Measurement Invariance, Entropy, and Probability

We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use measurement scale as a type of information constraint. We argue that a very common measurement scale is linear at small magnitudes grading into logarithmic at large magnitudes, leading to observations that often follow Student's probability distribution which has a Gaussian shape for small fluctuations from the mean and a power law shape for large fluctuations from the mean. An inverse scaling often arises in which measures naturally grade from logarithmic to linear as one moves from small to large magnitudes, leading to observations that often follow a gamma probability distribution. A gamma distribution has a power law shape for small magnitudes and an exponential shape for large magnitudes. The two measurement scales are natural inverses connected by the Laplace integral transform. This inversion connects the two major scaling patterns commonly found in nature. We also show that superstatistics is a special case of an integral transform, and thus can be understood as a particular way in which to change the scale of measurement. Incorporating information about measurement scale into maximum entropy provides a general approach to the relations between measurement, information and probability

Sequence effects in the categorization of tones varying in frequency

In contrast to exemplar and decision-bound categorization models, the memory and contrast models described here do not assume that long-term representations of stimulus magnitudes are available. Instead, stimuli are assumed to be categorized using only their differences from a few recent stimuli. To test this alternative, the authors examined sequential effects in a binary categorization of 10 tones varying in frequency. Stimuli up to 2 trials back in the sequence had a significant effect on the response to the current stimulus. The effects of previous stimuli interacted with one another. A memory and contrast model, according to which only ordinal information about the differences between the current stimulus and recent preceding stimuli is used, best accounted for these dat

Social inequalities in breast cancer mortality among French women: disappearing educational disparities from 1968 to 1996

We investigated the time trends in social inequalities in breast cancer mortality with an analysis by age at death and birth cohort using a representative 1% sample of the French population and four subcohorts (1968–1974, 1975–1981, 1982–1988 and 1990–1996). Causes of death were obtained by direct linkage with the French national death registry. Education was measured at the beginning of each period, and educational disparities in breast cancer mortality were studied among women aged 35–74 at the beginning of each period. In the 1970s, higher breast cancer mortality was found among higher educated women. This positive association progressively weakened and no association remained in the 1990s although it disappeared earlier among younger women. In an analysis by birth cohort, the same pattern was found among women born before 1925, whereas no association between education and mortality was observed among women born after 1925. Educational disparities in breast cancer mortality are currently changing and the previously observed positive gradient has disappeared. An important question is whether these relations are indirect, and due to changes in the prevalence of risk factors associated with education, but which we could not study

Phase I–II trial design for biologic agents using conditional auto‐regressive models for toxicity and efficacy

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147824/1/rssc12314_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147824/2/rssc12314.pd

The Use of the Signal at an Optimal Distance from the Shower Core as a Surrogate for Shower Size

When analysing data from air-shower arrays, it has become common practice to use the signal at a considerable distance from the shower axis (_opt) as a surrogate for the size of the shower. This signal, (_opt), can then be related to the primary energy in a variety of ways. After a brief review of the reasons behind the introduction of opt laid out in a seminal paper by Hillas in 1969, it will be shown that _opt, is a more effective tool when detectors are laid out on a triangular grid than when detectors are deployed on a square grid. This result may have implications for explaining the differences between the flux observed by the Auger and Telescope collaborations above 10 EeV and should be kept in mind when designing new shower arrays

The Use of the Signal at an Optimal Distance from the Shower Core as a Surrogate for Shower Size

When analysing data from air-shower arrays, it has become common practice to use the signal at a considerable distance from the shower axis (ropt) as a surrogate for the size of the shower. This signal, S(ropt), can then be related to the primary energy in a variety of ways. After a brief review of the reasons behind the introduction of ropt laid out in a seminal paper by Hillas in 1969, it will be shown that ropt, is a more effective tool when detectors are laid out on a triangular grid than when detectors are deployed on a square grid. This result may have implications for explaining the differences between the flux observed by the Auger and Telescope collaborations above 10\,EeV and should be kept in mind when designing new shower arrays

Absolute identification by relative judgment

In unidimensional absolute identification tasks, participants identify stimuli that vary along a single dimension. Performance is surprisingly poor compared with discrimination of the same stimuli. Existing models assume that identification is achieved using long-term representations of absolute magnitudes. The authors propose an alternative relative judgment model (RJM) in which the elemental perceptual units are representations of the differences between current and previous stimuli. These differences are used, together with the previous feedback, to respond. Without using long-term representations of absolute magnitudes, the RJM accounts for (a) information transmission limits, (b) bowed serial position effects, and (c) sequential effects, where responses are biased toward immediately preceding stimuli but away from more distant stimuli (assimilation and contrast)

Reaction Time of a Group of Physics Students

The reaction time of a group of students majoring in Physics is reported here. Strong co-relation between fatigue, reaction time and performance have been seen and may be useful for academicians and administrators responsible of working out time-tables, course structures, students counsellings etc.Comment: 10 pages, 4 figure

Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment