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Odds

About: Odds is a research topic. Over the lifetime, 3561 publications have been published within this topic receiving 98421 citations.


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Journal ArticleDOI
TL;DR: The hierarchical model of Lonnstedt and Speed (2002) is developed into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples and the moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom.
Abstract: The problem of identifying differentially expressed genes in designed microarray experiments is considered. Lonnstedt and Speed (2002) derived an expression for the posterior odds of differential expression in a replicated two-color experiment using a simple hierarchical parametric model. The purpose of this paper is to develop the hierarchical model of Lonnstedt and Speed (2002) into a practical approach for general microarray experiments with arbitrary numbers of treatments and RNA samples. The model is reset in the context of general linear models with arbitrary coefficients and contrasts of interest. The approach applies equally well to both single channel and two color microarray experiments. Consistent, closed form estimators are derived for the hyperparameters in the model. The estimators proposed have robust behavior even for small numbers of arrays and allow for incomplete data arising from spot filtering or spot quality weights. The posterior odds statistic is reformulated in terms of a moderated t-statistic in which posterior residual standard deviations are used in place of ordinary standard deviations. The empirical Bayes approach is equivalent to shrinkage of the estimated sample variances towards a pooled estimate, resulting in far more stable inference when the number of arrays is small. The use of moderated t-statistics has the advantage over the posterior odds that the number of hyperparameters which need to estimated is reduced; in particular, knowledge of the non-null prior for the fold changes are not required. The moderated t-statistic is shown to follow a t-distribution with augmented degrees of freedom. The moderated t inferential approach extends to accommodate tests of composite null hypotheses through the use of moderated F-statistics. The performance of the methods is demonstrated in a simulation study. Results are presented for two publicly available data sets.

11,864 citations

Journal ArticleDOI
TL;DR: In this article, a meta-analysis of 51 prevalence studies, five incidence studies, and four persistence studies was carried out to evaluate the magnitude, shape, and modifiers of such an association.
Abstract: Low socioeconomic status (SES) is generally associated with high psychiatric morbidity, more disability, and poorer access to health care. Among psychiatric disorders, depression exhibits a more controversial association with SES. The authors carried out a meta-analysis to evaluate the magnitude, shape, and modifiers of such an association. The search found 51 prevalence studies, five incidence studies, and four persistence studies meeting the criteria. A random effects model was applied to the odds ratio of the lowest SES group compared with the highest, and meta-regression was used to assess the dose-response relation and the influence of covariates. Results indicated that low-SES individuals had higher odds of being depressed (odds ratio = 1.81, p < 0.001), but the odds of a new episode (odds ratio = 1.24, p = 0.004) were lower than the odds of persisting depression (odds ratio = 2.06, p < 0.001). A dose-response relation was observed for education and income. Socioeconomic inequality in depression is heterogeneous and varies according to the way psychiatric disorder is measured, to the definition and measurement of SES, and to contextual features such as region and time. Nonetheless, the authors found compelling evidence for socioeconomic inequality in depression. Strategies for tackling inequality in depression are needed, especially in relation to the course of the disorder.

2,163 citations

Journal ArticleDOI
TL;DR: The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel, generalized to include the case of arbitrary odds.
Abstract: If the input symbols to a communication channel represent the outcomes of a chance event on which bets are available at odds consistent with their probabilities (i.e., “fair” odds), a gambler can use the knowledge given him by the received symbols to cause his money to grow exponentially. The maximum exponential rate of growth of the gambler's capital is equal to the rate of transmission of information over the channel. This result is generalized to include the case of arbitrary odds. Thus we find a situation in which the transmission rate is significant even though no coding is contemplated. Previously this quantity was given significance only by a theorem of Shannon's which asserted that, with suitable encoding, binary digits could be transmitted over the channel at this rate with an arbitrarily small probability of error.

1,398 citations

Posted Content
TL;DR: In this article, the authors explored the expectations of entrepreneurs in newly established businesses regarding their own chances of success and theirpredictions regarding the chances for success of others with similar startup ideas, in one of the first such studies.
Abstract: Explores the expectations of entrepreneurs in newlyestablished businesses regarding their own chances of success and theirpredictionsregarding the chances for success of others with similarstartup ideas, in one of the first such studies. Past research suggests that,at best, fewer than 50% of firms survive for more than five years with a givenowner/manager. Based on this past research, three hypotheses are posited:entrepreneurs will perceive their odds of success at less than or equal to 50%,entrepreneurs' prediction of others' success will not differ significantly fromtheir prediction of their own success, and entrepreneurs' expectations ofsuccess will be related to a number of personal factors including theirbusiness experience, prior ownership, and educational level. Data were gathered from surveys sent in 1985 to members of the NationalFederation of Independent Business (NFIB) who reported that they had openedtheir own businesses in the United States. Of those responding, 2994entrepreneurs were selected from the original sample. Findings did not support any of the three original hypotheses of cautiousoptimism (as prior research predicted). In fact, the results show thatentrepreneurs' perceptions of their own odds for success display a noteworthydegree of optimism. In addition, entrepreneurs believe their own odds ofsuccess to be greater than other new business owners with similar ideas.Furthermore, an analysis of the predicted factors for success showed aremarkable lack of relationship between an entrepreneur's belief of their ownpotential and the objective predictors. In fact, those who were poorly preparedseemed just as optimistic as those who were well prepared. One implication isthat business founders should seek advice from more objective outsiders.(SFL)

1,282 citations

Journal ArticleDOI
TL;DR: In this article, the authors conduct a firm-level analysis of the impact of breadth in both innovation objectives and knowledge sources and find that broader horizons with respect to innovation objectives are associated with successful innovation.
Abstract: Given the inherent risk of innovative activity. firms can improve the odds of success by pursuing multiple parallel objectives. Because innovation draws on many sources of ideas, firms also may improve their odds of successful innovation by accessing a large number of knowledge sources. In this study, we conduct one of the first firm-level statistical analyses of the impact on innovation of breadth in both innovation objectives and knowledge sources. The empirical results suggest that broader horizons with respect to innovation objectives and knowledge sources are associated with successful innovation. We do not find diminishing returns to breadth in innovation objectives, which suggests that firms may tend to search too narrowly. We interpret these results in light of well-known cognitive biases toward searching in relatively familiar domains. Copyright (C) 2009 John Wiley & Sons, Ltd.

1,145 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
20232,162
20225,138
2021334
2020208
2019202