The relationship between Fisher's exact test and Pearson's chi-square test: A bayesian perspective

It is demonstrated in this paper that two major tests for 2 × 2 talbes are highly related from a Bayesian perspective. Although it is well-known that Fisher's exact and Pearson's chi-square tests are asymptotically equivalent, the present analysis shows that a formal similarity also exists in small samples. The key assumption that leads to the resemblance is the presence of a continuous parameter measuring association. In particular, it is shown that Pearson's probability can be obtained by integrating a two-moment approximation to the posterior distribution of the log-odds ratio. Furthermore, Pearson's chi-square test gave an excellent approximation to the actual Bayes probability in all 2×2 tables examined, except for those with extremely disproportionate marginal frequencies.     

The influence of caloric information on cafeteria food choices

We evaluated the effect of posting caloric information on food purchases at a cafeteria. Purchases of more than 14,300 entrees, vegetables, and salads by 6,970 customers were unobtrusively monitored via the cash register inventory control system during 15 evening observations. A quasi-multiple-baseline design across food groups was used to test the additive effect of labeling the three lowest caloric choices for vegetables, salads, and entrees. A linear logit analysis confirmed that labeling increased the probability of low calorie selections for vegetables and salads, but not for entrees. Observations of meals purchased by a subsample of 413 customers indicated labeling did not change the total caloric content of meals. The number of customers and total sales per evening were unaffected by the labeling intervention. The results suggest that manipulating environmental cues may be an effective method for changing food purchases in a cafeteria, but labeling individual items may not be the best way to decrease total calories purchased.     

Comparing item characteristic curves

Test items are often evaluated and compared by contrasting the shapes of their item characteristics curves (ICC's) or surfaces. The current paper develops and applies three general (i.e., nonparametric) comparisons of the shapes of two item characteristic surfaces: (i) proportional latent odds, (ii) uniform relative difficulty, and (iii) item sensitivity. Two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items, and no assumption about the dimensionality of the latent variable. Also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations.The author is grateful to Paul Holland, Robert Mislevy, Tue Tjur, Rebecca Zwick, the editor and reviewers for valuable comments on the subject of this paper, to Mari A. Pearlman for advice on the pairing of items in the examples, and to Dorothy Thayer for assistance with computing.     

Binary programming and test design

An algorithmic approach to test design, using information functions, is presented. The approach uses a special branch of linear programming, i.e. binary programming. In addition, results of some benchmark problems are presented. Within the same framework, it is also possible to formulate the problem of individualized testing.I would like to thank my colleagues N. Veldhuijzen, H. Verstralen and M. Zwarts for their suggestions and comments. Furthermore, I would like to thank Professor W. van der Linden, Department of Educational Measurement and Data Analysis, Technological University Twente, for offering facilities at his department; Ellen Timminga of the same department and S. Baas, department of Operational Research at the same University for their efforts in linear programming.     

Rat choice in rapidly changing concurrent schedules

In two experiments, experimentally naïve rats were trained in concurrent variable‐interval schedules in which the reinforcer ratios changed daily according to a pseudorandom binary sequence. In Experiment 1, relative response rates showed clear sensitivity to current‐session reinforcer ratios, but not to previous sessions' reinforcer ratios. Within sessions, sensitivity to the current session's reinforcement rates increased steadily, and by session end, response ratios approached matching to the current‐session reinforcer ratios. Across sessions, sensitivity to the current session's reinforcer ratio decreased with continued exposure to the pseudorandom binary sequence, contrary to expectations based on previous studies demonstrating learning sets. Using a second group of naïve rats, Experiment 2 replicated the main results from Experiment 1 and showed that although there were increases over sessions in both changeover rate and response rate during the changeover delay, neither could explain the accompanying reductions in sensitivity. We consider the role of reinforcement history, showing that our results can be simulated using two separate representations, one local and one nonlocal, but a more complex approach will be needed to bring together these results and other history effects such as learning sets and spontaneous recovery.     

Probabilistic Subset Conjunction

The authors introduce subset conjunction as a classification rule by which an acceptable alternative must satisfy some minimum number of criteria. The rule subsumes conjunctive and disjunctive decision strategies as special cases. Subset conjunction can be represented in a binary-response model, for example, in a logistic regression, using only main effects or only interaction effects. This results in a confounding of the main and interaction effects when there is little or no response error. With greater response error, a logistic regression, even if it gives a good fit to data, can produce parameter estimates that do not reflect the underlying decision process. The authors propose a model in which the binary classification of alternatives into acceptable/unacceptable categories is based on a probabilistic implementation of a subset-conjunctive process. The satisfaction of decision criteria biases the odds toward one outcome or the other. The authors then describe a two-stage choice model in which a (possibly large) set of alternatives is first reduced using a subset-conjunctive rule, after which an alternative is selected from this reduced set of items. They describe methods for estimating the unobserved consideration probabilities from classification and choice data, and illustrate the use of the models for cancer diagnosis and consumer choice. They report the results of simulations investigating estimation accuracy, incidence of local optima, and model fit. The authors thank the Editor, the Associate Editor, and three anonymous reviewers for their constructive suggestions, and also thank Asim Ansari and Raghuram Iyengar for their helpful comments. They also thank Sawtooth Software, McKinsey and Company, and Intelliquest for providing the PC choice data, and the University of Wisconsin for making the breast-cancer data available at the machine learning archives.     

Bayesian factor analysis for multilevel binary observations

Multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs. We develop practical simulation based procedures for Bayesian inference of multilevel binary factor analysis models. We illustrate how Markov Chain Monte Carlo procedures such as Gibbs sampling and Metropolis-Hastings methods can be used to perform Bayesian inference, model checking and model comparison without the need for multidimensional numerical integration. We illustrate the proposed estimation methods using three simulation studies and an application involving student's achievement results in different areas of mathematics. The authors thank Ian Westbury, University of Illinois at Urbana Champaign for kindly providing the SIMS data for the application.     

Brain tumor detection using fusion of hand crafted and deep learning features

The perilous disease in the worldwide now a days is brain tumor. Tumor affects the brain by damaging healthy tissues or intensifying intra cranial pressure. Hence, rapid growth in tumor cells may lead to death. Therefore, early brain tumor diagnosis is a more momentous task that can save patient from adverse effects. In the proposed work, the Grab cut method is applied for accurate segmentation of actual lesion symptoms while Transfer learning model visual geometry group (VGG-19) is fine-tuned to acquire the features which are then concatenated with hand crafted (shape and texture) features through serial based method. These features are optimized through entropy for accurate and fast classification and fused vector is supplied to classifiers. The presented model is tested on top medical image computing and computer-assisted intervention (MICCAI) challenge databases including multimodal brain tumor segmentation (BRATS) 2015, 2016, and 2017 respectively. The testing results with dice similarity coefficient (DSC) achieve 0.99 on BRATS 2015, 1.00 on BRATS 2015 and 0.99 on BRATS 2017 respectively.