A parsimonious stochastic model for forecasting gamers' revenues in casinos

The gaming industry is the largest entertainment industry in the United States, with more than $80 billion in revenue annually. Because of the stochasticity of gambling outcomes and the complexity of the casino context, forecasting individual‐level revenues in a casino setting is extremely challenging, and yet crucial for customer relationship management. Current approaches for customer base analysis are usually too general to handle the unique context of the casino setting. To fill this gap between research and practice, this paper develops a stochastic model that incorporates visitation, wagering, and gambling outcomes to forecast gamers' revenues for a major casino operator. The proposed model is parsimonious and can be scaled to handle massive casino customer databases. Despite its parsimony, a holdout prediction test shows that the proposed model provides more accurate individual‐level revenue predictions than other forecasting methods that are based only on the observed data. Copyright © 2012 John Wiley & Sons, Ltd.     

A stochastic programming model for water resource planning

A framework is offered for the evaluation of electricity generation and water supply for agricultural irrigation. This assessment is conducted through the construction of an appropriate stochastic optimization model. A recursive least squares algorithm is incorporated in the model which enables more accurate estimation of model parameters.     

Statistical forecasting for stochastic processes

The main purpose of this paper is to review the efficiency properties of least-squares predictors when the parameters are estimated. It is shown that the criterion of asymptotic best unbiased predictors for general stochastic models is a natural analogue of the minimum mean-square error criterion used traditionally in linear prediction for linear models. The results are applied to log-linear models and autoregressive processes. Both stationary and non-stationary processes are considered.This paper is based on a key note lecture given at the meeting of The Institute of Management Sciences and the Operations Research Society of America, held in Williamsburg, Virginia, January 7–9, 1985.     

A stochastic model for solitons

The soliton physics for the propagation of waves is represented by a stochastic model in which the particles of the wave can jump ahead according to some probability distribution. We demonstrate the presence of a steady state (stationary distribution) for the wavelength. It is shown that the stationary distribution is a convolution of geometric random variables. Approximations to the stationary distribution are investigated for a large number of particles. The model is rich and includes Gaussian cases as limit distribution for the wavelength (when suitably normalized). A sufficient Lindeberg‐like condition identifies a class of solitons with normal behavior. Our general model includes, among many other reasonable alternatives, an exponential aging soliton, of which the uniform soliton is one special subcase (with Gumbel's stationary distribution). With the proper interpretation, our model also includes the deterministic model proposed in Takahashi and Satsuma [A soliton cellular automaton, J Phys Soc Japan 59 (1990), 3514–3519]. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Volatility forecasting using stochastic conditional range model with leverage effect

In this paper, we propose a stochastic conditional range model with leverage effect (henceforth SCRL) for volatility forecasting. A maximum likelihood method based on the particle filters is developed to estimate the parameters of the SCRL model. Simulation results show that the proposed methodology performs well. We apply the proposed model and methodology to four stock market indices, the Shanghai Stock Exchange Composite Index of China, the Hang Seng Index of Hong Kong, the Nikkei 225 Index of Japan, and the S&P 500 Index of US. Empirical results highlight the value of incorporating leverage effect into range modeling and forecasting. In particular, the results show that our SCRL model outperforms the conditional autoregressive range model, the conditional autoregressive range model with leverage effect, and the stochastic conditional range model in both in‐sample fit and out‐of‐sample forecast.     

A stochastic model for drilling optimization

Drilling optimization problems in oilfields are usually formulated and solved by using deterministic mathematical models, in which uncertain (indeterminate) factors or random issues are not taken into consideration. However, it has been widely experienced that random factors (such as those from soil layers, drill bits, and surface equipment) greatly affect the drilling performance. This paper introduces a new stochastic model for describing such random effects. This model, when used to optimization design, is more practical and provides a better characterization for real oilfield situations as compared with other deterministic models, and has been demonstrated to be more efficient in solving real design problems of drilling optimizations.     

A stochastic model for wound healing

Three separate activities of wound healing have been identified: migration, proliferation and differentiation. In this paper we present a mathematical model for the activities of migration and proliferation in an invitro system. The motion of a cell is modelled by a two-dimensional Brownian motion in the “unwounded” media. To reflect the proliferative activity in the wound area, we shall impose growth dynamics on the cells which are position dependent. From the resulting motile-growth stochastic model, we are able to estimate the expected number of cells in the wound at time t. From this, the expected time of wound closure can be predicted.     

我国水路货运量短期预测模型

本文对我国逐月水路货运量进行了趋势、季节分析，并利用时间序列分析方法建立了简单、实用的短期预测模型。     

A stochastic block model for interaction lengths

Advances in Data Analysis and Classification - We propose a new stochastic block model that focuses on the analysis of interaction lengths in dynamic networks. The model does not rely on a...     

A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.     

A hyperspherical transformation forecasting model for compositional data

Although Aitchison’s [Aitchison, J., 1986. The Statistical Analysis of Compositional Data, Chapman and Hall, London] method of logratio transformation of compositional data is widely used in various domains, it is limited by the assumption of a strict non-negativity of the components and the requirement of special treatments in practice of the zero components. We propose a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the difficulty in maintaining non-negativity and unit-sum in forecasting compositional data over time. Applying the proposed model to a numerical simulation with a 4D compositional data embedded with zero components and forecasting the three production sectors in the Chinese economy both demonstrate the usefulness and validity of the new approach.     

A two-stage stochastic model for labour wastage

A stochastic model for labour wastage is presented which accounts for the employee's variability on the propensity to leave through dependence on both his length of service and his tenure-in-current-state. The basic assumption underlying the model is that the employee's personal characteristics, the job characteristics and the external labour market conditions are stochastic over time, therefore affecting his decision to stay or leave the company. It is shown that the model provides a good fit to a variety of observed leaving patterns for several companies reported in the literature, explains the relationships among a number of important occupational variables, and is useful for planning purposes in predicting future developments.     

A stochastic model for two interacting species

An exactly solvable stochastic model for two interacting species with a prey-predator relationship in the presence of self-interaction is investigated. The parameters describing the interactions are assumed to be represented by a dichotomic Markov process. Explicit expressions are derived for the time development of the average of the logarithm of the population size in respect of each species and their asymptotic behaviours are discussed.     

A stochastic back-up model

Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 52–63, 1991.     

A stochastic inventory model

Summary In some cases arising in certain industries or military installations not only the demand for a particular commodity is a stochastic variable but its supply as well. In these cases it is convenient to consider the inventory level resulting from the interaction of supply and demand as a third stochastic variable. The variation of the inventory level in time can then be considered as a stochastic process. If this process is ergodic, the total inventory cost over a certain timeT may be represented as a function of the mean inventory level. This mean level can then be manipulated in such a way as to minimize the total inventory cost.

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Zusammenfassung Es kommt vor, daß in gewissen Industriezweigen sowohl der Verbrauch, als auch die Anlieferung eines bestimmten Gutes stochastische Variable sind. In solchen Fällen ist es zweckmäßig, wenn man die aus der Zusammenwirkung von Verbrauch und Anlieferung resultierende Vorratsmenge als eine dritte stochastische Variable einführt. Man kann dann die Oszillationen der Vorratsmenge in der Zeit als einen stochastischen Prozeß auffassen. Falls dieser Prozeß ergodisch ist, können die gesamten Vorratshaltungskosten für eine bestimmte ZeitT dargestellt werden als eine Funktion der mittleren Vorratsmenge. Diese mittlere Vorratsmenge kann dann so bestimmt werden, daß sie die gesamten Vorratshaltungskosten minimalisiert.

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SHAPE Air Defence Technical Centre. Formerly with Tidewater Oil Company, Los Angeles, California, where the present problem was originally investigated.

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Vorgel. v.:J. Nitsche.     

A valuation model for firms with stochastic earnings

A model is proposed to value a firm with stochastic earnings. It is assumed that the earnings of the firm follow a time‐varying mean reverting stochastic process. It is shown that the value of the firm satisfies a boundary value problem of a second‐order partial differential equation, which can be solved numerically. Some special cases are discussed. An analytic solution is found for one special case. Moreover, it is shown that the analytic solution is consistent with a previous result obtained by other researchers. Numerical solutions are obtained for the other special cases. Finally, the model is also applied to value the debt issued by the firm.     

A modified stochastic model for closed birth interval

"Based on some simple assumptions regarding [the] human reproduction process, a continuous time stochastic model for describing the variation in any closed birth interval of a woman of marital duration (t) has been developed. The model incorporates the possibility of the variation of the amenorrhea period among the women under observation. For illustration, the model is applied to an observed closed birth interval between first and second births of the women with marital duration of seven years."     

A mega-trend-diffusion grey forecasting model for short-term manufacturing demand

Accurate short-term demand forecasting is critical for developing effective production plans; however, a short forecasting period indicates that the product demands are unstable, rendering tracking of product development trends difficult. Determining the actual developing data patterns by using forecasting models generated using historical observations is difficult, and the forecasting performance of such models is unfavourable, whereas using the latest limited data for forecasting can improve management efficiency and maintain the competitive advantages of an enterprise. To solve forecasting problems related to a small data set, this study applied an adaptive grey model for forecasting short-term manufacturing demand. Experiments involving the monthly demand data for thin film transistor liquid crystal display panels and wafer-level chip-scale packaging process data showed that the proposed grey model produced favourable forecasting results, indicating its appropriateness as a short-term forecasting tool for small data sets.     

A stochastic model for cell survival after irradiation

This paper deals with the theory of cell survival after irradiation. It is based on the assumption that the cell is composed of two regions with different sensitivities and takes into account phenomena with general repair-time distribution different for each region. Expressions are obtained for the probability that the cell will be damaged and for the mean life time of the cell.     

A novel two-factor forecasting model for fuzzy time series

The study of fuzzy time series has increasingly attracted much attention due to its salient capabilities of tackling vague and incomplete data. A variety of forecasting models have devoted to improving forecasting accuracy, however, the issue of partitioning intervals has rarely been investigated. Recently, we proposed a novel deterministic forecasting model to eliminate the major overhead of determining the k-order issue in high-order models. This paper presents a continued work with focusing on handling the interval partitioning issue by applying the fuzzy c-means technology, which can take the distribution of data points into account and produce unequal-sized intervals. In addition, the forecasting model is extended to allow process twofactor problems. The accuracy superiority of the proposed model is demonstrated by conducting two empirical experiments and comparison to other existing models. The reliability of the forecasting model is further justified by using a Monte Carlo simulation and box plots. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)