关于Polya罐子模型的几个结论

在Polya罐子模型中,分别以Xn,Sn表示第n次抽球并放回后罐中的黑球比例数和在前n次抽球中抽到黑球的次数,得到了Sn/n的极限分布为贝塔分布以及E（Xn）等于E（X∞）,D（Xn）不等于D（X∞）等几个重要结论,并分别运用概率论知识和随机过程的鞅理论知识从不同角度证明结论.     

Forecasting under model uncertainty: Non-homogeneous hidden Markov models with Pòlya-Gamma data augmentation

We consider finite state-space non-homogeneous hidden Markov models for forecasting univariate time series. Given a set of predictors, the time series are modeled via predictive regressions with state-dependent coefficients and time-varying transition probabilities that depend on the predictors via a logistic/multinomial function. In a hidden Markov setting, inference for logistic regression coefficients becomes complicated and in some cases impossible due to convergence issues. In this paper, we aim to address this problem utilizing the recently proposed Pólya-Gamma latent variable scheme. Also, we allow for model uncertainty regarding the predictors that affect the series both linearly — in the mean — and non-linearly — in the transition matrix. Predictor selection and inference on the model parameters are based on an automatic Markov chain Monte Carlo scheme with reversible jump steps. Hence the proposed methodology can be used as a black box for predicting time series. Using simulation experiments, we illustrate the performance of our algorithm in various setups, in terms of mixing properties, model selection and predictive ability. An empirical study on realized volatility data shows that our methodology gives improved forecasts compared to benchmark models.     

Microbes,mathematics, and models

Microbial model systems have a long history of fruitful use in fields that include evolution and ecology. In order to develop further insight into modelling practice, we examine how the competitive exclusion and coexistence of competing species have been modelled mathematically and materially over the course of a long research history. In particular, we investigate how microbial models of these dynamics interact with mathematical or computational models of the same phenomena. Our cases illuminate the ways in which microbial systems and equations work as models, and what happens when they generate inconsistent findings about shared targets. We reveal an iterative strategy of comparative modelling in different media, and suggest reasons why microbial models have a special degree of epistemic tractability in multimodel inquiry.     

Long Memory of Financial Time Series and Hidden Markov Models with Time‐Varying Parameters

Hidden Markov models are often used to model daily returns and to infer the hidden state of financial markets. Previous studies have found that the estimated models change over time, but the implications of the time‐varying behavior have not been thoroughly examined. This paper presents an adaptive estimation approach that allows for the parameters of the estimated models to be time varying. It is shown that a two‐state Gaussian hidden Markov model with time‐varying parameters is able to reproduce the long memory of squared daily returns that was previously believed to be the most difficult fact to reproduce with a hidden Markov model. Capturing the time‐varying behavior of the parameters also leads to improved one‐step density forecasts. Finally, it is shown that the forecasting performance of the estimated models can be further improved using local smoothing to forecast the parameter variations. Copyright © 2016 John Wiley & Sons, Ltd.     

非下采样Contourlet HMT模型

非下采样Contourlet变换（NSCT）不仅具有类似传统小波变换和Contourlet变换的多尺度和多方向特性,而且还具有良好的平移不变特性．文中对NSCT变换系数进行研究,获得NSCT变换的方向子带系数同样具有持续性和聚集性的结论;在此基础上结合隐Markov树模型,建立了一种新的基于NSCT域的隐Markov树模型NSCT—HMT,并且给出了该模型的参数结构以及模型参数的训练方法;最后将所提出的模型应用于图像去噪中取得了很好的仿真效果．     

改进萤火虫算法及其收敛性分析

萤火虫算法因具有结构简单、控制参数少、易于实现的特点而得到广泛的关注和应用,但其易陷入局部最优导致过早收敛,从而影响寻优精度。针对这一问题,本文在位置更新规则中加入随机扰动因子,并剔除了冗余的随机项,以提高算法搜索能力;引入位置置换变异和差分进化算法中的最优变异策略,在保持种群多样性的同时,增强算法跳出局部最优的能力。采用马尔可夫过程证明了算法以概率1收敛到全局最优。利用基准函数和装箱问题对算法进行仿真测试,结果表明,改进后的算法能够有效跳出局部最优,对给出的所有问题均能找到理论最优解,寻优精度和成功率有明显提升。     

一种高识别率的语音密码锁

采用基于统计模型的隐马尔可夫模型(hidden Markov model,HMM)来描述语音模型,进行语音模型库训练,并使用模板匹配的Viterbi算法进行语音识别,实现了以凌阳16位单片机SPCE061A为核心的语音密码锁系统,包括键盘模块、电源模块、门锁控制模块、LCD显示模块。该密码锁将语音密码和键盘密码技术相结合以保证系统安全性,通过测试,系统对特定人语音识别率为98%。     

语音识别中HMM与自组织神经网络结合的混合模型

基于隐马尔可夫模型和自组织神经网络模型提出了一种用于语音识别的混合模型,给出了训练调整权向量的算法,实验结果表明其在语音识别中具有很好的性能·     

The Constructive Realist Account of Science and Its Application to Ilya Prigogine’s Conception of Laws of Nature

Sciences are often regarded as providing the best, or, ideally, exact, knowledge of the world, especially in providing laws of nature. Ilya Prigogine, who was awarded the Nobel Prize for his theory of non-equilibrium chemical processes—this being also an important attempt to bridge the gap between exact and non-exact sciences [mentioned in the Presentation Speech by Professor Stig Claesson (nobelprize.org, The Nobel Prize in Chemistry 1977)]—has had this ideal in mind when trying to formulate a new kind of science. Philosophers of science distinguish theory and reality, examining relations between these two. Nancy Cartwright’s distinction of fundamental and phenomenological laws, Rein Vihalemm’s conception of the peculiarity of the exact sciences, and Ronald Giere’s account of models in science and science as a set of models are deployed in this article to criticise the common view of science and analyse Ilya Prigogine’s view in particular. We will conclude that on a more abstract, philosophical level, Prigogine’s understanding of science doesn’t differ from the common understanding.

Models as products of interdisciplinary exchange: Evidence from evolutionary game theory

The development of evolutionary game theory (EGT) is closely linked with two interdisciplinary exchanges: the import of game theory into biology, and the import of biologists’ version of game theory into economics. This paper traces the history of these two import episodes. In each case the investigation covers what exactly was imported, what the motives for the import were, how the imported elements were put to use, and how they related to existing practices in the respective disciplines. Two conclusions emerged from this study. First, concepts derived from the unity of science discussion or the unification accounts of explanation are too strong and too narrow to be useful for analysing these interdisciplinary exchanges. Secondly, biology and economics—at least in relation to EGT—show significant differences in modelling practices: biologists seek to link EGT models to concrete empirical situations, whereas economists pursue conceptual exploration and possible explanation.