Numerical indications of a q-generalised central limit theorem

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) \beta(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $\beta(N)$ approaching finite values $\beta(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figure

Emergence of long memory in stock volatility from a modified Mike-Farmer model

The Mike-Farmer (MF) model was constructed empirically based on the continuous double auction mechanism in an order-driven market, which can successfully reproduce the cubic law of returns and the diffusive behavior of stock prices at the transaction level. However, the volatility (defined by absolute return) in the MF model does not show sound long memory. We propose a modified version of the MF model by including a new ingredient, that is, long memory in the aggressiveness (quantified by the relative prices) of incoming orders, which is an important stylized fact identified by analyzing the order flows of 23 liquid Chinese stocks. Long memory emerges in the volatility synthesized from the modified MF model with the DFA scaling exponent close to 0.76, and the cubic law of returns and the diffusive behavior of prices are also produced at the same time. We also find that the long memory of order signs has no impact on the long memory property of volatility, and the memory effect of order aggressiveness has little impact on the diffusiveness of stock prices.Comment: 6 pages, 6 figures and 1 tabl

On the future of astrostatistics: statistical foundations and statistical practice

This paper summarizes a presentation for a panel discussion on "The Future of Astrostatistics" held at the Statistical Challenges in Modern Astronomy V conference at Pennsylvania State University in June 2011. I argue that the emerging needs of astrostatistics may both motivate and benefit from fundamental developments in statistics. I highlight some recent work within statistics on fundamental topics relevant to astrostatistical practice, including the Bayesian/frequentist debate (and ideas for a synthesis), multilevel models, and multiple testing. As an important direction for future work in statistics, I emphasize that astronomers need a statistical framework that explicitly supports unfolding chains of discovery, with acquisition, cataloging, and modeling of data not seen as isolated tasks, but rather as parts of an ongoing, integrated sequence of analyses, with information and uncertainty propagating forward and backward through the chain. A prototypical example is surveying of astronomical populations, where source detection, demographic modeling, and the design of survey instruments and strategies all interact.Comment: 8 pp, 2 figures. To appear in "Statistical Challenges in Modern Astronomy V," (Lecture Notes in Statistics, Vol. 209), ed. Eric D. Feigelson and G. Jogesh Babu; publication planned for Sep 2012; see http://www.springer.com/statistics/book/978-1-4614-3519-

The propensity to bargain while on a vacation

This article assesses how tourists' bargaining motivations and attitudes moderate their willingness to return to Italy, where bargaining is perceived as one of the best ways to deal with sellers. A non-probability quota sampling technique was used to survey domestic tourists in Italy through an online questionnaire which encompassed 26 bargaining values and one item to measure the likelihood that the tourists would bargain at the same destination in the future. The data comprised a total of 812 observations. An order probit model and marginal effects were estimated to measure the tourists' propensity to return to Italy for bargaining purposes. The study findings indicate that tourists' propensity to return for bargaining purposes is taken with the awareness that they will not obtain what they expected; as a matter of fact, they are unlikely to care about the final result but instead engage in this behaviour to have fun.FCT - National Funding Agency for Science, Research and Technology [UID/ECO/04007/2013 CEFAGE

Visual masking and the dynamics of human perception, cognition, and consciousness A century of progress, a contemporary synthesis, and future directions

The 1990s, the “decade of the brain,” witnessed major advances in the study of visual perception, cognition, and consciousness. Impressive techniques in neurophysiology, neuroanatomy, neuropsychology, electrophysiology, psychophysics and brain-imaging were developed to address how the nervous system transforms and represents visual inputs. Many of these advances have dealt with the steady-state properties of processing. To complement this “steady-state approach,” more recent research emphasized the importance of dynamic aspects of visual processing. Visual masking has been a paradigm of choice for more than a century when it comes to the study of dynamic vision. A recent workshop (http://lpsy.epfl.ch/VMworkshop/), held in Delmenhorst, Germany, brought together an international group of researchers to present state-of-the-art research on dynamic visual processing with a focus on visual masking. This special issue presents peer-reviewed contributions by the workshop participants and provides a contemporary synthesis of how visual masking can inform the dynamics of human perception, cognition, and consciousness

Linear Estimation of Location and Scale Parameters Using Partial Maxima

Consider an i.i.d. sample X^*_1,X^*_2,...,X^*_n from a location-scale family, and assume that the only available observations consist of the partial maxima (or minima)sequence, X^*_{1:1},X^*_{2:2},...,X^*_{n:n}, where X^*_{j:j}=max{X^*_1,...,X^*_j}. This kind of truncation appears in several circumstances, including best performances in athletics events. In the case of partial maxima, the form of the BLUEs (best linear unbiased estimators) is quite similar to the form of the well-known Lloyd's (1952, Least-squares estimation of location and scale parameters using order statistics, Biometrika, vol. 39, pp. 88-95) BLUEs, based on (the sufficient sample of) order statistics, but, in contrast to the classical case, their consistency is no longer obvious. The present paper is mainly concerned with the scale parameter, showing that the variance of the partial maxima BLUE is at most of order O(1/log n), for a wide class of distributions.Comment: This article is devoted to the memory of my six-years-old, little daughter, Dionyssia, who leaved us on August 25, 2010, at Cephalonia isl. (26 pages, to appear in Metrika

Lockdown measures in response to COVID-19 in nine sub-Saharan African countries

Lockdown measures have been introduced worldwide to contain the transmission of COVID-19. However, the term ‘lockdown’ is not well-defined. Indeed, WHO’s reference to ‘so-called lockdown measures’ indicates the absence of a clear and universally accepted definition of the term ‘lockdown’. We propose a definition of ‘lockdown’ based on a two-by-two matrix that categorises different communicable disease measures based on whether they are compulsory or voluntary; and whether they are targeted at identifiable individuals or facilities, or whether they are applied indiscriminately to a general population or area. Using this definition, we describe the design, timing and implementation of lockdown measures in nine countries in sub-Saharan Africa: Ghana, Nigeria, South Africa, Sierra Leone, Sudan, Tanzania, Uganda, Zambia and Zimbabwe. While there were some commonalities in the implementation of lockdown across these countries, a more notable finding was the variation in the design, timing and implementation of lockdown measures. We also found that the number of reported cases is heavily dependent on the number of tests carried out, and that testing rates ranged from 2031 to 63 928 per million population up until 7 September 2020. The reported number of COVID-19 deaths per million population also varies (0.4 to 250 up until 7 September 2020), but is generally low when compared with countries in Europe and North America. While lockdown measures may have helped inhibit community transmission, the pattern and nature of the epidemic remains unclear. However, there are signs of lockdown harming health by affecting the functioning of the health system and causing social and economic disruption

Lockdown measures in response to COVID-19 in nine sub-Saharan African countries

Lockdown measures have been introduced worldwide to contain the transmission of COVID-19. However, the term ‘lockdown’ is not well-defined. Indeed, WHO’s reference to ‘so-called lockdown measures’ indicates the absence of a clear and universally accepted definition of the term ‘lockdown’. We propose a definition of ‘lockdown’ based on a two-by-two matrix that categorises different communicable disease measures based on whether they are compulsory or voluntary; and whether they are targeted at identifiable individuals or facilities, or whether they are applied indiscriminately to a general population or area. Using this definition, we describe the design, timing and implementation of lockdown measures in nine countries in sub-Saharan Africa: Ghana, Nigeria, South Africa, Sierra Leone, Sudan, Tanzania, Uganda, Zambia and Zimbabwe. While there were some commonalities in the implementation of lockdown across these countries, a more notable finding was the variation in the design, timing and implementation of lockdown measures. We also found that the number of reported cases is heavily dependent on the number of tests carried out, and that testing rates ranged from 2031 to 63 928 per million population up until 7 September 2020. The reported number of COVID-19 deaths per million population also varies (0.4 to 250 up until 7 September 2020), but is generally low when compared with countries in Europe and North America. While lockdown measures may have helped inhibit community transmission, the pattern and nature of the epidemic remains unclear. However, there are signs of lockdown harming health by affecting the functioning of the health system and causing social and economic disruption