Learning from a lot: Empirical Bayes for high‐dimensional model‐based prediction

Empirical Bayes is a versatile approach to “learn from a lot” in two ways: first, from a large number of variables and, second, from a potentially large amount of prior information, for example, stored in public repositories. We review applications of a variety of empirical Bayes methods to several well‐known model‐based prediction methods, including penalized regression, linear discriminant analysis, and Bayesian models with sparse or dense priors. We discuss “formal” empirical Bayes methods that maximize the marginal likelihood but also more informal approaches based on other data summaries. We contrast empirical Bayes to cross‐validation and full Bayes and discuss hybrid approaches. To study the relation between the quality of an empirical Bayes estimator and p, the number of variables, we consider a simple empirical Bayes estimator in a linear model setting. We argue that empirical Bayes is particularly useful when the prior contains multiple parameters, which model a priori information on variables termed “co‐data”. In particular, we present two novel examples that allow for co‐data: first, a Bayesian spike‐and‐slab setting that facilitates inclusion of multiple co‐data sources and types and, second, a hybrid empirical Bayes–full Bayes ridge regression approach for estimation of the posterior predictive interval.     

Linear scalar-on-surface random effects regression models

Many research fields increasingly involve analyzing data of a complex structure. Models investigating the dependence of a response on a predictor have moved beyond the ordinary scalar-on-vector regression. We propose a regression model for a scalar response and a surface (or a bivariate function) predictor. The predictor has a random component and the regression model falls in the framework of linear random effects models. We estimate the model parameters via maximizing the log-likelihood with the ECME (Expectation/Conditional Maximization Either) algorithm. We use the approach to analyze a data set where the response is the neuroticism score and the predictor is the resting-state brain function image. In the simulations we tried, the approach has better performance than two other approaches, a functional principal component regression approach and a smooth scalar-on-image regression approach.     

Noninformative priors for the between-group variance in the unbalanced one-way random effects model with heterogeneous error variances

For the unbalanced one-way random effects model with heterogeneous error variances, we propose the non-informative priors for the between-group variance and develop the first- and second-order matching priors. It turns out that the second-order matching priors do not exist and the reference prior and Jeffreys prior do not satisfy a first-order matching criterion. We also show that the first-order matching prior meets the frequentist target coverage probabilities much better than the Jeffreys prior and reference prior through simulation study, and the Bayesian credible intervals based on the matching prior and reference prior give shorter intervals than the existing confidence intervals by examples.     

A Graphical Tool for Interpreting Regression Coefficients of Trinomial Logit Models

Multinomial logit (also termed multi-logit) models permit the analysis of the statistical relation between a categorical response variable and a set of explicative variables (called covariates or regressors). Although multinomial logit is widely used in both the social and economic sciences, the interpretation of regression coefficients may be tricky, as the effect of covariates on the probability distribution of the response variable is nonconstant and difficult to quantify. The ternary plots illustrated in this article aim at facilitating the interpretation of regression coefficients and permit the effect of covariates (either singularly or jointly considered) on the probability distribution of the dependent variable to be quantified. Ternary plots can be drawn both for ordered and for unordered categorical dependent variables, when the number of possible outcomes equals three (trinomial response variable); these plots allow not only to represent the covariate effects over the whole parameter space of the dependent variable but also to compare the covariate effects of any given individual profile. The method is illustrated and discussed through analysis of a dataset concerning the transition of master’s graduates of the University of Trento (Italy) from university to employment.     

A dynamic business modelling approach to design and experiment new business venture strategies

Business Modelling has evolved as a key activity to reflect new business venture strategy by framing the way a firm will operate and how it will function in achieving its goals (e.g., profitability, growth, innovation, social impact). However, scholars and practitioners have criticized the adoption of a too static perspective in the design and use of conventional Business Model representations. Such a static perspective prevents nascent entrepreneurs experimenting with their Business Models and, as a result, identifying the most effective strategies, especially in terms of business sustainability and profitability. In this paper, we argue that combining conventional Business Model schemas with System Dynamics modelling results in a strategy design tool that may overcome several limitations related to a static view of Business Model representation. Mapping the different key elements underlying value creation processes into a system of causal interdependencies – through the use of simulation – allows strategy analysts and entrepreneurs to experiment and learn how the business reacts to strategic and organizational changes in terms of performance, innovation and value creation. As such, Dynamic Business Models provide useful insights to strategy formulation and business venturing by capturing how critical Business Model elements interact to produce enduring competitive advantages over time.     

Fast and approximate exhaustive variable selection for generalised linear models with APES

We present APproximated Exhaustive Search (APES), which enables fast and approximated exhaustive variable selection in Generalised Linear Models (GLMs). While exhaustive variable selection remains as the gold standard in many model selection contexts, traditional exhaustive variable selection suffers from computational feasibility issues. More precisely, there is often a high cost associated with computing maximum likelihood estimates (MLE) for all subsets of GLMs. Efficient algorithms for exhaustive searches exist for linear models, most notably the leaps‐and‐bound algorithm and, more recently, the mixed integer optimisation (MIO) algorithm. The APES method learns from observational weights in a generalised linear regression super‐model and reformulates the GLM problem as a linear regression problem. In this way, APES can approximate a true exhaustive search in the original GLM space. Where exhaustive variable selection is not computationally feasible, we propose a best‐subset search, which also closely approximates a true exhaustive search. APES is made available in both as a standalone R package as well as part of the already existing mplot package.     

The Eurasian Economic Union: Development Prospects and Possible Obstacles

This article analyzes the development prospects and problems for the Eurasian Economic Union (EAEU). It examines issues of integration within the EAEU, as well as interactions with other countries, both CIS (Commonwealth of Independent States) and non-CIS. The main problem of integration within the EAEU is the dominance of redistributive motives over productive ones. This article assesses the extent of Russian oil and gas transfers to EAEU partners and the impact of tax maneuvers on their size. It shows that the creation of mechanisms for redistributing profits within the EAEU will allow a positive economic effect to materialize from free trade agreements with non-CIS countries. The article assesses the risks for the EAEU related to Russia’s introduction of a unilateral ban on food imports from countries on the sanctions list and to the possible establishment of tariffs on trade with Ukraine.     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.     

影子银行、地方政府债务及金融发展动态关系研究——基于省级面板VAR模型

基于2004—2017年中国省级面板数据,运用面板向量自回归(PVAR)模型,使用系统GMM估计、脉冲响应函数、方差分解以及格兰杰因果关系检验等方法分析了影子银行、地方政府债务及金融发展之间的动态关系.结果表明:影子银行、地方政府债务与金融发展水平三者之间存在动态耦合关系.在地方政府融资能力受到约束的情况下,影子银行为地方政府提供了多元的融资方式,在增加政府融资能力的同时提升了政府债务水平;而地方政府债务需求显著推动了影子银行规模的快速发展.同时,影子银行过度扩张危害了金融市场的健康发展,降低金融发展水平,继而使地方政府的融资渠道受到约束.但金融发展并不能有效约束影子银行规模,原因在于,政府融资需求是影子银行的主要动力,若不能控制地方政府的借贷行为则无法从源头解决问题.监管机构在去杠杆的过程中,应该综合考虑影子银行与地方政府债务、金融发展之间的动态关系,如此才能够实现预期的政策效果.     

A Bayesian Analysis of Abundance,Trend, and Population Viability for Harbor Seals in Iliamna Lake,Alaska

Harbor seals in Iliamna Lake, Alaska, are a small, isolated population, and one of only two freshwater populations of harbor seals in the world, yet little is known about their abundance or risk for extinction. Bayesian hierarchical models were used to estimate abundance and trend of this population. Observational models were developed from aerial survey and harvest data, and they included effects for time of year and time of day on survey counts. Underlying models of abundance and trend were based on a Leslie matrix model that used prior information on vital rates from the literature. We developed three scenarios for variability in the priors and used them as part of a sensitivity analysis. The models were fitted using Markov chain Monte Carlo methods. The population production rate implied by the vital rate estimates was about 5% per year, very similar to the average annual harvest rate. After a period of growth in the 1980s, the population appears to be relatively stable at around 400 individuals. A population viability analysis assessing the risk of quasi‐extinction, defined as any reduction to 50 animals or below in the next 100 years, ranged from 1% to 3%, depending on the prior scenario. Although this is moderately low risk, it does not include genetic or catastrophic environmental events, which may have occurred to the population in the past, so our results should be applied cautiously.