining power-law flow parameters for the mantle, and the shear zone viscosity.   We assimilate 3D GEONET GNSS displacement time series acquired before and after the 2011 Tohoku earthquake. The data require separate viscoelastic domains in the mantle wedge above and below ~50 km depth, and in the sub-slab mantle. Power-law viscosity parameters are successfully retrieved for all three domains. The trade-off between the power-law activation energy and water fugacity hinders their individual estimation. The wedge viscosity is >1019 Pa·s during the interseismic phase. Postseismic afterslip and bulk viscoelastic relaxation can be individually resolved from the surface deformation data. Afterslip is substantial between 40-50 km depth and extends to 80 km depth. Bulk viscoelastic relaxation in the wedge concentrates above 150 km depth with viscosities <1018 Pa·s. Landward motion of the near-trench region occurs during the early postseismic period without the need for a separate low-viscosity channel below the slab.

ABSTRACTA step-stress model has received a considerable amount of attention in recent years. In the usual step-stress experiment, a stress level is allowed to increase at each step to get rapid failure of the experimental units. The expected lifetime of the experimental unit is shortened as the stress level increases. Although extensive amount of work has been done on step-stress models, not enough attention has been paid to analyze step-stress models incorporating this information. We consider a simple step-stress model and provide Bayesian inference of the unknown parameters under cumulative exposure model assumption. It is assumed that the lifetime of the experimental units are exponentially distributed with different scale parameters at different stress levels. It is further assumed that the stress level increases at each step, hence the expected lifetime decreases. We try to incorporate this restriction using the prior assumptions. It is observed that different censoring schemes can be incorporated very easily under a general setup. Monte Carlo simulations have been performed to see the effectiveness of the proposed method, and two datasets have been analyzed for illustrative purposes.

A recent article in this journal by Tabak (2006) highlighted a potentially serious source of bias that can arise when multiple statistical tests of a damages theory are performed and even one test rejecting the null hypothesis is regarded as supporting the damages theory. Repeated testing will eventually produce a “false discovery,” that is, rejection of the null hypothesis in favor of the alternative hypothesis when the null hypothesis is true, which statisticians refer to as type I error. Consequently, performing multiple tests without adjusting the critical value can be problematical because it can lead to improperly accepting statistical evidence that apparently supports rejection of the null hypothesis as reliable when it is not. Tabak (2006) recommends making the Sidak (1968, 1971) multiple-comparison adjustment to the standard statistical t-test to correct for the false-discovery bias inherent in multiple-comparison testing. In particular, he recommends making this adjustment when performing 10b-5 securities fraud event studies when more than one corrective disclosure date is involved. This article clarifies the circumstances in which a multiple-comparison adjustment is appropriate and explains why the correction is normally not needed in securities fraud event-study testing. More generally, I explain why it is not required when each of several tests is performed and its results are reported separately, as for example, where the objective is simply to test the statistical significance of the abnormal stock return on each day on which a new and distinct curative disclosure occurred. I show that the Sidak multiple-comparison adjustment is nearly as stringent as the classical Bonferroni procedure (Simes, 1986), which can increase the risk of type II error. This article discusses a more powerful alternative to the Sidak adjustment due to Benjamini and Hochberg (1993), which directly corrects for the false-discovery bias in multiple-comparison testing and reduces the risk of type II error. II. Application of Multiple-Comparison Adjustments to Securities Fraud Event Studies Multiple-comparison-false-discovery bias can arise when (a) several statistical tests are performed on subsets of the same larger data set in an effort to

Genetically modified (GM) corn hybrids have been recently compared against their isogenic reference counterparts in order to establish proof of safety as feedstuffs for dairy cattle. Most such studies have been based on the classical hypothesis test, whereby the null hypothesis is that of equivalence. Because the null hypothesis cannot be accepted, bioequivalence-testing procedures in which the alternative hypothesis is specified to be the equivalence hypothesis are proposed for these trials. Given a Type I error rate of 5%, this procedure is simply based on determining whether the 90% confidence interval on the GM vs. reference hybrid mean difference falls between two limits defining equivalence. Classical and bioequivalence power of test are determined for 4 x 4 Latin squares and double-reversal designs, the latter of which are ideally suited to bioequivalence studies. Although sufficient power likely exists for classical hypothesis testing in recent GM vs. reference hybrid studies, the same may not be true for bioequivalence testing depending on the equivalence limits chosen. The utility of observed or retrospective power to provide indirect evidence of bioequivalence is also criticized. Design and analysis issues pertain to Latin square and crossover studies in dairy nutrition studies are further reviewed. It is recommended that future studies should place greater emphasis on the use of confidence intervals relative to P-values to unify inference in both classical and bioequivalence-testing frameworks.

Theory development is essential for the generation and support of research ideas. Traditional Null Hypothesis Significance Testing (NHST) has been the modus operandi for testing research questions across many branches of science since the early 20th century. The focus of a statistical test under the NHST framework considers the rejection or acceptance of a null hypothesis based on a conditional probability of the data given that the null hypothesis is true (i.e. a p-value). This approach provides no direct support for a specific theory, which often takes the form of an alternative hypothesis. Furthermore, rejection of a null hypothesis based on a p-value provides no information on the magnitude of a difference and is affected by sample size, alpha level, and effect size. Such dependency on p-values can lead to misunderstanding and misinterpretation of results and conclusions. Therefore, the limitations of NHST warrant the investigation and development of new, more rigorous approaches to theory testing. A quantitative approach, called “Testing Theory-Based Quantitative Predictions” (TTQP), has been proposed using effect size indices and confidence intervals to directly test predictions posited by theory (Velicer et al, 2008). Effect size indices provide information regarding the magnitude and direction of an effect while confidence intervals provide a means of “testing” specific predictions. This approach is an iterative process, allowing the researcher to tailor the theory as empirical data is collected. The use of the TTQP approach contributes to the movement away from NHST and the reliance on p-values, while promoting a stronger and more informative method. A quantitative orientation represents an essential change in thinking about theory testing by emphasizing the numeric strength of a measure, leading researchers away from a simple binary accept/reject framework. Predictions are made relative to the specific measure/variable, but the use of effect sizes allows for comparison across studies and across theories. Therefore, the TTQP approach actually provides more information than traditional NHST. The TTQP approach involves several steps. First, verbal descriptions of the expected values are designated a priori. These predictions are theory-based and guided by previous empirical findings (e.g. “small effect”). Second, verbal predictions are translated into quantitative values based on traditional guidelines or empirical results (e.g. “0.01”). Then, observed effect size estimates with surrounding confidence intervals are generated from sample data. If a confidence interval contains the predicted value, the prediction is confirmed. If the predicted value falls outside of the confidence interval, the prediction is

IntroductionIn the last three decades, a critical movement occurring within quantitative psychological research began to develop. This development emerged in response to the misguided use of classical based on null hypothesis significance testing (NHST). promotes dichotomous thinking and provides limited information regarding the essence of investigated phenomena. Dichotomous thinking in science -- manifested as only accepting or rejecting research hypotheses -- prevents the advancement of science and may even skew the accumulation of knowledge by stimulating the exclusive publication of studies whose hypotheses have been accepted. The so-called new statistics movement critically challenges postulates and operations. This movement is an approach based on the analytical tool of estimation (Cummings, 2014), which promotes the use of effect size as descriptive statistic, confidence intervals as inferential statistics, and meta-analysis as a reliable form of knowledge accumulation. This paper is intended to analyze the disadvantages of and the advantages of using effect size, confidence intervals and statistical power in quantitative psychological research, especially in clinical studies. Also noted and stressed is the need for editors of scientific psychological journals to adhere to policies recommended by the A.P.A. in this regard.Quantitative research in psychologyTypically, quantitative psychological research is focused on detecting the occurrence of certain population phenomena by analyzing data from a sample. An example is the case in which a researcher wishes to know if a treatment to improve the quality of life of those who suffer from breast cancer performs better than a placebo treatment for another group or those on a waiting list (also known as the control group or contrast group) (Wilkinson, 1999). Similarly, to make the decision to confirm that an independent variable or treatment did or did not have an important effect, is used. In quantitative research methodology, there are two ways of quantifying this effect: (1) Null Hypothesis Significance Testing and (2) Effect Size (ES), as well as its respective confidence intervals (Cl). These two approaches are reviewed below.Null Hypothesis Significance Testing (NHST)NHST comes from the effect size on the population, the size of the sample used and the alpha level or that is selected (p being the abbreviation for probability). Most psychology research is focused on rejecting the null hypothesis and obtaining a small instead of observing the relevance of the results that are obtained (Kirk, 2001).Among the limitations of NHST, we found its sensitivity to sample size, its inability to accept the null hypothesis, and its lack of capacity to determine the practical significance of the statistical results.Kirk (2001) states that only establishes the probability of obtaining a more or less extreme effect if the null hypothesis is true. It does not, however, communicate the magnitude of the effect or its practical significance, meaning whether the effect is found to be useful or important. As a result, inferential statistical testing has been criticized; as expressed by Ivarsson, Andersen, Johnson, and Lindwall (2013): p levels may have little, if anything, to do with real-world meaning and practical value (p.97). Some authors, such as Schmidt (1996), even suggest that statistical contrast is unnecessary and recommend focusing only on ES estimation, and Cohen (1994) suggests that NHST has not only failed to support the advance of psychology as a science but also has seriously impeded it. (p. 997).Ronald Fisher was the father of modern and experimental design. Since his time, it has been established as a convention that the for statistical significance must be less than .05, which means that an observed difference between two groups has less than a 5% probability of occurring by chance or sampling error if the null hypothesis is assumed to be true initially. …

BackgroundBayesian phylogenetic inference holds promise as an alternative to maximum likelihood, particularly for large molecular-sequence data sets. We have investigated the performance of Bayesian inference with empirical and simulated protein-sequence data under conditions of relative branch-length differences and model violation.ResultsWith empirical protein-sequence data, Bayesian posterior probabilities provide more-generous estimates of subtree reliability than does the nonparametric bootstrap combined with maximum likelihood inference, reaching 100% posterior probability at bootstrap proportions around 80%. With simulated 7-taxon protein-sequence datasets, Bayesian posterior probabilities are somewhat more generous than bootstrap proportions, but do not saturate. Compared with likelihood, Bayesian phylogenetic inference can be as or more robust to relative branch-length differences for datasets of this size, particularly when among-sites rate variation is modeled using a gamma distribution. When the (known) correct model was used to infer trees, Bayesian inference recovered the (known) correct tree in 100% of instances in which one or two branches were up to 20-fold longer than the others. At ratios more extreme than 20-fold, topological accuracy of reconstruction degraded only slowly when only one branch was of relatively greater length, but more rapidly when there were two such branches. Under an incorrect model of sequence change, inaccurate trees were sometimes observed at less extreme branch-length ratios, and (particularly for trees with single long branches) such trees tended to be more inaccurate. The effect of model violation on accuracy of reconstruction for trees with two long branches was more variable, but gamma-corrected Bayesian inference nonetheless yielded more-accurate trees than did either maximum likelihood or uncorrected Bayesian inference across the range of conditions we examined. Assuming an exponential Bayesian prior on branch lengths did not improve, and under certain extreme conditions significantly diminished, performance. The two topology-comparison metrics we employed, edit distance and Robinson-Foulds symmetric distance, yielded different but highly complementary measures of performance.ConclusionsOur results demonstrate that Bayesian inference can be relatively robust against biologically reasonable levels of relative branch-length differences and model violation, and thus may provide a promising alternative to maximum likelihood for inference of phylogenetic trees from protein-sequence data.

Nonsignificant p values derived from null hypothesis significance testing do not distinguish between true null effects or cases where the data are insensitive in distinguishing the hypotheses. This study aimed to investigate the prevalence of Bayesian analyses in gerontological psychology, a statistical technique that can distinguish between conclusive and inconclusive nonsignificant results, by using Bayes factors (BFs) to reanalyze nonsignificant results from published gerontological research. Nonsignificant results mentioned in abstracts of articles published in 2017 volumes of 10 top gerontological psychology journals were extracted (N = 409) and categorized based on whether Bayesian analyses were conducted. BFs were calculated from nonsignificant t-tests within this sample to determine how frequently the null hypothesis was strongly supported. Nonsignificant results were directly tested with BFs in 1.22% of studies. Bayesian reanalyses of 195 nonsignificant t-tests found that only 7.69% of the findings provided strong evidence in support of the null hypothesis. Bayesian analyses are rarely used in gerontological research, and a large proportion of null findings were deemed inconclusive when reanalyzed with BFs. Researchers are encouraged to use BFs to test the validity of nonsignificant results and ensure that sufficient sample sizes are used so that the meaningfulness of null findings can be evaluated.