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Springer Series in Statistics

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Abstract

In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.

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... Calves were not included as their capture probability is not independent of their mothers (Hammond, 2010). The Akaike Information Criterion corrected for small sample size (AICc) (Akaike, 1973;Burnham and Anderson, 2002) was used for model selection, considering models within DAICc ≤ 2 as the most supported and using model averaging to account for uncertainty in model selection when more than one model had an DAICc value less than 2 (Burnham and Anderson, 2002). The estimated abundance was then divided by the mark ratio, calculated as the estimated proportion of animals with longlasting marks in the local population (Wilson et al., 1999). ...
... The effect of survey effort (amount of surveyed km) on capture probabilities was tested in both models. The Akaike Information Criterion corrected for small sample size (AICc) (Akaike, 1973;Burnham and Anderson, 2002) was used for model selection as for the closed population models. ...
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The most eastern population of common dolphins (Delphinus delphis) in the Mediterranean Sea inhabits the southern coastal waters of Israel. They are mainly observed in the shallow waters off Ashdod and Ashkelon, between the 15-30 m isobaths, with no reported observations north or west of this area. These dolphins were observed and studied year-round between 2016-2021 using boat-based surveys and photo identification methods. Common dolphins were encountered and photographed 43 times during the study period, resulting in 2,851 identifications of 25 distinctive mature individuals and 12 calves. Most individuals (62%) were sighted over multiple years, with high yearly and monthly sighting rates, indicating long-term site fidelity and residency. Closed population mark-recapture models estimated a total abundance of 25 (95% CI 24 – 37) individuals in 2016 that declined to only 15 (95% CI 15 – 15) individuals in 2021. Social network analysis described these remaining individuals as one closed and well-associated social unit. Survival probabilities for this population appeared lower than those of other delphinid populations. The decrease in their abundance, coupled with their apparent isolation level, qualifies the local population for a re-assessment of their conservation status. This study first describes the Israeli local population of common dolphins, their dynamics and an assessment of their status based on the IUCN Red List framework.
... Third, after establishing final base models, we used a stepwise procedure to simplify the base models (i.e., sequentially fit a series of a priori models with fewer parameters than the base model) to streamline the number of models fit. A more complex model (i.e., the model with greater number of parameters) was retained if the AIC of the model was > 2 AIC units lower than a simpler model, otherwise the simpler model was chosen (Akaike, 1973;Burnham and Anderson, 2002). AIC, rather than AICc or QAIC, was appropriate for our data because the ratio of observations N to parameters K in models was high for all datasets (N/K>>40, Burnham and Anderson, 2002) and our models were more complex than previously fit for these data where goodness-of-fit was judged adequate (Hastings et al., 2011;Fritz et al., 2014;Maniscalco, 2014). ...
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The North Pacific marine heatwave of 2014–2016 (PMH), one of the most geographically-extensive and severe marine heatwaves on record, resulted in widespread and persistent perturbation of the Gulf of Alaska and California Current ecosystems. Negative effects of the PMH on marine mammals have been observed, but are not yet well understood. The endangered Steller sea lion Eumetopias jubatus is an important top predator in the Gulf of Alaska that is also particularly vulnerable to sudden or severe ecosystem shifts. We examined survival of 4,178 known-aged Steller sea lions marked from 2000 to 2016 from Kodiak Island through Southeast Alaska, using mark-recapture models and 12,811 resightings collected from 2001 to 2021. Survival of adult females aged 3–15 was reduced -0.05 to -0.23 during the PMH in the areas east, but not west, of Cook Inlet. Survival of Kodiak females was unaffected by the PMH, but survival of Sugarloaf females aged 5–8 was reduced -0.13 from summer 2015 to summer 2016. Lowest survival in Southeast Alaska occurred from summer 2016 to summer 2017, but was also reduced from summer 2014 to summer 2016. Reduced survival continued post-PMH in Kenai Peninsula/Prince William Sound, but not in Southeast Alaska. Survival of adult males was insensitive to the PMH, except in Southeast Alaska where male survival was reduced -0.25 from summer 2016 to summer 2017. Prolonged or intermittent high adult female mortality may reduce population growth and initiate regional declines. Survival response of Steller sea lions to the PMH varied regionally despite similar patterns of ocean warming throughout our study area, suggesting areas east versus west of Cook Inlet were affected differently by the PMH, perhaps due to habitat and oceanographic differences.
... Significance tests on the factor loadings should ideally be significant, indicating the effective measurement of the latent variable. For model comparison, we consulted Akaike Information Criterion (Akaike, 1973) and Bayesian Information Criterion (Raftery, 1995;Schwarz, 1978), two indices that take into consideration the degree of model parsimony and complexity. A better model is indicated by a smaller Akaike information criteria or Bayesian information criteria. ...
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People can report summary statistics for various features about a group of objects. One theory is that different abilities support ensemble judgments about low-level features like color versus high-level features like identity. Existing research mostly evaluates such claims based on evidence of correlations within and between feature domains. However, correlations between two identical tasks that only differ in the type of feature that is used can be inflated by method variance. Another concern is that conclusions about high-level features are mostly based on faces. We used latent variable methods on data from 237 participants to investigate the abilities supporting low-level and high-level feature ensemble judgments. Ensemble judgment was measured with six distinct tests, each requiring judgments for a distinct low-level or high-level feature, using different task requirements. We also controlled for other general visual abilities when examining how low-level and high-level ensemble abilities relate to each other. Confirmatory factor analyses showed a perfect correlation between the two factors, suggesting a single ability. There was a unique relationship between these two factors beyond the influence of object recognition and perceptual speed. Additional results from 117 of the same participants also ruled out the role of working memory. This study provides strong evidence of a general ensemble judgment ability across a wide range of features at the latent level and characterizes its relationship to other visual abilities.
... When the number of features is small, regression models are often used as they perform well in cases where the dataset is linearly separable. The Akaike information criterion (AIC) (Akaike, 1973) and the Bayesian information criterion (BIC) (Schwarz, 1978) are statistical tools for comparative evaluation among time series models and can be used in model selection based on the relative quality of statistical models for a given set of data. ...
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There is an ever-present need to objectively measure and analyze sports motion for the determination of correct patterns of motion for skill execution. Developments in performance analysis technologies such as inertial measuring units (IMUs) have resulted in enormous data generation. However, these advances present challenges in analysis, interpretation, and transformation of data into useful information. Artificial intelligence (AI) systems can process and analyze large amounts of data quickly and efficiently through classification techniques. This study aimed to systematically review the literature on Machine Learning (ML) and Deep Learning (DL) methods applied to IMU data inputs for evaluating techniques or skills in individual swing and team sports. Electronic database searches (IEEE Xplore, PubMed, Scopus, and Google Scholar) were conducted and aligned with the PRISMA statement and guidelines. A total of 26 articles were included in the review. The Support Vector Machine (SVM) was identified as the most utilized model, as per 7 studies. A deep learning approach was reported in 6 studies, in the form of a Convolutional Neural Network (CNN) architecture. The in-depth analysis highlighted varying methodologies across all sports inclusive of device specifications, data preprocessing techniques and model performance evaluation. This review highlights that each step of the ML modeling process is iterative and should be based on the specific characteristics of the movement being analyzed.
... Models were double-checked before and after removal of nonsignificant interaction terms and minimal changes were seen in the classification table or to coefficients of main effects. We adopted the Akaike Information Criterion (Akaike, 1992) to assess the relative efficiency of each model. We used the classification table to assess the overall accuracy of the model. ...
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Demonstratives are cross-linguistically widespread deictic expressions. Demonstrative systems exhibit variation in number of terms, and parameters affecting their usage. The present paper assesses the relationship between spatial deixis and bilingualism: how language dominance affects speakers of two languages with different demonstrative systems. Here, we compare the use of demonstratives by 72 European Spanish-Catalan simultaneous bilinguals in Mallorca to 30 European Spanish monolinguals. Our results confirmed a significant effect of physical distance between speaker and referent on demonstrative choice in both languages, and differences between languages in the use of the middle term. We did not find the expected effect of language dominance in simultaneous bilinguals. Moreover, we found no influence of the hearer's position on demonstrative choice in monolinguals or bilinguals in European Spanish or Majorcan Catalan. In view of our results, the present study contributes to the debate on how bilingual speakers employ different deictic expressions.
... To account for the heterogeneity among different participants, we included the random intercept as a random effect predictor in each model. When we compared competing models of different complexity, the selection of the best statistical model was based on the Akaike information criterion (AIC 66,81 ), with the best model being the one with the smallest AIC. ...
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Spatial cognition and mobility are typically impaired in congenitally blind individuals, as vision usually calibrates space perception by providing the most accurate distal spatial cues. We have previously shown that sight restoration from congenital bilateral cataracts guides the development of more accurate space perception, even when cataract removal occurs years after birth. However, late cataract-treated individuals do not usually reach the performance levels of the typically-sighted population. Here we developed a brief multisensory training that associated audio-visual feedback with body movements. Late cataract-treated participants quickly improved their space representation and mobility, performing as well as typically-sighted controls in most tasks. Their improvement was comparable to that of a group of blind participants, who underwent training coupling their movements with auditory feedback alone. These findings suggest that spatial cognition can be enhanced by a training program which strengthens the association between bodily movements and their sensory feedback (either auditory or audio-visual).
... Unadjusted model and adjusted linear regression models (adjusting for all the characteristics presented in Table 1) were applied to evaluate the effect of the blood concentration of heavy metals on TT, E2, SHBG, FT, FE2, and TT/E2. Akaike's Information Criterion (AIC) was used to determine which model fits the data better (32). Each blood concentration of heavy metals (quantile) was used as an ordinal variable for tests for trend. ...
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Introduction Environmental pollutants could be implicated in female endocrine setting Q6 beyond traditional factors. Until now, few study has focused on the association of environmental exposure to heavy metals with sex hormones in postmenopausal women. This study intended to investigate whether serum levels of heavy metals(i.e., Cd, Pb, Hg, Mn, Se) would influence sex hormones in postmenopausal women. Methods and results A cross-sectional study was performed on 614 nationally representative participants from 2013-2016 National Health and Nutrition Examination Survey (NHANES) in the US. Multivariate linear regression models and restricted cubic spline plots revealed cadmium(Cd) had linear positive association with TT(β=3.25, 95%CI= 1.12, 5.38), bioavailable TT(β=1.78, 95%CI=0.36,3.21) and TT/E2(β=0.76, 95%CI=0.28,1.24), which was more apparent in natural menopausal and obese women. Lead(Pb) had linear positive association with SHBG(β=12.84, 95%CI= 6.77,18.91), which was apparent in nearly all subgroups except in normal BMI group, and TT/E2 (β=0.69, 95%CI 0.134,1.25), which was apparent in natural menopausal and normal BMI women. Manganese(Mn) had non-linear association with SHBG, which was more apparent in natural menopausal and obese women, and TT/E2, which was more apparent in natural menopausal and normal BMI women. Selenium(Se) had U shaped non-linear association with TT, which was more apparent in hysterectomy, overweight and obese women, and SHBG, which was apparent in nearly all subgroups except in normal BMI group. Conclusion In summary, this cross-sectional study indicates a possible role that various degree of environmental exposure to heavy metals plays in the disruption of sex Q5 hormone levels in postmenopausal women. Further experiments are needed to elucidate the underlying mechanisms.
... Akaike Information Criterion (AIC) was proposed by Japanese statistician Akaike (Akaike 1973). AIC is a weighted function of fitting accuracy and the number of parameters: the calculation method is as follows: ...
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RH is a physical quantity measuring atmospheric water vapor content. Predicting RH is of great importance in weather, climate, industrial production, crops, human health, and disease transmission, since it is helpful in making critical decisions. In this paper, the effects of covariates and error correction on relative humidity (RH) prediction have been studied, and a hybrid model based on seasonal autoregressive integrated moving average (SARIMA) model, cointegration (EG), and error correction model (ECM) named SARIMA-EG-ECM (SEE) has been proposed. The prediction model was performed in the meteorological observations of Hailun Agricultural Ecology Experimental Station, China. Based on the SARIMA model, the meteorological variables that interact with RH were used as covariates to perform EG tests. A cointegration model has been constructed. It revealed that RH had a cointegration relationship with air temperature (TEMP), dew point temperature (DEWP), precipitation (PRCP), atmospheric pressure (ATMO), sea-level pressure (SLP), and 40 cm soil temperature (40ST), which revealed the long-term equilibrium relationship between series. An ECM was established which indicated that the current fluctuations of DEWP, ATMO, and SLP have a significant impact on the current fluctuations of RH. The established ECM describes the short-term fluctuation relationship between the series. With the increase of the forecast horizon from 6 to 12 months, the prediction performance of the SEE model decreased slightly. A comparative study has also been introduced, indicating that the SEE performs superior to SARIMA and Long Short-Term Memory (LSTM) network.
... P. Piepho, 2010). Assessment of model fit can be compared using LRT (Lewis et al., 2011) or AIC (Akaike, 1973). ...
... Each variable within the final models presented were significant at < 0.05. Different combinations of variables were tested to generate different models, and finally, the best one was selected, using Akaike's information criterion (AIC) (Akaike, 1973), choosing those with a lower value. ...
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... Both AIC and BIC are commonly used for the determination of model order. AIC, also known as the minimum information criterion, was proposed by Akaike (1973) and is an established theory for AR models (Wang et al., 2018). It was further extended to determine the order of ARMA models as well as mixed regression models. ...
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Smallholder farmers in Ghana’s Savannah ecological zone face multiple climate stressors. Government and non-governmental organizations have introduced educative demonstrations on sustainable agriculture practices to help them cope. However, the effectiveness of these strategies in enhancing smallholder farmers’ climate resilience needs examination. Our study, guided by the Resilience Theory (RT), aimed to explore factors that shape smallholder farmers’ climate resilience and how their participation in Farmer Field Schools (FFSs) and Climate Action Plans (CAPs) affect their resilience to climate change. We analyzed data from a cross-sectional survey of 517 smallholder farmers in the Upper West region of Ghana using ordered logistic regression. Our findings showed that smallholder farmers’ “good” climate change resilience was associated with participation in Farmer Field Schools (OR: 7.809, p < 0.001) and active involvement in Climate Action Plans (OR: 1.976, p < 0.01). In addition, household food security (OR: 4.412, p < 0.001), access to credit (OR: 1.761, p < 0.01), and larger household sizes (OR: 2.255, p < 0.01) were associated with “good” climate resilience. However, larger land size (OR: 0.988, p < 0.01) and attainment of primary education (OR: 0.497, p < 0.01) showed a lesser likelihood of having “good” climate resilience. The study highlights the importance of practical learning platforms and participatory planning in improving climate resilience among smallholder farmers. Policies and programs should support these initiatives, improve resource accessibility, and tailor educational approaches. Our recommendations include expanding FFSs, integrating CAPs with agricultural services, developing scalable, adaptable, and sustainable agricultural practices, enhancing resource accessibility, and implementing monitoring and evaluation systems for these initiatives.
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Dietary supplements are gaining recognition as potential influencers of female reproductive health, but their connection to endometriosis risk remains underexplored. This study addressed this gap, examining the impact of daily dietary supplement intake on the initiation and progression of endometriosis. To explore this, a cross-sectional study was conducted involving 3950 participants representative of the US population from the 1999–2006 National Health and Nutrition Examination Survey (NHANES). Infertility was determined by a question on year-long attempts to become pregnant. Unweighted and weighted multivariate logistic regression analyses assessed the association between dietary supplements and endometriosis risk. Subgroup analysis was conducted based on the participants’ body mass index (BMI). The results revealed intriguing patterns. Specifically, higher dietary fiber content (Q4 vs Q1: OR = 0.56, 95% CI = (0.37,0.84), P = 0.0062) and density (Q4 vs Q1: OR = 0.55, 95% CI = (0.38,0.81), P = 0.0035) were linked to reduced risk of endometriosis. Protein content (Q4 vs Q1: OR = 0.47, 95% CI = (0.31,0.74), P = 0.0011) and density (Q4 vs Q1: OR = 0.63, 95% CI = (0.45,0.88), P = 0.0096) similarly exhibited a negative association with endometriosis risk. Interestingly, when stratified by BMI, these effects were pronounced in normal-weight women, whereas they were not evident in the overweight and obese subgroup. Protein content and density showed no significant associations across subpopulations. In conclusion, this study established a negative relationship between dietary fiber and endometriosis, particularly notable in normal-weight women. Future research is essential to validate these findings and establish a causal link between dietary fiber and endometriosis.
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The cultivation of Persian walnuts in Iran is concentrated in the mountainous regions of Zagros and Alborz, encompassing Kohgiluyeh and Boyer‐Ahmad, Isfahan and Fars provinces. Historically, these areas were renowned for their abundant growth of oak trees. However, due to environmental stressors, oak populations in the Zagros region have been declining, leading to an increased risk of diseases caused by new and aggressive pathogens, exacerbated by climate change. Understanding the distribution and association of pathogenic bacteria in the environment, especially for less common or uncommon species, has become crucial. In this study, 80 bacterial strains were isolated from 84 symptomatic walnut and 16 symptomatic oak trees to investigate bacterial canker agents in primary walnut cultivation regions of Iran. Following the hypersensitivity test and pathogenicity assays, 21 strains were classed as ‘ Brenneria nigrifluens ’ or ‘ Brenneria ‐like’, based on their similarities to the reference strain B . nigrifluens ICMP 20120 using phenotypic techniques and specific primers (F1/C3, B . nigrifluens ). Varying biochemical characteristics were exhibited by the ‘ Brenneria ‐like’ group in comparison to the ‘ B . nigrifluens ’ group. Multilocus sequence analysis was performed using the gyrB , rpoB , infB and atpD genes to determine the taxonomic classification of this group, revealing that it belonged to Gibbsiella quercinecans . The increasing reports of this bacterium from different woodland tree hosts suggest its opportunistic role as an individual causative agent, necessitating monitoring of its host expansion and morbidity.
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Abstract Managing for the effects of climate change on species whose populations are currently imperiled requires detailed knowledge of the relationship between their demographic rates and climate variables. We sought this information for the West Coast breeding population of snowy plover (Charadrius nivosus), which was federally listed as threatened in 1993 due to substantial declines in the numbers of plovers breeding along the coast and in the number of sites occupied for breeding. Snowy plovers employ a serially polygamous breeding system in which the male typically tends chicks to independence. This unusual breeding system is favored by male‐biased sex ratios in local populations. As part of a multispecies study of the effect of climate change on population growth, we used mark–capture models to examine climate drivers of adult survival for 1219 snowy plovers banded at Monterey Bay over 38 years and known to overwinter on the surrounding north‐central California outer coast. Nonclimate variables, including sex and unmeasured annual mortality risks (e.g., predator abundance), were the primary factors affecting adult survival. However, there is evidence that cold weather, particularly extended cold snaps with daily low temperatures below 2°C and daily high temperatures below 10°C, decreases overwinter survival. Exceptionally cold winters had a particularly strong effect on adult female plovers, contributing to the male‐biased adult sex ratios. Future winter climate on the north‐central California coast is projected to be generally warmer with fewer and shorter cold snaps. Reduced mortality from cold winter weather may mitigate other threats faced by plovers, such as anthropogenically enhanced predator populations, habitat loss, and accelerated sea level rise, while altering the adult sex ratio and potentially shifting the evolutionary landscape maintaining the plover's unusual breeding system.
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In the existing multidimensional extensions of the log-normal response time (LNRT) model, the log response times are decomposed into a linear combination of several latent traits. These models are fully compensatory as low levels on traits can be counterbalanced by high levels on other traits. We propose an alternative multidimensional extension of the LNRT model by assuming that the response times can be decomposed into two response time components. Each response time component is generated by a one-dimensional LNRT model with a different latent trait. As the response time components—but not the traits—are related additively, the model is partially compensatory. In a simulation study, we investigate the recovery of the model’s parameters. We also investigate whether the fully and the partially compensatory LNRT model can be distinguished empirically. Findings suggest that parameter recovery is good and that the two models can be distinctly identified under certain conditions. The utility of the model in practice is demonstrated with an empirical application. In the empirical application, the partially compensatory model fits better than the fully compensatory model.
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A bstract We determine the QCD equation of state at nonzero temperature in the presence of an isospin asymmetry between the light quark chemical potentials on the lattice. Our simulations employ N f = 2 + 1 flavors of dynamical staggered quarks at physical masses, using three different lattice spacings. The main results, obtained at the individual lattice spacings, are based on a two-dimensional spline interpolation of the isospin density, from which all relevant quantities can be obtained analytically. In particular, we present results for the pressure, the interaction measure, the energy and entropy densities, as well as the speed of sound. Remarkably, the latter is found to exceed its ideal gas limit deep in the pion condensed phase, the first account of the violation of this limit in first principles QCD. Finally, we also compute the phase diagram in the temperature — isospin density plane for the first time. Even though the results are not continuum extrapolated and thus not final, the data for all observables will be useful for the benchmarking of effective theories and low-energy models of QCD and are provided in ancillary files for simple reuse.
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Brucellosis, Rift Valley fever (RVF) and Q fever are zoonoses prevalent in many developing countries, causing a high burden on human and animal health. Only a few studies are available on these among agro-pastoralist communities and their livestock in Chad. The objective of our study was to estimate brucellosis, RVF and Q fever seroprevalence among Chadian agro-pastoralist communities and their livestock, and to investigate risk factors for seropositivity. We conducted a multi-stage cross-sectional serological survey in two rural health districts, Yao and Danamadji (966 human and 1041 livestock (cattle, sheep, goat and equine) samples)). The true seroprevalence were calculated applying a Bayesian framework to adjust for imperfect diagnostic test characteristics and accounting for clustering in the study design. Risk factors for each of the zoonotic diseases were estimated using mixed effects logistic regression models. The overall prevalence for brucellosis, Q fever and RVF combined for both regions was estimated at 0.2% [95% credibility Interval: 0-1.1], 49.1% [%CI: 38.9-58.8] and 28.1% [%CI: 23.4-33.3] in humans, and 0.3% [%CI: 0-1.5], 12.8% [%CI: 9.7-16.4] and 10.2% [%CI: 7.6-13.4] in animals. Risk factors correlating significantly with the respective disease seropositivity were sex for human brucellosis, sex and Q fever co-infection for animal brucellosis, age for human Q fever, species and brucellosis co-infection for animal Q fever, age and herd-level animal RVF seroprevalence within the same cluster for human RVF, and cluster-level human RVF seroprevalence within the same cluster for animal RVF. In Danamadji and Yao, Q fever and RVF are notably seroprevalent among agro-pastoralist human and animal communities, while brucellosis appears to have a low prevalence. Correlation between the seroprevalence between humans and animals living in the same communities was detected for RVF, highlighting the interlinkage of human and animal transmissible diseases and of their health, highlighting the importance of a One Health approach.
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Systematic reviews can be used not only to evaluate the efficacy and usefulness of a drug or food ingredient, but also as a safety assessment method. One of the aims of safety assessment is to estimate the no observed adverse effect level and the lowest observed adverse effect level. However, no methodology to statistically estimate the no observed adverse effect level from systematic review results has yet been reported. Estimation of the no observed adverse effect level involves a search for the dose above which adverse events occur is even exploration of the thresholds in dose response. To search for the dose above which adverse events occur, we examined an estimation method using the weighted change-point regression model, which includes the weights of each study used for systematic reviews in the model. This model could be applied to safety data of an omega-3 study in the form of a systematic review. We demonstrated that the dose response to omega-3 intake regarding adverse events had a threshold value and that the no observed adverse effect level could be estimated using the developed model.
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Research background: Taylor rule is a widely adopted approach to follow monetary policy and investigate various mechanisms related to or triggered by monetary policy. To date, no in-depth examination of scale, determinants and spillovers of state-level monetary policy stress, stemming from the Federal Reserve Board?s (Fed?s) policy has been performed. Purpose of the article: This paper aims to investigate the nature of monetary policy stress on US States delivered by the single monetary policy by using a quarterly dataset spanning the years between 1989 and 2017. Methods: We apply a wide array of time series and panel regressions, such as unit root tests, co-integration tests, co-integrating FMOLS and DOLS regressions, and Spatial Panel SAR and SEM models. Findings & value added: When average stress imposed on states is calculated, it is observed that the level of stress is moderate, but the distribution across states is asymmetric. The cross-state determinants behind the average stress show that states with a higher percentage of working-age and highly educated population, as well as those with higher population density and more export-oriented are negatively stressed (i.e. they experience excessively low interest rates), whereas higher unemployment rate contributes to a positive stress (too high interest rates). To the best of our knowledge, the contribution of this paper lies in estimating monetary policy stress at the state level and unveiling some of the determinants of this stress. Moreover, the paper makes the first attempt to empirically test spatial spillovers of the stress, which are indeed found significant and negative.
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This article introduces a causal discovery method to learn nonlinear relationships in a directed acyclic graph with correlated Gaussian errors due to confounding. First, we derive model identifiability under the sublinear growth assumption. Then, we propose a novel method, named the Deconfounded Functional Structure Estimation (DeFuSE), consisting of a deconfounding adjustment to remove the confounding effects and a sequential procedure to estimate the causal order of variables. We implement DeFuSE via feedforward neural networks for scalable computation. Moreover, we establish the consistency of DeFuSE under an assumption called the strong causal minimality. In simulations, DeFuSE compares favorably against state-of-the-art competitors that ignore confounding or nonlinearity. Finally, we demonstrate the utility and effectiveness of the proposed approach with an application to gene regulatory network analysis. The Python implementation is available at https://github.com/chunlinli/defuse.
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Animal conservation relies on assessing the distribution and habitat use of species, but for endangered/elusive animals this can prove difficult. The Monk Seal, Monachus monachus, is one of the world's most endangered species of pinniped, and the only one endemic to the Mediterranean Sea. During recent decades, direct observations have been few and scattered, making it difficult to determine its distribution away from the Aegean Sea (core distribution area of the post-decline relict population). This study relies on environmental DNA (eDNA) analysis to detect the presence of the Monk Seal in 135 samples collected in 120 locations of the central/western Mediterranean Sea, spanning about 1500 km longitudinally and 1000 km latitudinally. A recently described species-specific qPCR assay was used on marine-water samples, mostly collected during 2021 by a Citizen Science (CS) project. Positive detections occurred throughout the longitudinal range, including the westernmost surveyed area (Balearic archipelago). The distribution of the positive detections indicated six “hotspots”, mostly overlapping with historical Monk Seal sites, suggesting that habitat-specific characteristics play a fundamental role. We applied single-season occupancy models to correct for detection probability and to assess the importance of site-specific characteristics. The distance from small islets and protected (or access-restricted) areas was correlated negatively with the detection probability. This novel molecular approach, applied here for the first time in an extensive CS study, proved its potential as a tool for monitoring the distribution of this endangered/elusive species.
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Atlantic bonito, Sarda sarda (Bloch, 1793), is a valuable small tuna species to coastal countries and local communities. This species is heavily exploited by artisanal fisheries in the Senegalese Exclusive Economic Zone (SEEZ). The common gears used in artisanal fisheries for catching Atlantic bonito are gillnets, purse seines, longlines, and sleeping nets. Although catches of this species have increased in recent years, little is known about the Atlantic bonito catch per unit effort (CPUE) and size selectivity in the region. As this information is relevant for many stock assessments, available catch, effort and size data from Atlantic bonito harvested over 15 years (2004-2018) with different gears were used in the present study to calculate the nominal and standardized CPUE, size-frequency distribution and length at retentions (50 % and 95 % selectivity) of the species. To eliminate the effects of temporal, spatial, and environmental factors, the Atlantic bonito CPUE was standardized using generalized linear and additive models. The retention length at 50 % and 95 % for each year and gear was calculated from the cumulative length frequency distribution as a proxy for selectivity. Optimal model standardization CPUE results showed a significant trend for gillnets, ranging from 4.6 kg/trip in 2005-92.65 kg/trip in 2018, while sleeping nets showed lower CPUE values, ranging from 2.12 kg/trip in 2004 up to 0.83 kg/trip in 2018. This study showed that the year, month, and fishing Area variables were the main factors affecting the nominal CPUE for all scenarios evaluated in this study. Catch data, CPUE and selec-tivity results have shown that gillnets are the most selective and efficient among the four main gears used to catch Atlantic bonito in the SEEZ.
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Introduction and hypothesisOur objective was to evaluate the amount of opioids used by patients undergoing surgery for pelvic floor disorders and identify risk factors for opioid consumption greater than the median.Methods This was a prospective cohort study of 18- to 89-year-old women undergoing major urogynecological surgery between 1 November2020 and 15 October 2021. Subjects completed one preoperative questionnaire (“questionnaire 1”) that surveyed factors expected to influence postoperative pain and opioid use. At approximately 1 and 2 weeks following surgery, patients completed two additional questionnaires (“questionnaire 2” and “questionnaire 3”) about their pain scores and opioid use. Risk factors for opioid use greater than the median were assessed. Finally, a calculator was created to predict the amount of opioid used at 1 week following surgery.ResultsOne hundred and ninety patients were included. The median amount of milligram morphine equivalents prescribed was 100 (IQR 100–120), whereas the median amount used by questionnaire 2 was 15 (IQR 0–50) and by questionnaire 3 was 20 (IQR 0–75). On multivariate logistic regression, longer operative time (aOR 1.64 per hour of operative time, 95% CI 1.07–2.58) was associated with using greater than the median opioid consumption at the time of questionnaire 2; whereas for questionnaire 3, a diagnosis of fibromyalgia (aOR=16.9, 95% CI 2.24–362.9) was associated. A preliminary calculator was created using the information collected through questionnaires and chart review.Conclusions Patients undergoing surgery for pelvic floor disorders use far fewer opioids than they are prescribed.
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The Coral Triangle (CT) and the South China Sea (SCS) are the world’s great tropical seas, located in the Indo-Pacific (IP) region. It is home to the richest marine ecosystem on Earth, with a total of 76% reef-building coral species as well as 37% coral reef fish species. Unfortunately, this sensitive area is now vulnerable to Sea Surface Temperature (SST) warming. This research explored the possible consequences of SST warming on the rich ecosystems of the IP region, specifically on bleaching of its coral reefs. Reefbase provided coral bleaching records together with the daily NOAA AVHRR Optimum Interpolation (OI) SST V2 dataset (OISSTv2) were used to explore the relationship between coral bleaching and SST in the IP region. Three different categories of monthly mean SST were tested as potential covariates: minimum SST, mean SST and maximum SST, obtained from the OISSTv2. The fitted logistic regression (LR) model revealed a significant and large correlation between coral bleaching and annual maximum monthly mean SST in the study area using the bleaching data from an online database and the time-series of AVHRR images. Predicted maps of coral bleaching based on the LR model were highly consistent with NOAA Coral Reef Watch (CRW) Degree heating Weeks (DHW) maps. However, some important discrepancies resulted from the more specific local fitting used in the LR model. The maximum SST was forecasted from 2020 to 2100 based on the Coupled Model Intercomparison Project Phase 5 (CMIP5) dataset under the Representative Concentration Pathways (RCP2.6) scenario. The fitted logistic regression model was employed to transform the forecasted maximum SST values into maps of the probability of coral bleaching from 2020 to 2100. The results provide considerable cause for concern, including the likelihood of widespread coral bleaching in many places in the IP region over the next 30 years.
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In commercial fish farming, growth performance is the most influential factor in economic profitability; so, biomass optimization has become a growing concern. We analyzed the influence of 3 harvest densities (15, 20, and 22 kg·m–3) on the growth of spotted rose snappers reared in floating net cages during a production cycle. To assess the impact of stocking density on growth performance, we used 2 indicators: final total length-at-age (12 months) and the growth rate estimated from growth models (von Bertalanffy, logistic, and Gompertz). For the first indicator, we tested for normality. We did the Kruskal–Wallis and the post hoc Kruskal–Wallis tests to compare the mean total final length from each density. Accordingly, the means of densities D15 and D20 were the same (P value = 0.22). For the second indicator, we fitted the models with the subroutine optim of the R statistical package using the L-BFGS-B algorithm. Model selection was made with the Akaike and the Bayesian information criteria. Both criteria suggested that the logistic model fitted the data best. With the best model (logistic), we did 1,000 bootstrap simulations for each density scenario to determine the distribution of the maximum likelihood estimation for the instantaneous growth rate. Because the estimates were normally distributed, we used ANOVA to test the equality of the instantaneous growth. The Tukey HSD test suggested that all means were statistically different from each other. The fastest growth rate (K = 0.275) corresponded to the cage with a density of 20 kg·m–3. These findings demonstrate that the logistic model can predict the growth of spotted rose snappers under culture conditions using floating net cages. These results strengthen the productive potential and economic profitability of snapper aquaculture using floating cage and may help the start of commercial scale aquaculture.
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Çocuk işçiliği, dünya genelinde yürütülen çocuk işçiliğini azaltma ve önleme çalışmalarına karşın önemli bir sosyal ve ekonomik sorun olarak varlığını sürdürmeye devam etmektedir. Türkiye’de çocuk işçiliği oranı, dünya ortalamasının altında olmasına rağmen Avrupa ve Kuzey Amerika ülkelerine göre neredeyse iki kat daha fazladır. Bu çalışmanın amacı, Türkiye’de çocuk işçiliği üzerinde etkili olan faktörleri ulusal düzey mikro veride mevcut olabilecek asimetrik yapıyı dikkate alarak analiz etmektir. Bu amaçla, 2019 yılına ait Çocuk İşgücü Araştırması verilerinden yararlanılmıştır. Bilgimiz dahilinde bu çalışma çocuk işçiliğini araştırmalarda sıklıkla kullanılan simetrik logit ve probit modellerinin yanı sıra asimetrik log-log ve tamamlayıcı log-log modelleri ile analiz eden ilk çalışmadır. Bulgular, çocuk işçiliği verisinde asimetrik yapı olduğuna dair kanıtlar sunmaktadır. Çocuk işçiliğinin modellenmesinde, Gumbel dağılımından hareketle tahmin yapan log-log modelinin daha uygun olduğu belirlenmiştir. Analizler ışığında, çocuğun, ebeveynin ve hanehalkının sosyal, ekonomik ve demografik özelliklerinin çocuk işçiliği üzerinde önemli etkilere sahip olduğu bulunmuştur. Sonuçlar, çocuk işçiliğini önlemeye yönelik program, politika ve kanun önerilerinin, 15-17 yaş aralığında, özellikle kendinden küçük kardeşi bulunan ve kalabalık hanelerde ikamet eden erkek çocukları hedef alması gerektiğini ifade etmektedir.
Article
Aims The objective of this case series was to examine the feasibility of vibrotactile EMG-based biofeedback (BF) as a home-based intervention tool to enhance sensory information during everyday motor activities and to explore its effectiveness to induce changes in active ankle range of motion during gait in children with spastic cerebral palsy (CP). Methods Ten children ages 6 to 13 years with spastic CP were recruited. Participants wore two EMG-based vibro-tactile BF devices for at least 4 hours per day for 1-month on the ankle and knee joints muscles. The device computed the amplitude of the EMG signal of the target muscle and actuated a silent vibration motor proportional to the magnitude of the EMG. Results Our results demonstrated the feasibility of the augmented sensory information of muscle activity to induce changes of the active ankle range of motion during gait for 6 children with an increase ranging from 8.9 to 51.6% compared to a one-month period without treatment. Conclusions Preliminary findings of this case series demonstrate the feasibility of vibrotactile EMG-based BF and suggest potential effectiveness to increase active ankle range of motion, therefore serving as a promising therapeutic tool to improve gait in children with spastic CP.
Article
Effective and reliable biomarker is a promising means to achieve early diagnosis of cancer. The availability of high-throughput single-cell RNA sequencing (scRNA-seq) data opens an unprecedented opportunity of discovering biomarkers by developing machine learning and feature selection methods. At present, the existing biomarker screening methods, such as recursive feature elimination (RFE), often treat genes as isolated features, ignoring their embedding complex network relationship. In addition, the interpretability of a cancer biomarker discovery model is as important as its classification accuracy. To address these problems, we propose a game theoretic method to discover gene modules serving as biomarkers on gene regulatory network (GRN) that can better distinguish hepatocellular carcinoma (HCC) samples with healthy ones. Specifically, the network-based game theory method, called NGTM, is an interpretable module exploration of supervised feature selection procedure. We regard the process of gene-to-model selection as a cooperative game. The contribution of each feature in combination is evaluated by cooperative game theoretic metrics, that is, Shapley values. The extension strategy of gene module is conducted on GRN in the form of subnetwork, and NGTM makes the biomarker recognition easily interpretable. Furthermore, our method is statistically verified by Akaike information criterion (AIC) in model selection. There is a strong correlation between AIC and the area under curve in classification. In comparison study, we test the wrapper RFE and random feature extraction methods on random forest under the same conditions. NGTM achieves relatively better classification performances which prove its advantage. The enriched dysfunctions in biomarkers are also consistent with prior knowledge of the occurrence and development of HCC.
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This paper adopted the feature selection method for information gain calculation to screen factors for landslide hazard susceptibility evaluation in Wushan County, the reservoir area of the Three Gorges Reservoir Hub. A comparative experimental study of evaluation factor screening was conducted via the Bayesian information criterion method and information gain method. The following conclusions could be drawn: in the selection of regional landslide susceptibility evaluation factors, the information gain value could be used as a screening index. The screening method steps are as follows: the information gain value of each factor is calculated, and the corresponding evaluation factors are selected based on the order of the information gain values. The percentage of the information gain value of a single factor to the sum of the information gain values of all factors could be used as an evaluation factor screening criterion. Since the information gain value provides a clear meaning and is easy to calculate in terms of the contribution of each evaluation factor to the evaluation model accuracy, this index could play an important role in the screening process of landslide susceptibility evaluation factors.
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Despite increasing concern over wildfires in Fennoscandia, there are essentially no studies on the survivability of buildings within the wildland-urban interface of this region. We make use of four recent large-scale fires in Sweden to elucidate which factors are important for survival, using multiple logistic regression analysis of data collected at the sites. We obtained data on 187 buildings within the fire perimeters, nearly all with wood paneling and tile- or sheet metal roofing. 35 % of the buildings were lost or badly damaged. Results indicate that most buildings were approached by relatively low-intensity fire and that ignition primarily occurred through direct flame contact. The most important factor for survivability was the presence of a maintained lawn. The second most important was that no flammable material was present close to the building façade. Further, fire intensity often decreased close to buildings due to a larger portion of deciduous trees around gardens than in the surrounding forest. These factors were more important than specific features of the building itself, reflecting that the majority of buildings have combustible wooden façades. Our results suggest that the greatest potential for increasing building safety in the Swedish WUI is to keep the area immediately surrounding the building (∼5 m) free from tree litter and other flammable material. Also, since fire intensities are generally low, buildings can in most cases be defended with simple tools without compromising personal safety.
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The detection and estimation of sinusoids is a fundamental signal processing task for many applications related to sensing and communications. While algorithms have been proposed for this setting, quantization is a critical, but often ignored modeling effect. In wireless communications, estimation with low resolution data converters is relevant for reduced power consumption in wideband receivers. Similarly, low resolution sampling in imaging and spectrum sensing allows for efficient data collection. In this work, we propose SignalNet, a neural network architecture that detects the number of sinusoids and estimates their parameters from quantized in-phase and quadrature samples. We incorporate signal reconstruction internally as domain knowledge within the network to enhance learning and surpass traditional algorithms in mean squared error and Chamfer error. We introduce a worst-case learning threshold for comparing the results of our network relative to the underlying data distributions. This threshold provides insight into why neural networks tend to outperform traditional methods and into the learned relationships between the input and output distributions. In simulation, we find that our algorithm is always able to surpass the threshold for three-bit data but often cannot exceed the threshold for one-bit data. We use the learning threshold to explain, in the one-bit case, how our estimators learn to minimize the distributional loss, rather than learn features from the data.
Article
Background Anticipating the need for non-home discharge (NHD) enables improved patient counseling and expedites placement, potentially reducing length of stay and hospital readmission. The objective of this study was to create a simple, preoperative, clinical prediction tool for NHD using the Society of Thoracic Surgeons General Thoracic Surgery Database (STS GTSD). Methods The STS GTSD was queried for patients who underwent elective anatomic lung cancer resection between 2009-2019. Exclusion criteria included age<18, DLCO< 20% or >150%, N3 or M1 disease, incomplete datasets, and mortality. The primary outcome was defined as discharge to an extended care, transitional care, rehabilitation center, or another hospital. Multivariable logistic regression was used to select risk factors and a nomogram for predicting risk of NHD was developed. The approach was cross validated in 100 replications of a training set consisting of randomly selected 2/3rd of the cohort and a validation set of remaining patients. Results A total of 35948 patients from the STS GTSD met inclusion criteria. Final model variables used to derive the nomogram for NHD risk prediction included age (P<0.001), DLCO% (P<0.001), open surgery (P0.001), cerebrovascular history (P<0.001), and Zubrod score (P<0.001). The ROC curve, using sensitivities and specificities of the model, yielded AUC =0.74. In 100 replicated cross-validations, out-of-sample AUC ranged 0.72-0.76. Conclusions Using readily available preoperative variables, our nomogram prognosticates the risk of non-home discharge after anatomic lung resection with good discriminatory ability. Such risk stratification can enable improved patient counseling and facilitate better planning of patients’ post-operative needs.
Chapter
This chapter introduces mixture models and latent class models. After a motivating example, formal definitions of these models are presented in Sect. 2.2. In Sect. 2.3, several methods for maximum likelihood parameter estimation are outlined. In Sects. 2.4 and 2.5, parameter inference is discussed: Are parameters different from zero? Is there justification to constrain parameters to be equal to one another? What are the standard errors of parameter estimates? In Sect. 2.6, model selection is treated. A main question here is how many states (mixture components) a model should have and the various criteria that are used to decide this are defined and discussed. In Sect. 2.7, we then discuss how to model the effect of covariates on the prior probability of the states. Finally, in Sect. 2.8, we consider whether the parameters of mixture models are identifiable.
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The problem of choosing the number of PCs to retain is analyzed in the context of model selection, using so-called model selection criteria (MSCs). For a prespecified set of models, indexed by k=1,2,…,K, these model selection criteria (MSCs) take the form MSCk=nLLk+anmk, where, for model k,LLk is the maximum log likelihood, mk is the number of independent parameters, and the constant an is an=lnn for BIC and an=2 for AIC. The maximum log likelihood LLk is achieved by using the maximum likelihood estimates (MLEs) of the parameters. In Gaussian models, LLk involves the logarithm of the mean squared error (MSE). The main contribution of this chapter is to show how to best use BIC to choose the number of PCs, and to compare these results to ad hoc procedures that have been used. Findings include the following. These are stated as they apply to the eigenvalues of the correlation matrix, which are between 0 and p and have an average of 1. For considering an additional PCk + 1, with AIC, inclusion of the additional PCk + 1 is justified if the corresponding eigenvalue λk+1 is greater than exp−2/n. For BIC, the inclusion of an additional PCk + 1 is justified if λk+1>n1/n, which tends to 1 for large n. Therefore, this is in approximate agreement with the average eigenvalue rule for correlation matrices, stating that one should retain dimensions with eigenvalues larger than 1.
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Estimating the liquid level in an anaerobic digester can be disturbed by its closedness, bubbles and scum formation, and the inhomogeneity of the digestate. In our previous study, a soft-sensor approach using seven pressure meters has been proposed as an alternative for real-time liquid level estimation. Here, machine learning techniques were used to improve the estimation accuracy and optimize the number of sensors required in this approach. Four algorithms, multiple linear regression (MLR), artificial neural network (ANN), random forest (RF), and support vector machine (SVM) with radial basis function kernel were compared for this purpose. All models outperformed the cubic model developed in the previous study, among which the ANN and RF models performed the best. Variable importance analysis suggested that the pressure readings from the top (in the headspace) were the most significant, while the other pressure meters showed varying significance levels depending on the model type. The sensor that experienced both headspace and liquid phases depending on the level variation incurred a higher error than other sensors. The results showed that the ML techniques can provide an effective tool to estimate digester liquid levels by optimizing the number of sensors and reducing the error rate.
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Selecting a suitable equation to represent a set of multifactor data that was collected for other purposes in a plant, pilot-plant, or laboratory can be troublesome. If there are k independent variables, there are 2 possible linear equations to be examined; one equation using none of the variables, k using one variable, k(k – 1)/2 using two variables, etc. Often there are several equally good candidates. Selection depends on whether one needs a simple interpolation formula or estimates of the effects of individual independent variables. Fractional factorial designs for sampling the 2 possibilities and a new statistic proposed by C. Mallows simplify the search for the best candidate. With the new statistic, regression equations can be compared graphically with respect to both bias and random error.
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Summary The use of a multidimensional extension of the minimum final prediction error (FPE) criterion which was originally developed for the decision of the order of one-dimensional autoregressive process [1] is discussed from the standpoint of controller design. It is shown by numerical examples that the criterion will also be useful for the decision of inclusion or exclusion of a variable into the model. Practical utility of the procedure was verified in the real controller design process of cement rotary kilns.
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In a recent paper by the present author [1] a simple practical procedure of predictor identification has been proposed. It is the purpose of this paper to provide a theoretical and empirical basis of the procedure.
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A fully computerized cement rotary kiln process control was tested in a real production line and the results are presented in this paper. The controller design was based on the understanding of the process behavior obtained by careful statistical analyses, and it was realized by using a very efficient statistical identification procedure and the orthodox optimal controller design by the statespace method. All phases of analysis, design and adjustment during the practical application are discussed in detail. Technical impact of the success of the control on the overall kiln installation is also discussed. The computational procedure for the identification is described in an Appendix.
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Incluye bibliografía e índice
Article
The foundations of a general theory of statistical decision functions, including the classical non-sequential case as well as the sequential case, was discussed by the author in a previous publication [3]. Several assumptions made in [3] appear, however, to be unnecessarily restrictive (see conditions 1-7, pp. 297 in [3]). These assumptions, moreover, are not always fulfilled for statistical problems in their conventional form. In this paper the main results of [3], as well as several new results, are obtained from a considerably weaker set of conditions which are fulfilled for most of the statistical problems treated in the literature. It seemed necessary to abandon most of the methods of proofs used in [3] (particularly those in section 4 of [3]) and to develop the theory from the beginning. To make the present paper self-contained, the basic definitions already given in [3] are briefly restated in section 2.1.
Article
Sherman [8] and Stein [9] have shown that a method given by the author [1] for comparing two experiments is equivalent, for experiments with a finite number of outcomes, to the original method introduced by Bohnenblust, Shapley, and Sherman [4]. A new proof of this result is given, and the restriction to experiments with a finite number of outcomes is removed. A class of weaker comparisons--comparison in $k$-decision problems--is introduced, in three equivalent forms. For dichotomies, all methods are equivalent, and can be described in terms of errors of the first and second kinds.
Article
The principle of maximum entropy, together with some generalizations, is interpreted as a heuristic principle for the generation of null hypotheses. The main application is to $m$-dimensional population contingency tables, with the marginal totals given down to dimension $m - r$ ("restraints of the $r$th order"). The principle then leads to the null hypothesis of no "$r$th-order interaction." Significance tests are given for testing the hypothesis of no $r$th-order or higher-order interaction within the wider hypothesis of no $s$th-order or higher-order interaction, some cases of which have been treated by Bartlett and by Roy and Kastenbaum. It is shown that, if a complete set of $r$th-order restraints are given, then the hypothesis of the vanishing of all $r$th-order and higher-order interactions leads to a unique set of cell probabilities, if the restraints are consistent, but not only just consistent. This confirms and generalizes a recent conjecture due to Darroch. A kind of duality between maximum entropy and maximum likelihood is proved. Some relationships between maximum entropy, interactions, and Markov chains are proved.
Article
Thesis (Ph. D. in Statistics)--University of California, Berkeley, June 1952. Bibliography: p. 125-128.
Article
Standard real business cycle models must rely on total factor productivity (TFP) shocks to explain the observed comovement of consumption, investment, and hours worked. This paper shows that a neoclassical model consistent with observed heterogeneity in labor supply and consumption can generate comovement in the absence of TFP shocks. Intertemporal substitution of goods and leisure induces comovement over the business cycle through heterogeneity in the consumption behavior of employed and unemployed workers. This result owes to two model features introduced to capture important characteristics of U.S. labor market data. First, individual consumption is affected by the number of hours worked: Employed agents consume more on average than the unemployed do. Second, changes in the employment rate, a central factor explaining variation in total hours, affect aggregate consumption. Demand shocks--such as shifts in the marginal efficiency of investment, as well as government spending shocks and news shocks--are shown to generate economic fluctuations consistent with observed business cycles.
Article
The problems of statistics are broadly classified into problems of specification and problems of inference, and a brief recapitulation is given of some standard methods in statistics, based on the use of the probability p (S/H) of the data S on the specification H (or on the use of the equivalent likelihood function). The general problems of specification and inference for time-series are then also briefly surveyed. To conclude Part I, the relation is examined between the information (entropy) concept used in communication theory, associated with specification, and Fisher's information concept used in statistics, associated with inference. In Part II some detailed methods of analysis are described with special reference to stationary time-series. The first method is concerned with the analysis of probability chains (in which the variable X can assume only a finite number of values or 'states', and the time t is discrete). The next section deals with autoregressive and autocorrelation analysis, for series defined either for discrete or continuous time, including proper allowance for sampling fluctuations; in particular, least-squares estimation of unknown coefficients in linear autogressive representations, and Quenouille's goodness of fit test for the correlogram, are illustrated. Harmonic or periodogram analysis is theoretically equivalent to autocorrelation analysis, but in the case of time-series with continuous spectra is valueless in practice without some smoothing device, owing to the peculiar distributional properties of the observed periodogram; one such arithmetical device is described in Section 7. Finally the precise use of the likelihood function (when available) is illustrated by reference to two different theoretical series giving rise to the same autocorrelation function.
Determination of the number of factors by an extended maximum likelihood principle
  • H Akaike
On a semi-automatic power spectrum estimation procedure
  • H Akaike