Signaalstroomdiagrammen en Markov-ketens

The transient behavior of a simple two-state discrete Markov process can be studied by means of matrix-multiplication and z-transformations.
For linear systems the output is equal to the convolution of the input and the impulse response of the system. By taking z-transforms the convolution can be avoided: the transform of the output is equal to the transform of the input multiplied by the transform of the impulse response of the system.
The signal flow graph method is the transformation of the matrix-method of solving a system of simultaneous equations in a topological method.
The simple two-state discrete Markov process can be represented by such a flow graph and it is shown how to simplify this flow graph step by step. Taking as input the unit-impulse at time zero, the output of this system at time n turns out to be the n-step transition-probability.
The results for the transmission in a network are mentioned (Mason and Zimmermann [8]). With these results it is possible to give at once the n-step transition probability of a system without first simplifying the flow graph.
Building on this result signal flow graphs can be used to determine the chance to be for the first time in a certain state, the average number of times a system is in a certain state and the chance to reach a certain state for the first time before another state of the system has been reached.
Finally the results are extended to continuous Markov processes.     

Bayesian Model Selection of Gaussian Directed Acyclic Graph Structures

During the last years, graphical models have become a popular tool to represent dependencies among variables in many scientific areas. Typically, the objective is to discover dependence relationships that can be represented through a directed acyclic graph (DAG). The set of all conditional independencies encoded by a DAG determines its Markov property. In general, DAGs encoding the same conditional independencies are not distinguishable from observational data and can be collected into equivalence classes, each one represented by a chain graph called essential graph (EG). However, both the DAG and EG space grow super exponentially in the number of variables, and so, graph structural learning requires the adoption of Markov chain Monte Carlo (MCMC) techniques. In this paper, we review some recent results on Bayesian model selection of Gaussian DAG models under a unified framework. These results are based on closed-form expressions for the marginal likelihood of a DAG and EG structure, which is obtained from a few suitable assumptions on the prior for model parameters. We then introduce a general MCMC scheme that can be adopted both for model selection of DAGs and EGs together with a couple of applications on real data sets.     

Disconnecting graphs by removing vertices: a polyhedral approach

In this paper, we consider the problem of disconnecting a graph by removing as few vertices as possible, such that no component of the disconnected graph has more than a given number of vertices. We give applications of this problem, present a formulation for it, and describe some polyhedral results. Furthermore, we establish ties with other polytopes and show how these relations can be used to obtain facets of our polytope. Finally, we give some computational results.     

A top-down approach for approximate data anonymisation

Data sharing in today's information society poses a threat to individual privacy and organisational confidentiality. k-anonymity is a widely adopted model to prevent the owner of a record being re-identified. By generalising and/or suppressing certain portions of the released dataset, it guarantees that no records can be uniquely distinguished from at least other k?1 records. A key requirement for the k-anonymity problem is to minimise the information loss resulting from data modifications. This article proposes a top-down approach to solve this problem. It first considers each record as a vertex and the similarity between two records as the edge weight to construct a complete weighted graph. Then, an edge cutting algorithm is designed to divide the complete graph into multiple trees/components. The Large Components with size bigger than 2k?1 are subsequently split to guarantee that each resulting component has the vertex number between k and 2k?1. Finally, the generalisation operation is applied on the vertices in each component (i.e. equivalence class) to make sure all the records inside have identical quasi-identifier values. We prove that the proposed approach has polynomial running time and theoretical performance guarantee O(k). The empirical experiments show that our approach results in substantial improvements over the baseline heuristic algorithms, as well as the bottom-up approach with the same approximate bound O(k). Comparing to the baseline bottom-up O(logk)-approximation algorithm, when the required k is smaller than 50, the adopted top-down strategy makes our approach achieve similar performance in terms of information loss while spending much less computing time. It demonstrates that our approach would be a best choice for the k-anonymity problem when both the data utility and runtime need to be considered, especially when k is set to certain value smaller than 50 and the record set is big enough to make the runtime have to be taken into account.     

Generalized densities of order statistics

Let X ₁, ... , X _n be independent identically distributed random variables with distribution F . We derive expressions for generalized joint 'densities' of order statistics of X ₁, ... , X _n , for arbitrary distributions F , in terms of Radon–Nikodym derivatives with respect to product measures based on F . We then give formulae for conditional distributions of order statistics and use them to derive results concerning Markov properties of order statistics, formulae for distributions of trimmed sums, and other useful representations. Our approach leads to simple and natural expressions which appear not to have been given before.     

一类树的Hosoya指标序列

许多拓扑指标都与分子的某些物理化学性质密切相关,而不同的分子拓扑指标反映该分子的不同性能。其中Hosoya指标是较为重要的拓扑指标之一。设G一个分子结构图模型,即为一个具有n个顶点的连通图,则图G的Hosoya指标Z(G),是指这样一些子集的个数,每一个子集中的任意两条边在图G中都没有公共的顶点,即图G中匹配的个数,包括空集。本文讨论了一类四叶树的Hosoya指标序列。     

On a bivariate Markov process arising in the theory of single-server retrial queues

We introduce a bivariate Markov process which can be seen as the joint process of the channel state and the number of customers in orbit of a Markovian single-server retrial queue with state dependent intensities. We obtain a necessary and sufficient condition for the process to be regular, and necessary and sufficient conditions for ergodicity and recurrence. A product-form formula for the stationary distribution is obtained. Besides, we study the busy period, the number of served customers and other related quantities. We show that for all the above problems there exist "equivalent" birth-and-death processes. However, a "uniformly equivalent" birth-and-death process does not exist.     

禁忌搜索算法解决赋权覆盖问题

赋权覆盖问题在顶点个数很大的情况下很难用普通算法来解决,这篇试图用禁忌搜索算法来解决该问题,提出相应的各种技术指标,设计相应的算法,在计算机容许范围内求出一个图的边覆盖和最小覆盖数,具有较高的实用价值。     

ON THE FIRST–ORDER EFFICIENCY AND ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS OBTAINED FROM DEPENDENT OBSERVATIONS

Abstract. In this paper we study the first–order efficiency and asymptotic normality of the maximum likelihood estimator obtained from dependent observations. Our conditions are weaker than usual, in that we do not require convergences in probability to be uniform or third–order derivatives to exist.
The paper builds on Witting and Nolle's result concerning the asymptotic normality of the maximum likelihood estimator obtained from independent and identically distributed observations, and on a martingale theorem by McLeish.     

EMBEDDED MATRICES FOR FINITE MARKOV CHAINS

For an arbitrary subset A of the finite state space 5 of a Markov chain the so–called embedded matrix P _A is introduced. By use of these matrices formulas expressing all kinds of probabilities can be written down almost automatically, and calculated very easily on a computer. Also derivations can be given very systematically.     

Monotone dependence in graphical models for multivariate Markov chains

We show that a deeper insight into the relations among marginal processes of a multivariate Markov chain can be gained by testing hypotheses of Granger noncausality, contemporaneous independence and monotone dependence. Granger noncausality and contemporaneous independence conditions are read off a mixed graph, and the dependence of an univariate component of the chain on its parents—according to the graph terminology—is described in terms of stochastic dominance criteria. The examined hypotheses are proven to be equivalent to equality and inequality constraints on some parameters of a multivariate logistic model for the transition probabilities. The introduced hypotheses are tested on real categorical time series.     

Endogenously Asynchronous Entries into an Uncertain Industry

We model and analyze a priori symmetric duopoly where supply quantity adjustment is slow and time-consuming. The state of demand is ex ante uncertain, and becomes observable a certain time period after at least one firm's entry. We characterize those conditions under which sequential entries can be endogenously chosen either as an asymmetric pure-strategy equilibrium or as a consequence of a symmetric mixed-strategy equilibrium. Also, in the limit where information revelation is infinitely fast (i.e., the time period it requires becomes infinitesimally short), the expected waiting time until the first entry does not necessarily become proportionately short, whilst the time interval between the leader's entry and the follower's entry does become infinitesimally short. This suggests that chronologically nearly simultaneous entry should not necessarily be interpreted as counterevidence against leader-follower relations. In addition to equilibrium comparative statics, we also analyze some of the welfare issues associated with strategic timing of entry.     

Estimation and Solution of Models with Expectations and Structural Changes

In this paper, we develop solutions for linearized models with forward‐looking expectations and structural changes under a variety of assumptions regarding agents' beliefs about those structural changes. For each solution, we show how its associated likelihood function can be constructed by using a ‘backward–forward’ algorithm. We illustrate the techniques with two examples. The first considers an inflationary program in which beliefs about the inflation target evolve differently from the inflation target itself, and the second applies the techniques to estimate a new Keynesian model through the Volcker disinflation. We compare our methodology with the alternative in which structural change is captured by switching between regimes via a Markov switching process. We show that our method can produce accurate results much faster than the Markov switching method as well as being easily adapted to handle beliefs departing from reality. Copyright © 2016 John Wiley & Sons, Ltd.     

Latent Markov Modelling of Recidivism Data

This article discusses the application of latent Markov modelling for the analysis of recidivism data. We briefly examine the relations of Markov modelling with log–linear analysis, pointing out pertinent differences as well. We show how the restrictive Markov model may be more easily applicable by adding latent variables to the model, in which case the latent Markov model is a dynamic version of the latent class model. As an illustration, we apply latent Markov analysis on an empirical data set of juvenile prosecution careers, showing how the Markov analyses producing well-fitting and interpretable solutions. We end by comparing the possible contributions of Markov modelling in recidivism research, outlining its drawbacks as well. Recommendations and directions for future research conclude the article.     

Een model voor discreet verdeelde grootheden met negatieve correlatie

Summary
A model for negatively correlated variables.
A mathematical model is described with which a bivariate distribution of two negatively correlated binomially distributed variables can be constructed. Let be given a vase with W white, Z black and R red balls; N = W + Z + R; P1= W: N;P2 = Z: N.
Let be drawn a random sample with replacement of n balls. Let be w = number of white en z = number of black balls; w + z < n. Then and are binomially distributed variates, correlated according to (1).
At the end of the paper the author formulates the following statistical problem: let be drawn a finite number of times () such random samples of n balls. The pairs w, z furnish a correlation coefficient r, which itself is a stochastical variable. How is the distribution of? In particular what are the expectation (, N) and the standard deviation (k, n, N)     

Likelihood-based inference for regular functions with fractional polynomial approximations

This paper shows that regular fractional polynomials can approximate regular cost, production and utility functions and their first two derivatives on closed compact subsets of the strictly positive orthant of Euclidean space arbitrarily well. These functions therefore can provide reliable approximations to demand functions and other economically relevant characteristics of tastes and technology. Using canonical cost function data, it shows that full Bayesian inference for these approximations can be implemented using standard Markov chain Monte Carlo methods.     

Exit problems in regime-switching models

This paper provides a general framework for pricing of perpetual American and real options in regime-switching Lévy models. In each state of the Markov chain, which determines switches from one Lévy process to another, the payoff stream is a monotone function of the Lévy process labeled by the state. This allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). The pricing procedure is efficient even if the number of states is large provided the transition rates are not very large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. As an application, we solve exit problems for a price-taking firm, and study the dependence of the exit threshold on the interest rate uncertainty.     

Simultaneous search with heterogeneous firms and ex post competition

In this paper we study the allocation of workers over high and low productivity firms in a labor market with coordination frictions. Specifically, we consider a search model where workers can apply to high and or low productivity firms. Firms that compete for the same candidate can increase their wage offers as often as they like. We show that if workers apply to two jobs, there is a unique symmetric equilibrium where workers mix between sending both applications to the high and sending both to the low productivity sector. But, efficiency requires that they apply to both sectors because a higher matching rate in the high-productivity sector can then be realized with fewer applications (and consequently fewer coordination frictions) if workers always accept the offer of the most productive firm. However, in the market the worker's payoff is determined by how much the firm with the second highest productivity is willing to bid. This is what prevents them from applying to both sectors. For many configurations, the equilibrium outcomes are the same under directed and random search so our results are not driven by random search. We discuss the effects of increasing the number of applications and show that our results can easily be generalized to N-firms.     

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.     

具有不规则平面的高层建筑结构选型与设计

针对不规则平面的结构特征及高层建筑的特点，从概念设计和计算设计两方面入手，综合分析各相关因素，提出适应于不规则平面特征的结构选型及结构布置方法。经实践证明，该方法概念明确，结构受力合理，结构构造简便有效，达到安全、适用和经济的统一。可供类似工程的设计参考。