Bayesian Inference via Filtering for a Class of Counting Processes: Application to the Micromovement of Asset Price

This paper highlights recent developments in a rich class of counting process models for the micromovement of asset price and in the Bayesian inference (estimation and model selection) via filtering for the class of models. A specific micromovement model built upon linear Brownian motion with jumping stochastic volatility is used to demonstrate the procedure to develop a micromovement model with specific tick-level sample characteristics. The model is further used to demonstrate the procedure to implement Bayes estimation via filtering, namely, to construct a recursive algorithm for computing the trade-by-trade Bayes parameter estimates, especially for the stochastic volatility. The consistency of the recursive algorithm model is proven. Simulation and real-data examples are provided as well as a brief example of Bayesian model selection via filtering.     

Understanding GPU Programming for Statistical Computation: Studies in Massively Parallel Massive Mixtures

This article describes advances in statistical computation for large-scale data analysis in structured Bayesian mixture models via graphics processing unit (GPU) programming. The developments are partly motivated by computational challenges arising in fitting models of increasing heterogeneity to increasingly large datasets. An example context concerns common biological studies using high-throughput technologies generating many, very large datasets and requiring increasingly high-dimensional mixture models with large numbers of mixture components. We outline important strategies and processes for GPU computation in Bayesian simulation and optimization approaches, give examples of the benefits of GPU implementations in terms of processing speed and scale-up in ability to analyze large datasets, and provide a detailed, tutorial-style exposition that will benefit readers interested in developing GPU-based approaches in other statistical models. Novel, GPU-oriented approaches to modifying existing algorithms software design can lead to vast speed-up and, critically, enable statistical analyses that presently will not be performed due to compute time limitations in traditional computational environments. Supplemental materials are provided with all source code, example data, and details that will enable readers to implement and explore the GPU approach in this mixture modeling context.     

一类有序样品聚类的动态规划方法

变结构特征的识别在经济计量模型建立中具有重要价值 .本文用动态规划方法讨论了一类社会经济系统模型结构变化点的问题 ,并通过实例进行了验证 .文中引进了线性模型来划分变结构模型 ,并编写出用动态规划方法聚类的计算程序 .大量模拟计算表明该方法实用性强 ,算法简便 ,便于应用 .     

Multivariate dynamic modeling for Bayesian forecasting of business revenue

Forecasting enterprise-wide revenue is critical to many companies and presents several challenges and opportunities for significant business impact. This case study is based on model developments to address these challenges for forecasting in a large-scale retail company. Focused on multivariate revenue forecasting across collections of supermarkets and product categories, hierarchical dynamic models are natural: these are able to couple revenue streams in an integrated forecasting model, while allowing conditional decoupling to enable relevant and sensitive analysis together with scalable computation. Structured models exploit multi-scale modeling to cascade information on price and promotion activities as predictors relevant across categories and groups of stores. With a context-relevant focus on forecasting revenue 12 weeks ahead, the study highlights product categories that benefit from multi-scale information, defines insights into when, how, and why multivariate models improve forecast accuracy, and shows how cross-category dependencies can relate to promotion decisions in one category impacting others. Bayesian modeling developments underlying the case study are accessible in custom code for interested readers.     

Asymptotic Bayesian structure learning using graph supports for Gaussian graphical models

The theory of Gaussian graphical models is a powerful tool for independence analysis between continuous variables. In this framework, various methods have been conceived to infer independence relations from data samples. However, most of them result in stepwise, deterministic, descent algorithms that are inadequate for solving this issue. More recent developments have focused on stochastic procedures, yet they all base their research on strong a priori knowledge and are unable to perform model selection among the set of all possible models. Moreover, convergence of the corresponding algorithms is slow, precluding applications on a large scale. In this paper, we propose a novel Bayesian strategy to deal with structure learning. Relating graphs to their supports, we convert the problem of model selection into that of parameter estimation. Use of non-informative priors and asymptotic results yield a posterior probability for independence graph supports in closed form. Gibbs sampling is then applied to approximate the full joint posterior density. We finally give three examples of structure learning, one from synthetic data, and the two others from real data.     

Optimal greedy policies for stochastic control models

We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.     

近似Bayes计算前沿研究进展及应用

在大数据和人工智能时代,建立能够有效处理复杂数据的模型和算法,以从数据中获取有用的信息和知识是应用数学、统计学和计算机科学面临的共同难题.为复杂数据建立生成模型并依据这些模型进行分析和推断是解决上述难题的一种有效手段.从一种宏观的视角来看,无论是应用数学中常用的微分方程和动力系统,或是统计学中表现为概率分布的统计模型,还是机器学习领域兴起的生成对抗网络和变分自编码器,都可以看作是一种广义的生成模型.随着所处理的数据规模越来越大,结构越来越复杂,在实际问题中所需要的生成模型也变得也越来越复杂,对这些生成模型的数学结构进行精确地解析刻画变得越来越困难.如何对没有精确解析形式（或其解析形式的精确计算非常困难）的生成模型进行有效的分析和推断,逐渐成为一个十分重要的问题.起源于Bayes统计推断,近似Bayes计算是一种可以免于计算似然函数的统计推断技术,近年来在复杂统计模型和生成模型的分析和推断中发挥了重要作用.该文从经典的近似Bayes计算方法出发,对近似Bayes计算方法的前沿研究进展进行了系统的综述,并对近似Bayes计算方法在复杂数据处理中的应用前景及其和前沿人工智能方法的深刻联系进行了分析和讨论.     

Bayesian MAP model selection of chain event graphs

Chain event graphs are graphical models that while retaining most of the structural advantages of Bayesian networks for model interrogation, propagation and learning, more naturally encode asymmetric state spaces and the order in which events happen than Bayesian networks do. In addition, the class of models that can be represented by chain event graphs for a finite set of discrete variables is a strict superset of the class that can be described by Bayesian networks. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.     

On the use of loss functions in the changepoint problem

Summary We consider a sequence of independent random variables whose densities depend on a parameter which is subject to a change at an unknown time point. A Bayesian decision-theoretic approach is used to obtain an optimal choice of changepoint. The exponential and multivariate normal models are analyzed, and some numerical examples are given.     

广义非参数回归的B样本贝叶斯估计

本文主要研究广义非参数模型B样条Bayes估计 .将回归函数按照B样条基展开 ,我们不具体选择节点的个数 ,而是节点个数取均匀的无信息先验 ,样条函数系数取正态先验 ,用B样条函数的后验均值估计回归函数 .并给出了回归函数B样条Bayes估计的MCMC的模拟计算方法 .通过对Logistic非参数回归的模拟研究 ,表明B样条Bayes估计得到了很好的估计效果     

Optimal Goodwill Path to Introduce a New Product

We consider the problem of determining an optimal goodwill path for the introduction of a new product in a market, while looking for the maximum foreseen profit. The foreseen revenue depends on the product introduction time and on the goodwill level at the same time. We focus on the advertising costs associated with the goodwill evolution and assume that the cost function possesses some rather general features which are shared by the cost functions of the Nerlove-Arrow type models. The dynamic optimization problem is discussed in the calculus of variations framework. A few examples associated with special cost functions are discussed in detail.     

广义变系数模型的Bayesian B样条估计

提出了广义变系数模型函数系数的一种新的估计方法．我们用B样条函数逼近函数系数,不具体选择节点的个数,而是节点个数取均匀的无信息先验,样条函数系数取正态先验,用Bayesian模型平均的方法估计各个函数系数．这种估计方法一个主要特点是允许各个函数系数所需节点个数的后验分布不同,因此允许不同函数系数使用不同的光滑参数．另外,本文还给出了Bayesian B样条估计的计算方法,并通过模拟例子,说明广义变系数模型的函数系数可以由Bayesian B样条估计方法得到很好的估计．     

Dynamic Models for Sales Promotion Policies

This paper presents several models for decisions on budget and operational details (price-off and duration) of a sales promotion for consuLmer goods industries and retail sector. The solutions to the one-period problem are generalized using the dynamic programming methods to the more common case of a multi-period-situation. Several special cases of the general dynamic programming model are discussed along with numerical examples. Finally, the ways of utilizing historical data for an ongoing firm for estimating the parameters of the models are presented.     

Logarithmic Pooling of Priors Linked by a Deterministic Simulation Model

Abstract

We consider Bayesian inference when priors and likelihoods are both available for inputs and outputs of a deterministic simulation model. This problem is fundamentally related to the issue of aggregating (i.e., pooling) expert opinion. We survey alternative strategies for aggregation, then describe computational approaches for implementing pooled inference for simulation models. Our approach (1) numerically transforms all priors to the same space; (2) uses log pooling to combine priors; and (3) then draws standard Bayesian inference. We use importance sampling methods, including an iterative, adaptive approach that is more flexible and has less bias in some instances than a simpler alternative. Our exploratory examples are the first steps toward extension of the approach for highly complex and even noninvertible models.     

An efficient sampling scheme for dynamic generalized models

A multimove sampling scheme for the state parameters of non-Gaussian and nonlinear dynamic models for univariate time series is proposed. This procedure follows the Bayesian framework, within a Gibbs sampling algorithm with steps of the Metropolis–Hastings algorithm. This sampling scheme combines the conjugate updating approach for generalized dynamic linear models, with the backward sampling of the state parameters used in normal dynamic linear models. A quite extensive Monte Carlo study is conducted in order to compare the results obtained using our proposed method, conjugate updating backward sampling (CUBS), with those obtained using some algorithms previously proposed in the Bayesian literature. We compare the performance of CUBS with other sampling schemes using two real datasets. Then we apply our algorithm in a stochastic volatility model. CUBS significantly reduces the computing time needed to attain convergence of the chains, and is relatively simple to implement.     

Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data

We present a unified semiparametric Bayesian approach based on Markov random field priors for analyzing the dependence of multicategorical response variables on time, space and further covariates. The general model extends dynamic, or state space, models for categorical time series and longitudinal data by including spatial effects as well as nonlinear effects of metrical covariates in flexible semiparametric form. Trend and seasonal components, different types of covariates and spatial effects are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is fully Bayesian and uses MCMC techniques for posterior analysis. The approach in this paper is based on latent semiparametric utility models and is particularly useful for probit models. The methods are illustrated by applications to unemployment data and a forest damage survey.     

Exploring the latent segmentation space for the assessment of multiple change-point models

This paper addresses the retrospective or off-line multiple change-point detection problem. Multiple change-point models are here viewed as latent structure models and the focus is on inference concerning the latent segmentation space. Methods for exploring the space of possible segmentations of a sequence for a fixed number of change points may be divided into two categories: (i) enumeration of segmentations, (ii) summary of the possible segmentations in change-point or segment profiles. Concerning the first category, a dynamic programming algorithm for computing the top $N$ most probable segmentations is derived. Concerning the second category, a forward-backward dynamic programming algorithm and a smoothing-type forward-backward algorithm for computing two types of change-point and segment profiles are derived. The proposed methods are mainly useful for exploring the segmentation space for successive numbers of change points and provide a set of assessment tools for multiple change-point models that can be applied both in a non-Bayesian and a Bayesian framework. We show using examples that the proposed methods may help to compare alternative multiple change-point models (e.g. Gaussian model with piecewise constant variances or global variance), predict supplementary change points, highlight overestimation of the number of change points and summarize the uncertainty concerning the position of change points.     

Modeling mortality with a Bayesian vector autoregression

Parametric mortality models capture the cross section of mortality rates. These models fit the older ages better, because of the more complex cross section of mortality at younger and middle ages. Dynamic parametric mortality models fit a time series to the parameters, such as a Vector-auto-regression (VAR), in order to capture trends and uncertainty in mortality improvements. We consider the full age range using the Heligman and Pollard (1980) model, a cross-sectional mortality model with parameters that capture specific features of different age ranges. We make the Heligman–Pollard model dynamic using a Bayesian Vector Autoregressive (BVAR) model for the parameters and compare with more commonly used VAR models. We fit the models using Australian data, a country with similar mortality experience to many developed countries. We show how the Bayesian Vector Autoregressive (BVAR) models improve forecast accuracy compared to VAR models and quantify parameter risk which is shown to be significant.     

Discussion of “Multivariate Dynamic Modeling for Bayesian Forecasting of Business Revenue”

This paper, “Multivariate Dynamic Modeling for Bayesian Forecasting of Business Revenue,” proposes a novel Bayesian approach based on dynamic linear models to share information from different sectors, LSG (Local Store Group), and item category, through the use of auxiliary information (the discount information). The authors demonstrate the feasibility of parallel computing with multiple item categories, making the Bayesian method highly scalable. The proposed method in the paper should have wide applicability in inventory and revenue management. We suggest in this discussion potential areas for further development.     

基于动态因子结构的贝叶斯分位面板协整研究

针对传统面板协整检验在建模过程中易受异常值影响以及其原假设设置的主观选择问题,本文利用动态公共因子刻画面板数据潜在的截面相关结构,提出基于动态因子的截面相关结构的贝叶斯分位面板协整检验,结合各个主要分位数水平下参数的条件后验分布,设计结合卡尔曼滤波的Gibbs抽样算法,进行贝叶斯分位面板协整检验;并进行Monte Carlo仿真实验验证贝叶斯分位面板协整检验的可行性与有效性。同时,采用中国各省金融发展和经济增长的面板数据进行实证研究,结果发现在各主要分位数水平下中国金融发展和经济增长之间具有协整关系。研究结果表明:贝叶斯分位面板协整检验方法避免了传统面板数据协整方法由于原假设设置不同而发生误判的问题,克服了异常值的影响,能够提供全面准确的模型参数估计和协整检验结果。