Calculating the random guess scores of multiple-response and matching test items

For achievement tests, the guess score is often used as a baseline for the lowest possible grade for score to grade transformations and setting the cut scores. For test item types such as multiple-response, matching and drag-and-drop, determin-ing the guess score requires more elaborate calculations than the more straight-forward calculation of the guess score for True-False and multiple-choice test item formats. For various variants of multiple-response and matching types with respect to dichotomous and polytomous scoring, methods for determining the guess score are presented and illustrated with practical applications. The implica-tions for theory and practice are discussed

Violating the Modified Helstrom Bound with Nonprojective Measurements

We consider the discrimination of two pure quantum states with three allowed outcomes: a correct guess, an incorrect guess, and a non-guess. To find an optimum measurement procedure, we define a tunable cost that penalizes the incorrect guess and non-guess outcomes. Minimizing this cost over all projective measurements produces a rigorous cost bound that includes the usual Helstrom discrimination bound as a special case. We then show that nonprojective measurements can outperform this modified Helstrom bound for certain choices of cost function. The Ivanovic-Dieks-Peres unambiguous state discrimination protocol is recovered as a special case of this improvement. Notably, while the cost advantage of the latter protocol is destroyed with the introduction of any amount of experimental noise, other choices of cost function have optima for which nonprojective measurements robustly show an appreciable, and thus experimentally measurable, cost advantage. Such an experiment would be an unambiguous demonstration of a benefit from nonprojective measurements.Comment: 5 pages, 2 figure

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Take-and-Guess Games

This paper studies two classes of two-person zero-sum games in which the strategies of both players are of a special type.Each strategy can be split into two parts, a taking and a guessing part.In these games two types of asymmetry between the players can occur.In the first place, the number of objects available for taking does not need to be the same for both players.In the second place, the players can be guessing sequentially instead of simultaneously; the result is asymmetric information.The paper studies the value and equilibria of these games, for all possible numbers of objects available to the players, for the case with simultaneous guessing as well as for the variant with sequential guessing.zero-sum games;morra;coin-guessing;asymmetric information

The Performance of MLEM for Dynamic Imaging From Simulated Few-View, Multi-Pinhole SPECT

Stationary small-animal SPECT systems are being developed for rapid dynamic imaging from limited angular views. This work quantified, through simulations, the performance of Maximum Likelihood Expectation Maximization (MLEM) for reconstructing a time-activity curve (TAC) with uptake duration of a few seconds from a stationary, three-camera multi-pinhole SPECT system. The study also quantified the benefits of a heuristic method of initializing the reconstruction with a prior image reconstructed from a conventional number of views, for example from data acquired during the late-study portion of the dynamic TAC. We refer to MLEM reconstruction initialized by a prior-image initial guess (IG) as MLEMig. The effect of the prior-image initial guess on the depiction of contrast between two regions of a static phantom was quantified over a range of angular sampling schemes. A TAC was modeled from the experimentally measured uptake of 99mTc-hexamethylpropyleneamine oxime (HMPAO) in the rat lung. The resulting time series of simulated images was quantitatively analyzed with respect to the accuracy of the estimated exponential washin and washout parameters. In both static and dynamic phantom studies, the prior-image initial guess improved the spatial depiction of the phantom, for example improved definition of the cylinder boundaries and more accurate quantification of relative contrast between cylinders. For example in the dynamic study, there was ~ 50% error in relative contrast for MLEM reconstructions compared to ~ 25-30% error for MLEMig. In the static phantom study, the benefits of the initial guess decreased as the number of views increased. The prior-image initial guess introduced an additive offset in the reconstructed dynamic images, likely due to biases introduced by the prior image. MLEM initialized with a uniform initial guess yielded images that faithfully reproduced the time dependence of the simulated TAC; there were no s- atistically significant differences in the mean exponential washin/washout parameters estimated from MLEM reconstructions compared to the true values. Washout parameters estimated from MLEMig reconstructions did not differ significantly from the true values, however the estimated washin parameter differed significantly from the true value in some cases. Overall, MLEM reconstruction from few views and a uniform initial guess accurately quantified the time dependance of the TAC while introducing errors in the spatial depiction of the object. Initializing the reconstruction with a late-study initial guess improved spatial accuracy while decreasing temporal accuracy in some cases

Continuous transition of social efficiencies in the stochastic strategy Minority Game

We show that in a variant of the Minority Game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guess value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guess value becomes worse. Hence, people can optimize their guess value for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population that follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every two-days interval on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.Comment: 8 pages, 6 fig