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Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical function T(r) with its simulated counterparts from the null model. However, the type I error probability α is conventionally controlled for a fixed distance r only, whereas the functions are inspected on an interval of distances I. In this study, we propose two approaches related to Barnard's Monte Carlo test for building global envelope tests on l: ordering the empirical and simulated functions on the basis of their r-wise ranks among each other, and the construction of envelopes for a deviation test. These new tests allow the a priori choice of the global and they yield p-values. We illustrate these tests by using simulated and real point pattern data.

We propose a family of tests to assess the goodness of fit of a high dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and interaction effects, or for testing the significance of groups of variables. The methodology is based on extracting left-over signal in the residuals from an initial fit of a generalized linear model. This can be achieved by predicting this signal from the residuals by using modern powerful regression or machine learning methods such as random forests or boosted trees. Under the null hypothesis that the generalized linear model is correct, no signal is left in the residuals and our test statistic has a Gaussian limiting distribution, translating to asymptotic control of type I error. Under a local alternative, we establish a guarantee on the power of the test.We illustrate the effectiveness of the methodology on simulated and real data examples by testing goodness of fit in logistic regression models. Software implementing the methodology is available in the R package GRPtests.

Checking that models adequately represent data is an essential component of applied statistical inference. Ecologists increasingly use hierarchical Bayesian statistical models in their research. The appeal of this modeling paradigm is undeniable, as researchers can build and fit models that embody complex ecological processes while simultaneously accounting for observation error. However, ecologists tend to be less focused on checking model assumptions and assessing potential lack of fit when applying Bayesian methods than when applying more traditional modes of inference such as maximum likelihood. There are also multiple ways of assessing the fit of Bayesian models, each of which has strengths and weaknesses. For instance, Bayesian P values are relatively easy to compute, but are well known to be conservative, producing P values biased toward 0.5. Alternatively, lesser known approaches to model checking, such as prior predictive checks, cross-validation probability integral transforms, and pivot discrepancy measures may produce more accurate characterizations of goodness-of-fit but are not as well known to ecologists. In addition, a suite of visual and targeted diagnostics can be used to examine violations of different model assumptions and lack of fit at different levels of the modeling hierarchy, and to check for residual temporal or spatial autocorrelation. In this review, we synthesize existing literature to guide ecologists through the many available options for Bayesian model checking. We illustrate methods and procedures with several ecological case studies including (1) analysis of simulated spatiotemporal count data, (2) N-mixture models for estimating abundance of sea otters from an aircraft, and (3) hidden Markov modeling to describe attendance patterns of California sea lion mothers on a rookery. We find that commonly used procedures based on posterior predictive P values detect extreme model inadequacy, but often do not detect more subtle cases of lack of fit. Tests based on cross-validation and pivot discrepancy measures (including the \"sampled predictive P value\") appear to be better suited to model checking and to have better overall statistical performance. We conclude that model checking is necessary to ensure that scientific inference is well founded. As an essential component of scientific discovery, it should accompany most Bayesian analyses presented in the literature.

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA’s tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.

The study of pneumatic muscles requires investigating the phenomenon where a balloon enclosed within a braided mesh expands and shortens upon inflation. Based on the working principle of pneumatic muscles, this paper establishes a mathematical model of its axial cross-section and reasonably approximates the pneumatic muscle as a “spring-damper” model. Thermodynamic analysis demonstrates that the interior of the rubber balloon can be considered isothermal during motion, and a relationship between the shortened axial length of the balloon and its internal pressure is derived. In the experimental section, the control variable method is employed to explore the relationship between the axial length of the mesh and the internal pressure of the balloon by varying the initial length of the mesh, the material of the mesh, and the load attached to the pneumatic muscle. The experimental results show a high consistency between theory and practice, with an average goodness-of-fit of approximately 0.93.

Purpose This study aims to examine the role of an overall model fit assessment in the context of partial least squares path modeling (PLS-PM). In doing so, it will explain when it is important to assess the overall model fit and provides ways of assessing the fit of composite models. Moreover, it will resolve major concerns about model fit assessment that have been raised in the literature on PLS-PM. Design/methodology/approach This paper explains when and how to assess the fit of PLS path models. Furthermore, it discusses the concerns raised in the PLS-PM literature about the overall model fit assessment and provides concise guidelines on assessing the overall fit of composite models. Findings This study explains that the model fit assessment is as important for composite models as it is for common factor models. To assess the overall fit of composite models, researchers can use a statistical test and several fit indices known through structural equation modeling (SEM) with latent variables. Research limitations/implications Researchers who use PLS-PM to assess composite models that aim to understand the mechanism of an underlying population and draw statistical inferences should take the concept of the overall model fit seriously. Practical implications To facilitate the overall fit assessment of composite models, this study presents a two-step procedure adopted from the literature on SEM with latent variables. Originality/value This paper clarifies that the necessity to assess model fit is not a question of which estimator will be used (PLS-PM, maximum likelihood, etc). but of the purpose of statistical modeling. Whereas, the model fit assessment is paramount in explanatory modeling, it is not imperative in predictive modeling.

1. Information criteria (ICs) are used widely for data summary and model building in ecology, especially in applied ecology and wildlife management. Although ICs are useful for distinguishing among rival candidate models, ICs do not necessarily indicate whether the \"best\" model (or a model-averaged version) is a good representation of the data or whether the model has useful \"explanatory\" or \"predictive\" ability. 2. As editors and reviewers, we have seen many submissions that did not evaluate whether the nominal \"best\" model(s) found using IC is a useful model in the above sense. 3. We scrutinized six leading ecological journals for papers that used IC to models. More than half of papers using IC for model comparison did not evaluate the adequacy of the best model(s) in either \"explaining\" or \"prdicting\" the data. 4. Synthesis and applications. Authors need to evaluate the adequacy of the model identified as the \"best\" model by using information criteria methods to provide convincing evidence to readers and users that inferences from the best models are useful and reliable.

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Hölder density with exponent 0 < s ≤ 1, with possibly unbounded support, in the low-smoothness regime where the Hölder parameter is not assumed to be constant. In contrast to existing results, we show that the minimax rate and critical testing radius in these settings depend strongly, and in a precise way, on the null distribution being tested and this motivates the study of the (local) minimax rate as a function of the null distribution. For multinomials, the local minimax rate has been established in recent work. We revisit and extend these results and develop two modifications to the χ²-test whose performance we characterize. For testing Hölder densities, we show that the usual binning tests are inadequate in the low-smoothness regime and we design a spatially adaptive partitioning scheme that forms the basis for our locally minimax optimal tests. Furthermore, we provide the first local minimax lower bounds for this problem which yield a sharp characterization of the dependence of the critical radius on the null hypothesis being tested. In the low-smoothness regime, we also provide adaptive tests that adapt to the unknown smoothness parameter. We illustrate our results with a variety of simulations that demonstrate the practical utility of our proposed tests.

In section 1 of this paper, I consider the logical validity of four versions of Aquinas’ arguments to this conclusion that being and good are identical, as presented by Stump and Kretzmann. Subsequently, I formalize the arguments in order to make their validity logically explicit. In section 2, I show how the formal reality of the identity of being grounds moral arguments for theism. In section 3, I then consider the application of this formal reality, to a simplified contemporary “moral argument” for theism. I argue that Aquinas’ arguments for the identity of being and goodness should play a vital role in moral arguments for theism to militate against atheistic objections to them.

Time series analysis has gained popularity in forest disturbance monitoring thanks to the availability of satellite and airborne remote sensing images and the development of different time series methods for change detection. Previous research has focused on time series data noise reduction, the magnitude of breakpoints, and accuracy assessment; however, few have looked in detail at how the trend and seasonal model components contribute to disturbance detection in different forest types. Here, we use Landsat time series images spanning 1994–2018 to map forest disturbance in a western Pacific area of Mexico, where both temperate and tropical dry forests have been subject to severe deforestation and forest degradation processes. Since these two forest types have distinct seasonal characteristics, we investigate how trend and seasonal model components, such as the goodness-of-fit (R2), magnitude of change, amplitude, and model length in a stable historical period, affect forest disturbance detection. We applied the Breaks For Additive Season and Trend Monitor (BFAST) algorithm and after accuracy assessment by stratified random sample points, and we obtained 68% and 86% of user accuracy and 75.6% and 86% of producer’s accuracy in disturbance detection, in tropical dry forests and temperate forests, respectively. We extracted the noncorrelated trend and seasonal model components R2, magnitude, amplitude, length of the stable historical period, and percentage of pixels with NA and tested their effects on disturbance detection employing forest-type specific logistic regression. Our results showed that, for all forests combined, the amplitude and stable historical period length contributed to disturbance detection. While for tropical dry forest alone, amplitude was the main predictor, and for the temperate forest alone, the stable historical period length contributed most to the prediction, although it was not statistically significant. These findings provide insights for improving the results of forest disturbance detection in different forest types.