Forecasting educational enrolments: Comparison of a Markov chain and circuitless flow network model

Entrants into large complex educational systems typically follow one of many different paths to a successful graduation, transfer-out or drop-out. In contrast to the usual simple Markov chain simulation model employing ‘stock data’, the educational system is presented as a circuitless flow network model employing sub-population student attributes and ‘flow data’. A simple linear model readily projects flow patterns into future grade enrolments. The statistics of a secondary school cohort are used to illustrate the methodologies and contrast the results of the Markov and circuitless flow models.     

Dynamic properties of the welfare caseload

The welfare caseload evolves through a process of flows onto and off of welfare that can be described with a Markov Chain model. Using formal results for Markov models, this paper examines the dynamic properties of the welfare caseload. In particular, we examine steady states, the speed of convergence, and the relative importance of entry and exit for changes in the caseload. Implementing these models with administrative data for California, we find that the welfare caseload has considerable momentum and that adjustments are far from instantaneous. In addition, we find that changes in the entry rate are empirically more important than changes in the exit rate for explaining changes in the overall caseload. These findings have several implications for the conventional methods that are used to study the changing caseload.     

Continuous and discrete models in finance,in particular for stochastic interest rates

The paper explains a general method for constructing interest rate models in discrete time. The relevant term structure can be computed recursively in the Markovian case with finite state space. Calculations become particularly easy for binary and ternary tree structures.It is instructive to look at the diffusion limits of such Markov Chains. This diffusion limit does not inherit all properties of the Markov Chain which it approximates.     

随机波动率LIBOR市场利率动态模型的理论估计与蒙特卡罗模拟

本文首先基于诸多Libor市场模型改进方法的基础之上,在标准市场模型中加入Heston随机波动率过程,建立随机波动率假设的新型Libor市场模型;其次,运用Black逆推参数校正方法和MCMC参数估计方法对该Libor利率市场模型中的局部波动率和随机波动率过程中的参数进行校正和估计;最后是实证模拟。研究结论认为,在构建Libor利率动态模型时,若在单因子Libor利率市场模型基础上引入随机波动率过程,可大大提高利率模型的解释力。     

A Bayesian mixed logit–probit model for multinomial choice

In this paper, we introduce a new flexible mixed model for multinomial discrete choice where the key individual- and alternative-specific parameters of interest are allowed to follow an assumption-free nonparametric density specification, while other alternative-specific coefficients are assumed to be drawn from a multivariate Normal distribution, which eliminates the independence of irrelevant alternatives assumption at the individual level. A hierarchical specification of our model allows us to break down a complex data structure into a set of submodels with the desired features that are naturally assembled in the original system. We estimate the model, using a Bayesian Markov Chain Monte Carlo technique with a multivariate Dirichlet Process (DP) prior on the coefficients with nonparametrically estimated density. We employ a “latent class” sampling algorithm, which is applicable to a general class of models, including non-conjugate DP base priors. The model is applied to supermarket choices of a panel of Houston households whose shopping behavior was observed over a 24-month period in years 2004–2005. We estimate the nonparametric density of two key variables of interest: the price of a basket of goods based on scanner data, and driving distance to the supermarket based on their respective locations. Our semi-parametric approach allows us to identify a complex multi-modal preference distribution, which distinguishes between inframarginal consumers and consumers who strongly value either lower prices or shopping convenience.     

Regression density estimation using smooth adaptive Gaussian mixtures

We model a regression density flexibly so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the components changing smoothly as a function of the covariates. The model extends the existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need fewer components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mechanism that prevents overfitting and makes it feasible to fit flexible high-dimensional surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities, but also that special cases of the general model are interesting models for economic data.     

基于GSPN的装备器材供应链建模与分析

研究了广义随机Petri网（GSPN）的建模及分析方法,建立了基于GSPN的装备器材供应链流程模型,并将Petri网模型转化为等价的马尔可夫链,得出了供应链模型的主要性能指标,据此分析制约供应链的瓶颈。     

Bayesian International Evidence on Heavy Tails, Non-Stationarity and Asymmetry over the Business Cycle

Although leptokurtosis is fairly common in macroeconomic time series, agreement over what non-normal distributions are plausible, is rare. The paper proposes a linear model that allows for trend versus difference stationarity and asymmetric behavior over the business cycle along with several distributional alternatives for the disturbance terms. It proposes computationally feasible Markov Chain Monte Carlo methods to perform Bayesian computations, applies the model to industrial production data of seven industrialized countries, and relies on prior predictive densities to compare models with Student- t , symmetric stable, EGARCH, exponential power family and finite-mixture-of-normals errors. The relationship between unit root inference, asymmetry and leptokurtosis is examined in detail using the exact, finite-sample posteriors corresponding to the different models.     

FORMASY FOrecasting and Recruitment in MAnpower Systems

In this paper the tools are developed for forecasting and recruitment planning in a graded manpower system. Basic features of the presented approach are:
- the system contains several grades or job categories in which the employees stay for a certain time before being promoted or leaving the system,
- promotability and leaving rate for any employee depend on time spent in the job category and personal qualifications (like education, experience, age),
- recruitment is not necessarily restricted to the lowest level in the system,
- several planning aims and restrictions are allowed.
The approach is based on a generalized Markov model for the dynamic behaviour of an individual employee. A forecasting procedure and a recruitment-scheduling procedure are based on this Markov model.     

Modeling node heterogeneity in latent space models for multidimensional networks

Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This article introduces a class of models for multidimensional network data, where different levels of heterogeneity within and between networks can be considered. The proposed framework is developed in the family of latent space models, and it aims to distinguish symmetric relations between the nodes and node-specific features. Model parameters are estimated via a Markov Chain Monte Carlo algorithm. Simulated data and an application to a real example, on fruits import/export data, are used to illustrate and comment on the performance of the proposed models.     

Stick-breaking autoregressive processes

This paper considers the problem of defining a time-dependent nonparametric prior for use in Bayesian nonparametric modelling of time series. A recursive construction allows the definition of priors whose marginals have a general stick-breaking form. The processes with Poisson-Dirichlet and Dirichlet process marginals are investigated in some detail. We develop a general conditional Markov Chain Monte Carlo (MCMC) method for inference in the wide subclass of these models where the parameters of the marginal stick-breaking process are nondecreasing sequences. We derive a generalised Pólya urn scheme type representation of the Dirichlet process construction, which allows us to develop a marginal MCMC method for this case. We apply the proposed methods to financial data to develop a semi-parametric stochastic volatility model with a time-varying nonparametric returns distribution. Finally, we present two examples concerning the analysis of regional GDP and its growth.     

Regime switches and commonalities of the cryptocurrencies asset class

In this paper we test for regime changes and possible regime commonalities in the price dynamics of Bitcoin, Ethereum, Litecoin and Monero, as representatives of the cryptocurrencies asset class. Several parametric models are considered for the joint dynamics of the basket price where parameters are modulated through a Hidden Markov Chain with finite state space. Best specifications within Gaussian and Autoregressive models for price differences are selected by means of the AIC and BIC information criteria and through an out-of-sample forecasting performance. The empirical results, within the period January 2016 to October 2019, suggest that three or four states may be relevant to describe the dynamics of each individual cryptocurrency, depending on the selection criteria, while the entire basket displays at most three common states. Finally, we show how the identification of appropriate models may be exploited in order to build profitable investment strategies on the considered cryptocurrencies.     

A model for identifying and ranking dangerous accident locations: a case study in Flanders

These days, road safety has become a major concern in most modern societies. In this respect, the determination of road locations that are more dangerous than others (black spots or also called sites with promise) can help in better scheduling road safety policies. The present paper proposes a multivariate model to identify and rank sites according to their total expected cost to the society. Bayesian estimation of the model via a Markov Chain Monte Carlo approach is discussed in this paper. To illustrate the proposed model, accident data from 23,184 accident locations in Flanders (Belgium) are used and a cost function proposed by the European Transport Safety Council is adopted to illustrate the model. It is shown in the paper that the model produces insightful results that can help policy makers in prioritizing road infrastructure investments.     

Markov models and the utilization of mental health services: a study of endogenously depressed patients.

Patients in the mental health care system typically make more or less irregularly spaced visits to psychiatrists, both within and between episodes of a given illness. A Markov model is constructed which can predict the utilization of psychiatric services for such patients. Unlike previous Markov models of utilization, the current model takes as its starting point a model of an actual disease, specifically, endogenous depression. It is shown how one can estimate the parameters of both the model of utilization and the model of depression using data which were collected for clinical research purposes. The models provide reasonable fits to the data. Several applications of the models are worked out. In addition to predicting the utilization of mental health services, the models can be used to predict incidence, prevalence and recovery rates and to predict the changes in utilization which parallel changes in treatment regimens.     

The structure of dynamic correlations in multivariate stochastic volatility models

This paper proposes two types of stochastic correlation structures for Multivariate Stochastic Volatility (MSV) models, namely the constant correlation (CC) MSV and dynamic correlation (DC) MSV models, from which the stochastic covariance structures can easily be obtained. Both structures can be used for purposes of determining optimal portfolio and risk management strategies through the use of correlation matrices, and for calculating Value-at-Risk (VaR) forecasts and optimal capital charges under the Basel Accord through the use of covariance matrices. A technique is developed to estimate the DC MSV model using the Markov Chain Monte Carlo (MCMC) procedure, and simulated data show that the estimation method works well. Various multivariate conditional volatility and MSV models are compared via simulation, including an evaluation of alternative VaR estimators. The DC MSV model is also estimated using three sets of empirical data, namely Nikkei 225 Index, Hang Seng Index and Straits Times Index returns, and significant dynamic correlations are found. The Dynamic Conditional Correlation (DCC) model is also estimated, and is found to be far less sensitive to the covariation in the shocks to the indexes. The correlation process for the DCC model also appears to have a unit root, and hence constant conditional correlations in the long run. In contrast, the estimates arising from the DC MSV model indicate that the dynamic correlation process is stationary.     

Chain-Store Pricing Across Local Markets

Chain‐stores now dominate most areas of retailing. While retailers may operate nationally or even internationally, the markets they compete in are largely local. How should they best operate pricing policy in respect of the different markets served—price uniformly across the local markets or on a local basis according to market conditions? We model this by allowing local market differences, with retail markets differing by their size and the number of players present. We show that practising price discrimination is not always best for a chain‐store. Competitive conditions exist under which uniform pricing can raise profits.     

A Guide to Exact Simulation

Markov Chain Monte Carlo (MCMC) methods are used to sample from complicated multivariate distributions with normalizing constants that may not be computable in practice and from which direct sampling is not feasible. A fundamental problem is to determine convergence of the chains. Propp & Wilson (1996) devised a Markov chain algorithm called Coupling From The Past (CFTP) that solves this problem, as it produces exact samples from the target distribution and determines automatically how long it needs to run. Exact sampling by CFTP and other methods is currently a thriving research topic. This paper gives a review of some of these ideas, with emphasis on the CFTP algorithm. The concepts of coupling and monotone CFTP are introduced, and results on the running time of the algorithm presented. The interruptible method of Fill (1998) and the method of Murdoch & Green (1998) for exact sampling for continuous distributions are presented. Novel simulation experiments are reported for exact sampling from the Ising model in the setting of Bayesian image restoration, and the results are compared to standard MCMC. The results show that CFTP works at least as well as standard MCMC, with convergence monitored by the method of Raftery & Lewis (1992, 1996).     

A unified approach to nonlinearity,structural change,and outliers

This paper demonstrates that the class of conditionally linear and Gaussian state-space models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach.     

Ein Referenzmodell für das Sustainable Supply Chain Management

Sustainable Supply Chain Management entails both risks and chances for companies: on the one hand (environmental) legislation often disregards economic interests; on the other hand customers increasingly choose eco-friendly products. But how can sustainable management, i.e. a balanced consideration of ecological, economic and social aspects be ensured for logistics networks? First, the authors of this article determine the state of the art of Sustainable Supply Chain Management by conducting a systematic literature review. On the basis of the review results they develop a reference model which is suitable to serve as a framework for the design of future Sustainable Supply Chain Management (SSCM) models. The model elements “Maturity Model”, “Stakeholder Model” and “Steering Model” are implemented by means of the software ADOit.     

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.