A Short Note on Almost Sure Convergence of Bayes Factors in the General Set-Up

ABSTRACT

Although there is a significant literature on the asymptotic theory of Bayes factor, the set-ups considered are usually specialized and often involves independent and identically distributed data. Even in such specialized cases, mostly weak consistency results are available. In this article, for the first time ever, we derive the almost sure convergence theory of Bayes factor in the general set-up that includes even dependent data and misspecified models. Somewhat surprisingly, the key to the proof of such a general theory is a simple application of a result of Shalizi to a well-known identity satisfied by the Bayes factor. Supplementary materials for this article are available online.     

Process modelling and industrial energy use in developing countries—The steel industry in India

A process model is used to study energy use and conservation in the steel industry in India. Production is modelled by a set of inter-connected process activities, each of which defines unique relationships between process output and a number of inputs. Contrary to that in process models for the U.S., we do not assume cost minimizing behavior. Simulation results show that although a number of cost-effective energy conservation measures exist, none of them would lead to significant reductions in energy use. Effective policy for the Indian Steel industry would require combining the strategies.     

On two-stage shrinkage testtimation

The general procedure of two stage shrinkage testimation formulated in Adlce and Gokhale [Commun. Statist.- Theory Meth. 18, 633-627 (1989)] k further generalized and extended to the multiparameter case. Local optimal-ity result of that paper, in the restricted set up of univariate location families and scalar families, is generalized without any restriction on the parametric family. The local unbiasedness result of that paper is also generalized and in addition local risk- unbiasedness is considered. The optimality and risk-unbiasedness results are proved for the usual matrix loss and their validity for an arbitrary quadratic loss deduced as corollaries.     

Private versus public old-age security

We directly compare two institutions, a family compact—a parent makes a transfer to her parent in anticipation of a possible future gift from her children—with a pay-as-you-go, public pension system, in a life cycle model with endogenous fertility wherein children are valued both as consumption and investment goods. Absent intragenerational heterogeneity, we show that a benevolent government has no welfare justification for introducing public pensions alongside thriving family compacts since the former is associated with inefficiently low fertility. This result hinges critically on a fiscal externality—the inability of middle age agents to internalize the impact of their fertility decisions on old-age transfers under a public pension system. With homogeneous agents, a strong-enough negative aggregate shock to middle-age incomes destroys all family compacts, and in such a setting, an optimal public pension system cannot enter. This suggests the raison d’être for social security must lie outside of its function as a pension system—specifically its redistributive function which emerges with heterogeneous agents. In a simple modification of our benchmark model—one that allows for idiosyncratic frictions to compact formation such as differences in infertility/mating status—a welfare-enhancing role for a public pension system emerges; such systems may flourish even when family compacts cannot.     

Outlier detection based on extreme value theory and applications

Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behavior of the underlying distribution. We develop an automatic, data-driven method rooted in the mathematical theory of extremes to identify observations that deviate from the intermediate and central characteristics. The proposed algorithm is an extension of a method previously proposed in the literature for the specific case of heavy tailed Pareto-type distributions to all max-domains of attraction. We propose some applications such as a tail-adjusted boxplot which yields a more accurate representation of possible outliers, and the identification of outliers in a multivariate context through an analysis of associated random variables such as local outlier factors. Several examples and simulation results illustrate the finite sample behavior of the algorithm and its applications.     

Comparison of Deliberate and Spontaneous Facial Movement in Smiles and Eyebrow Raises

We investigated movement differences between deliberately posed and spontaneously occurring smiles and eyebrow raises during a videotaped interview that included a facial movement assessment. Using automated facial image analysis, we quantified lip corner and eyebrow movement during periods of visible smiles and eyebrow raises and compared facial movement within participants. As in an earlier study, maximum speed of movement onset was greater in deliberate smiles. Maximum speed and amplitude were greater and duration shorter in deliberate compared to spontaneous eyebrow raises. Asymmetry of movement did not differ within participants. Similar patterns contrasting deliberate and spontaneous movement in both smiles and eyebrow raises suggest a common pattern of signaling for spontaneous facial displays.

Multi-phase Algorithms for Throughput Maximization for Real-Time Scheduling

We consider the problem of off-line throughput maximization for job scheduling on one or more machines, where each job has a release time, a deadline and a profit. Most of the versions of the problem discussed here were already treated by Bar-Noy et al. (Proc. 31st ACM STOC, 1999, pp. 622–631; http://www.eng.tau.ac.il/amotz/). Our main contribution is to provide algorithms that do not use linear programming, are simple and much faster than the corresponding ones proposed in Bar-Noy et al. (ibid., 1999), while either having the same quality of approximation or improving it. More precisely, compared to the results of in Bar-Noy et al. (ibid., 1999), our pseudo-polynomial algorithm for multiple unrelated machines and all of our strongly-polynomial algorithms have better performance ratios, all of our algorithms run much faster, are combinatorial in nature and avoid linear programming. Finally, we show that algorithms with better performance ratios than 2 are possible if the stretch factors of the jobs are bounded; a straightforward consequence of this result is an improvement of the ratio of an optimal solution of the integer programming formulation of the JISP2 problem (see Spieksma, Journal of Scheduling, vol. 2, pp. 215–227, 1999) to its linear programming relaxation.     

Labor Market Search and Optimal Retirement Policy

A popular and long‐standing view is that social security is a means for young, unemployed people to “purchase” jobs from older workers. Can social security, by encouraging retirement and hence creating job vacancies for the young, improve the allocation of workers to jobs? Maybe, according to a standard model of labor market search, but public retirement programs currently pay the elderly substantially more than their jobs are worth. An important effect is that retirement reduces the value of other vacant jobs. Our results imply that recent reforms aimed at reducing retirement incentives are likely to improve labor market efficiency.     

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent variation (EV) and compensating variation (CV) resulting from price change of a discrete good using individual‐level data when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV and CV can be expressed as simple closed‐form functionals of conditional choice probabilities under essentially unrestricted preference distributions. These results hold even when the distribution and dimension of unobserved heterogeneity are neither known nor identified, and utilities are neither quasilinear nor parametrically specified. The welfare distributions take simple forms that are easy to compute in applications. In particular, average EV for a price rise equals the change in average Marshallian consumer surplus and is smaller than average CV for a normal good. These nonparametric point‐identification results fail for ordered choice if the unit price is identical for all alternatives, thereby providing a connection to Hausman–Newey's (2014) partial identification results for the limiting case of continuous choice.