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Although in principle prior information can significantly improve inference, incorporating incorrect prior information will bias the estimates of any inferential analysis. This fact deters many scientists from incorporating prior information into their inferential analyses. In the natural sciences, where experiments are more regularly conducted, and can be combined with other relevant information, prior information is often used in inferential analysis, despite it being sometimes nontrivial to specify what that information is and how to quantify that information. In the social sciences, however, prior information is often hard to come by and very hard to justify or validate. We review a number of ways to construct such information. This information emerges naturally, either from fundamental properties and characteristics of the systems studied or from logical reasoning about the problems being analyzed. Borrowing from concepts and philosophical reasoning used in the natural sciences, and within an info-metrics framework, we discuss three different, yet complimentary, approaches for constructing prior information, with an application to the social sciences.

Several inferential procedures are advocated in the literature. The most commonly used techniques are the frequentist and the Bayesian inferential procedures. Bayesian methods afford inferences based on small data sets and are especially useful in studies with limited data availability. Bayesian approaches also help incorporate prior knowledge, especially subjective knowledge, into predictions. Considering the increasing difficulty in data acquisition, the application of Bayesian techniques can be hugely beneficial to managers, especially in analysing limited data situations like a study of expert opinion. Another factor constraining the broader application of Bayesian statistics in business was computational power requirements and the availability of appropriate analytical tools. However, with the increase in computational power, connectivity and the development of appropriate software programmes, Bayesian applications have become more attractive. This chapter attempts to unravel the applications of the Bayesian inferential procedure in marketing management.

We provide a Bayesian inference for a mixture of two Pareto distributions which is then used to approximate the upper tail of a wage distribution. The model is applied to the data from the CPS Outgoing Rotation Group to analyze the recent structure of top wages in the United States from 1992 through 2009. We find an enormous earnings inequality between the very highest wage earners (the “superstars”), and the other high wage earners. These findings are largely in accordance with the alternative explanations combining the model of superstars and the model of tournaments in hierarchical organization structure. The approach can be used to analyze the recent pay gaps among top executives in large firms so as to exhibit the “superstar” effect.

The global slack hypothesis is central to the discussion of the trade-offs that monetary policy faces in an increasingly more integrated world. The workhorse New Open Economy Macro (NOEM) model of Martínez-García and Wynne (2010), which fleshes out this hypothesis, shows how expected future local inflation and global slack affect current local inflation. In this chapter, I propose the use of the orthogonalization method of Aoki (1981) and Fukuda (1993) on the workhorse NOEM model to further decompose local inflation into a global component and an inflation differential component. I find that the log-linearized rational expectations model of Martínez-García and Wynne (2010) can be solved with two separate subsystems to describe each of these two components of inflation.

I estimate the full NOEM model with Bayesian techniques using data for the United States and an aggregate of its 38 largest trading partners from 1980Q1 until 2011Q4. The Bayesian estimation recognizes the parameter uncertainty surrounding the model and calls on the data (inflation and output) to discipline the parameterization. My findings show that the strength of the international spillovers through trade – even in the absence of common shocks – is reflected in the response of global inflation and is incorporated into local inflation dynamics. Furthermore, I find that key features of the economy can have different impacts on global and local inflation – in particular, I show that the parameters that determine the import share and the price-elasticity of trade matter in explaining the inflation differential component but not the global component of inflation.

The purpose of this paper is to present an economic–statistical design (ESD) for the Bayesian X‾ control chart based on predictive distribution with two types of informative and noninformative prior distributions.

The design used in this study is based on determining the control chart of the predictive distribution and then its ESD. The new proposed cost model is presented by considering the conjugate and Jeffrey's prior distribution in calculating the expected total cycle time and expected cost per cycle, and finally, the optimal design parameters and related costs are compared with the fixed ratio sampling (FRS) mode.

Numerical results show decreases in costs in this Bayesian approach with both Jeffrey's and conjugate prior distribution compared to the FRS mode. This result shows that the Bayesian approach which is based on predictive density works better than the classical approach. Also, for the Bayesian approach, however, there is no significant difference between the results of using Jeffrey's and conjugate prior distributions. Using sensitivity analysis, the effect of cost parameters and shock model parameters and deviation from the mean on the optimal values of design parameters and related costs have been investigated and discussed.

This research adds to the body of knowledge related to quality control of process monitoring systems. This paper may be of particular interest to quality system practitioners for whom the effect of the prior distribution of parameters on the quality characteristic distribution is important.

economic statistical design (ESD) of Bayesian control charts based on predictive distribution is presented for the first time.

The purpose of this paper is to use Bayesian probability theory to analyze the software reliability model with multiple types of faults. The probability that all faults are detected and corrected after a series of independent software tests and correction cycles is presented. This in turn has a number of applications, such as how long to test a software, estimating the cost of testing, etc.

The use of Bayesian probabilistic models, when compared to traditional point forecast estimation models, provides tools for risk estimation and allows decision makers to combine historical data with subjective expert estimates. Probability evaluation is done both prior to and after observing the number of faults detected in each cycle. The conditions under which these two measures, the conditional and unconditional probabilities, are the same is also shown. Expressions are derived to evaluate the probability that, after a series of sequential independent reviews have been completed, no class of fault remains in the software system by assuming the prior distribution as Poisson and binomial.

From results in Sections 4 and 5 it can be observed that the conditional and unconditional probabilities are the same if the prior probability distribution is Poisson and binomial. In these cases the confidence that all faults are deleted is not a function of the number of faults observed during the successive reviews but it is a function of the number of reviews, the detection probabilities and the mean of the prior distribution. This is a remarkable result because it gives a circumstance in which the statistical confidence from a Bayesian analysis is actually independent of all observed data. From the result in Section 4 it can be seen that exponential formula could be used to evaluate the probability that no fault remains when a Poisson prior distribution is combined with a multinomial detection process in each review cycle.

The paper is part of research work for a PhD degree.

This chapter extends the work of Baltagi, Bresson, Chaturvedi, and Lacroix (2018) to the popular dynamic panel data model. The authors investigate the robustness of Bayesian panel data models to possible misspecification of the prior distribution. The proposed robust Bayesian approach departs from the standard Bayesian framework in two ways. First, the authors consider the ε-contamination class of prior distributions for the model parameters as well as for the individual effects. Second, both the base elicited priors and the ε-contamination priors use Zellner’s (1986) g-priors for the variance–covariance matrices. The authors propose a general “toolbox” for a wide range of specifications which includes the dynamic panel model with random effects, with cross-correlated effects à la Chamberlain, for the Hausman–Taylor world and for dynamic panel data models with homogeneous/heterogeneous slopes and cross-sectional dependence. Using a Monte Carlo simulation study, the authors compare the finite sample properties of the proposed estimator to those of standard classical estimators. The chapter contributes to the dynamic panel data literature by proposing a general robust Bayesian framework which encompasses the conventional frequentist specifications and their associated estimation methods as special cases.

Inverse problems are often marked by highly dimensional state vectors. The high dimension affects the quality of the estimation result as well as the computational complexity of the estimation problem. This paper aims to present a state reduction technique based on prior knowledge.

Ill-posed inverse problems require prior knowledge to find a stable solution. The prior distribution is constructed for the high-dimensional data space. The authors use the prior distribution to construct a reduced state description based on a lower-dimensional basis, which they derive from the prior distribution. The approach is tested for the inverse problem of electrical capacitance tomography.

Based on a singular value decomposition of a sample-based prior distribution, a reduced state model can be constructed, which is based on principal components of the prior distribution. The approximation error of the reduced basis is evaluated, showing good behavior with respect to the achievable data reduction. Owing to the structure, the reduced state representation can be applied within existing algorithms.

The full state description is a linear function of the reduced state description. The reduced basis can be used within any existing reconstruction algorithm. Increased noise robustness has been found for the application of the reduced state description in a back projection-type reconstruction algorithm.

The paper presents the construction of a prior-based state reduction technique. Several applications of the reduced state description are discussed, reaching from the use in deterministic reconstruction methods up to proposal generation for computational Bayesian inference, e.g. Markov chain Monte Carlo techniques.