A numerical study of tournament structure and seeding policy for the soccer World Cup Finals

Tournament outcome uncertainty depends on: the design of the tournament; and the relative strengths of the competitors – the competitive balance. A tournament design comprises the arrangement of the individual matches, which we call the tournament structure, the seeding policy and the progression rules. In this paper, we investigate the effect of seeding policy for various tournament structures, while taking account of competitive balance. Our methodology uses tournament outcome uncertainty to consider the effect of seeding policy and other design changes. The tournament outcome uncertainty is measured using the tournament outcome characteristic which is the probability P_q,R that a team in the top 100q pre‐tournament rank percentile progresses forward from round R, for all q and R. We use Monte Carlo simulation to calculate the values of this metric. We find that, in general, seeding favours stronger competitors, but that the degree of favouritism varies with the type of seeding. Reseeding after each round favours the strong to the greatest extent. The ideas in the paper are illustrated using the soccer World Cup Finals tournament.     

Patterns on an ancient artifact: a coincidence?

The Phaistos Disk is an ancient artifact from Crete. At each side of the disk, a series of unknown signs is written along a spiral. Professional archaeologists expect that we will only learn what it is until similar objects are found. A statistical analysis in this article shows what it is not: it is not a one‐dimensional text, since there are relations between the signs in adjacent windings of the spiral. Three patterns of such relations have been identified. A Monte Carlo simulation of one of them has been performed, using a model of the spiral form. It is concluded that the probability of this pattern being coincidental is small, well below the conventional threshold.     

Bayesian inference in cointegrated systems

In this paper I deal with Bayesian methods for conducting inference on important features of (potentially) cointegrated VAR models involving I(1) variables. Firstly, (informal) inference is made on the cointegrating rank of the system. Secondly, posterior analysis is used to verify the validity of over-identifying restrictions on the cointegration parameters. Thirdly, posterior distributions are obtained for impulse response functions and predictive densities at different horizons. The relevant posterior distributions are obtained by means of Monte Carlo integration. The analysis is based on the use of simple weakly informative priors. Two applications on simulated data and on the Danish money demand data are presented.     

Random walk and efficiency tests in the Asia-Pacific foreign exchange markets: Evidence from the post-Asian currency crisis data

This paper empirically tests the random walk and efficiency hypothesis for 12 Asia-Pacific foreign exchange markets. The hypothesis is tested using individual as well as panel unit root tests and two variance-ratio tests. The study covers the high (daily) and medium (weekly) frequency post-Asian crisis spot exchange rate data from January 1998 to July 2007. The inferential outcomes do not differ substantially between the unit root tests and the variance-ratio tests when using daily data but differ significantly when using weekly data. With the daily data, both types of unit root tests identify unit root components for all the series and two variance-ratio tests provide the evidence of martingale behavior for majority of the exchange rates tested. With the weekly data, panel unit root tests identify unit root component for the exchange rates and, the unit root tests on a single series basis identify unit root component for 10 foreign exchange markets. However, the variance-ratio tests reject the martingale null for the majority of the exchange rates when using weekly data.     

CONSUMER DIRECT FULFILLMENT PERFORMANCE IN INTERNET RETAILING: EMERGENCY TRANSSHIPMENTS AND DEMAND DISPERSION

The collaborative fulfillment of consumer orders by Internet retailers and wholesalers has proven important in the realization of sustainable levels of online profitability. Concentrating on consumer direct fulfillment (or drop shipping), an empirical simulation model evaluates avenues for improving logistical performance. The empirical simulation model centers on the online music CD retailing industry. It evaluates the effects of emergency transshipments and demand dispersion on inventory and product‐release performance, as well as on transportation costs, in consumer direct fulfillment operations. Results show that emergency transshipments improve inventory and product‐release performance in these operations. Furthermore, the inventory‐performance improvements are maximized when inventory facilities fulfill demand that is uniformly balanced across markets primarily assigned to each facility. Finally, gains in inventory and release performance obtained from emergency transshipments outweigh additional transportation costs incurred from a greater reliance on emergency transshipments for consumer direct fulfillment.     

Performance of empirical Bayes estimators of random coefficients in multilevel analysis: Some results for the random intercept-only model

For a multilevel model with two levels and only a random intercept, the quality of different estimators of the random intercept is examined. Analytical results are given for the marginal model interpretation where negative estimates of the variance components are allowed for. Except for four or five level-2 units, the Empirical Bayes Estimator (EBE) has a lower average Bayes risk than the Ordinary Least Squares Estimator (OLSE). The EBEs based on restricted maximum likelihood (REML) estimators of the variance components have a lower Bayes risk than the EBEs based on maximum likelihood (ML) estimators. For the hierarchical model interpretation, where estimates of the variance components are restricted being positive, Monte Carlo simulations were done. In this case the EBE has a lower average Bayes risk than the OLSE, also for four or five level-2 units. For large numbers of level-1 (30) or level-2 units (100), the performances of REML-based and ML-based EBEs are comparable. For small numbers of level-1 (10) and level-2 units (25), the REML-based EBEs have a lower Bayes risk than ML-based EBEs only for high intraclass correlations (0.5).     

微带压控振荡器设计与仿真

介绍了S波段微带压控振荡器的设计方法,并使用微波仿真软件Serenade8.5对振荡器进行仿真分析,给出了仿真和实际电路的结果。     

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.     

单信道连续波应答机距离零值仿真测试技术

本文阐述了单信道连续波应答机距离零值仿真测试方法。以及智能化高精度仿真测试仪的工作原理、设计及校准方法,并给出了测试结果。     

Bayesian time series analysis of periodic behaviour and spectral structure

Analysis, model selection and forecasting in univariate time series models can be routinely carried out for models in which the model order is relatively small. Under an ARMA assumption, classical estimation, model selection and forecasting can be routinely implemented with the Box–Jenkins time domain representation. However, this approach becomes at best prohibitive and at worst impossible when the model order is high. In particular, the standard assumption of stationarity imposes constraints on the parameter space that are increasingly complex. One solution within the pure AR domain is the latent root factorization in which the characteristic polynomial of the AR model is factorized in the complex domain, and where inference questions of interest and their solution are expressed in terms of the implied (reciprocal) complex roots; by allowing for unit roots, this factorization can identify any sustained periodic components. In this paper, as an alternative to identifying periodic behaviour, we concentrate on frequency domain inference and parameterize the spectrum in terms of the reciprocal roots, and, in addition, incorporate Gegenbauer components. We discuss a Bayesian solution to the various inference problems associated with model selection involving a Markov chain Monte Carlo (MCMC) analysis. One key development presented is a new approach to forecasting that utilizes a Metropolis step to obtain predictions in the time domain even though inference is being carried out in the frequency domain. This approach provides a more complete Bayesian solution to forecasting for ARMA models than the traditional approach that truncates the infinite AR representation, and extends naturally to Gegenbauer ARMA and fractionally differenced models.