Statistical Assessment of Numerical Models*

Evaluation of physically based computer models for air quality applications is crucial to assist in control strategy selection. The high risk of getting the wrong control strategy has costly economic and social consequences. The objective comparison of modeled concentrations with observed field data is one approach to assessment of model performance. For dry deposition fluxes and concentrations of air pollutants there is a very limited supply of evaluation data sets. We develop a formal method for evaluation of the performance of numerical models, which can be implemented even when the field measurements are very sparse. This approach is applied to a current U.S. Environmental Protection Agency air quality model. In other cases, exemplified by an ozone study from the California Central Valley, the observed field is relatively data rich, and more or less standard geostatistical tools can be used to compare model to data. Yet another situation is when the cost of model runs is prohibitive, and a statistical approach to approximating the model output is needed. We describe two ways of obtaining such approximations. A common technical issue in the assessment of environmental numerical models is the need for tools to estimate nonstationary spatial covariance structures. We describe in detail two such approaches.     

非寿险精算中的贝叶斯信用模型分析

针对传统B櫣hlmann-Straub信用模型不能有效地解决缺失数据信息处理问题,本文利用贝叶斯统计方法,构造了一类新的贝叶斯信用分析模型,引入基于吉布斯抽样的马尔科夫链蒙特卡洛方法进行数值计算,建立了一个索赔后验分层正态模型进行实证分析,证明模型的有效性。研究结果表明,基于MCMC的贝叶斯信用模型能够动态模拟模型参数的后验分布,提高模型估计的精度,对保险公司经验费率厘定方法的改进具有重要的现实意义。     

Comparison of Sampling Schemes for Dynamic Linear Models

Hyperparameter estimation in dynamic linear models leads to inference that is not available analytically. Recently, the most common approach is through MCMC approximations. A number of sampling schemes that have been proposed in the literature are compared. They basically differ in their blocking structure. In this paper, comparison between the most common schemes is performed in terms of different efficiency criteria, including efficiency ratio and processing time. A sample of time series was simulated to reflect different relevant features such as series length and system volatility.     

A Bayesian Multiple Comparison Procedure for Order-Restricted Mixed Models

A Bayesian hierarchical mixed model is developed for multiple comparisons under a simple order restriction. The model facilitates inferences on the successive differences of the population means, for which we choose independent prior distributions that are mixtures of an exponential distribution and a discrete distribution with its entire mass at zero. We employ Markov Chain Monte Carlo (MCMC) techniques to obtain parameter estimates and estimates of the posterior probabilities that any two of the means are equal. The latter estimates allow one both to determine if any two means are significantly different and to test the homogeneity of all of the means. We investigate the performance of the model-based inferences with simulated data sets, focusing on parameter estimation and successive-mean comparisons using posterior probabilities. We then illustrate the utility of the model in an application based on data from a study designed to reduce lead blood concentrations in children with elevated levels. Our results show that the proposed hierarchical model can effectively unify parameter estimation, tests of hypotheses and multiple comparisons in one setting.     

Density forecasting through disaggregation

In this paper, the revised expectations model (REM) is developed to incorporate economic agents’ price expectation formation effects. With this incorporation, two models, an aggregate one sector model and a disaggregated multi-sector model, are estimated and used in density forecasting of the US real GDP growth rate. The experiment shows that use of the disaggregated version of the model, which incorporates price expectation effects along with modern Bayesian MCMC estimation and prediction techniques, produces more precise density forecasts than those yielded by either an aggregate version or benchmark forecasting models.     

Space-varying Coefficient Simultaneous Autoregressive Models for the Structural Analysis of Residential Water Demand

Abstract

This study develops two space-varying coefficient simultaneous autoregressive (SVC-SAR) models for areal data and applies them to the discrete/continuous choice model, which is an econometric model based on the consumer's utility maximization problem. The space-varying coefficient model is a statistical model in which the coefficients vary depending on their location. This study introduces the simultaneous autoregressive model for the underlying spatial dependence across coefficients, where the coefficients for one observation are affected by the sum of those for the other observations. This model is named the SVC-SAR model. Because of its flexibility, we use the Bayesian approach and construct its estimation method based on the Markov chain Monte Carlo simulation. The proposed models are applied to estimate the Japanese residential water demand function, which is an example of the discrete/continuous choice model.     

城市物流系统模式的统计划分方法

本文首先论证了构建中心城市物流系统的必要性；其次以中心城市流通客体的流向、流量为主要参数，综合考虑影响中心城市物流系统的经济因素、产业结构和物流基础设施水平等，得出中心城市物流系统的三种模型，即产出型、消费型和综合型物流系统。     

Hierarchical Models in Environmental Science

Environmental systems are complicated. They include very intricate spatio-temporal processes, interacting on a wide variety of scales. There is increasingly vast amounts of data for such processes from geographical information systems, remote sensing platforms, monitoring networks, and computer models. In addition, often there is a great variety of scientific knowledge available for such systems, from partial differential equations based on first principles to panel surveys. It is argued that it is not generally adequate to consider such processes from a joint perspective. Instead, the processes often must be considered as a coherently linked system of conditional models. This paper provides a brief overview of hierarchical approaches applied to environmental processes. The key elements of such models can be considered in three general stages, the data stage, process stage, and parameter stage. In each stage, complicated dependence structure is mitigated by conditioning. For example, the data stage can incorporate measurement errors as well as multiple datasets with varying supports. The process and parameter stages can allow spatial and spatio-temporal processes as well as the direct inclusion of scientific knowledge. The paper concludes with a discussion of some outstanding problems in hierarchical modelling of environmental systems, including the need for new collaboration approaches.     

A direct Monte Carlo approach for Bayesian analysis of the seemingly unrelated regression model

Computationally efficient methods for Bayesian analysis of seemingly unrelated regression (SUR) models are described and applied that involve the use of a direct Monte Carlo (DMC) approach to calculate Bayesian estimation and prediction results using diffuse or informative priors. This DMC approach is employed to compute Bayesian marginal posterior densities, moments, intervals and other quantities, using data simulated from known models and also using data from an empirical example involving firms’ sales. The results obtained by the DMC approach are compared to those yielded by the use of a Markov Chain Monte Carlo (MCMC) approach. It is concluded from these comparisons that the DMC approach is worthwhile and applicable to many SUR and other problems.     

Approximate Bayesian Computation for a Class of Time Series Models

In the following article, we consider approximate Bayesian computation (ABC) for certain classes of time series models. In particular, we focus upon scenarios where the likelihoods of the observations and parameter are intractable, by which we mean that one cannot evaluate the likelihood even up to a non‐negative unbiased estimate. This paper reviews and develops a class of approximation procedures based upon the idea of ABC, but specifically maintains the probabilistic structure of the original statistical model. This latter idea is useful, in that one can adopt or adapt established computational methods for statistical inference. Several existing results in the literature are surveyed, and novel developments with regards to computation are given.     

The Statistical Interpretation of Forensic Glass Evidence

When examining a sample of glass fragments recovered from a suspect in a forensic case, many questions arise: “Did this man break that window?”, “Are these fragments from the crime scene source?”, “Do the fragments recovered from the suspect come from more than one source?”, “How common is it to find glass on someone unrelated with crime?” etc. Such questions are usually answered with the help of statistical methods. This paper reviews some of the statistical solutions and problems encountered in the interpretation and evaluation of forensic glass evidence.     

Interview with Professor Adrian FM Smith

Adrian Smith joined The Alan Turing Institute as Institute Director and Chief Executive in September 2018. In May 2020, he was confirmed as President Elect of the Royal Society. He is also a member of the government's AI Council, which helps boost AI growth in the UK and promote its adoption and ethical use in businesses and organisations across the country. Professor Smith's previous role was Vice-Chancellor of the University of London where he was in post from 2012. He is a past President of the Royal Statistical Society and was elected a Fellow of the Royal Society in 2001 in recognition of his contribution to statistics. In 2003-04 Professor Smith undertook an inquiry into Post-14 Mathematics Education for the UK Secretary of State for Education and Skills and in 2017, on behalf of Her Majesty's Treasury and the Department for Education, published a 16-18 Maths Review. In 2006 he completed a report for the UK Home Secretary on the issue of public trust in Crime Statistics. He received a knighthood in the 2011 New Year Honours list. The following conversation took place at the Alan Turing Institute in London, on July 19 2019.     

Bayesian estimation of transition probabilities from repeated cross sections

This paper discusses some simple practical advantages of Markov chain Monte Carlo (MCMC) methods in estimating entry and exit transition probabilities from repeated independent surveys. Simulated data are used to illustrate the usefulness of MCMC methods when the likelihood function has multiple local maxima. Actual data on the evaluation of an HIV prevention intervention program among drug users are used to demonstrate the advantage of using prior information to enhance parameter identificaiton. The latter example also demonstrates an important strength of the MCMC approach, namely the ability to make inferences on arbitrary functions of model parameters.     

Small-sample Properties of Panel Spatial Autoregressive Models: Comparison of the Bayesian and Maximum Likelihood Methods

Abstract

This article considers autoregressive (SAR) models. We method to estimate the parameters of likelihood (ML) method. Our Bayesian by the Monte Carlo studies. We found the efficient as the ML estimators.     

我国财政支出政策冲击效应的动态变化——基于包含随机波动的时变参数模型的考察

本文采用能够同时捕捉区制转换性变化和累积性变化的包含随机波动的时变参数结构向量自回归模型实证考察了1995~2009年间我国政府支出冲击效应的动态变化。结果表明虽然财政支出冲击的传导机制出现了局部的趋势性变化,但是对冲击效应的影响并不显著;冲击效应的大小主要取决于冲击本身的波动性。冲击的波动越大,冲击效应水平越高。这也使得冲击效应的动态变化在样本期间上表现出明显的区制转换性特征。     

Full Likelihood Inference in Normal-Gamma Stochastic Frontier Models

The paper takes up inference in the stochastic frontier model with gamma distributed inefficiency terms, without restricting the gamma distribution to known integer values of its shape parameter (the Erlang form). The paper shows that Gibbs sampling with data augmentation can be used in a computationally efficient way to explore the posterior distribution of the model and conduct inference regarding parameters as well as functions of interest related to technical inefficiency.     

General Bayesian time-varying parameter vector autoregressions for modeling government bond yields

US yield curve dynamics are subject to time-variation, but there is ambiguity about its precise form. This paper develops a vector autoregressive (VAR) model with time-varying parameters and stochastic volatility, which treats the nature of parameter dynamics as unknown. Coefficients can evolve according to a random walk, a Markov switching process, observed predictors, or depend on a mixture of these. To decide which form is supported by the data and to carry out model selection, we adopt Bayesian shrinkage priors. Our framework is applied to model the US yield curve. We show that the model forecasts well, and focus on selected in-sample features to analyze determinants of structural breaks in US yield curve dynamics.     

Conditional value-at-risk forecasts of an optimal foreign currency portfolio

This study provides daily conditional value-at-risk (C-VaR) forecasts for a foreign currency portfolio comprising the USD/EUR, USD/JPY, and USD/BRL currencies. To do so, we estimate multivariate stochastic volatility models with time-varying conditional correlations using a Bayesian Markov chain Monte Carlo algorithm. Then, given the model-specific currency return density forecasts, we make the optimal portfolio choice by minimizing the C-VaR through numerical optimization. According to out-of-sample experiment, including emerging markets into the currency basket is essential for downside risk management, and considering model uncertainty as well as the parameter uncertainty can improve the portfolio performance.     

The Statistical Education of Harold Jeffreys

The paper considers the statistical work of the physicist Harold Jeffreys. In 1933–4 Jeffreys had a controversy with R.A. Fisher, the leading statistician of the time. Prior to the encounter, Jeffreys had worked on probability as the basis for scientific inference and had used methods from the theory of errors in astronomy and seismology. He had also started to rework the theory of errors on the basis of his theory of probability. After the encounter Jeffreys produced a full-scale Bayesian treatment of statistics in the form of his Theory of Probability.