Alternative posterior consistency results in nonparametric binary regression using Gaussian process priors

We establish consistency of posterior distribution when a Gaussian process prior is used as a prior distribution for the unknown binary regression function. Specifically, we take the work of Ghosal and Roy [2006. Posterior consistency of Gaussian process prior for nonparametric binary regression. Ann. Statist. 34, 2413–2429] as our starting point, and then weaken their assumptions on the smoothness of the Gaussian process kernel while retaining a stronger yet applicable condition about design points. Furthermore, we extend their results to multi-dimensional covariates under a weaker smoothness condition on the Gaussian process. Finally, we study the extent to which posterior consistency can be achieved under a general model where, when additional hyperparameters in the covariance function of a Gaussian process are involved.     

Bootstrap confidence regions computed from autoregressions of arbitrary order

Given a linear time series, e.g. an autoregression of infinite order, we may construct a finite order approximation and use that as the basis for confidence regions. The sieve or autoregressive bootstrap, as this method is often called, is generally seen as a competitor with the better-understood block bootstrap approach. However, in the present paper we argue that, for linear time series, the sieve bootstrap has significantly better performance than blocking methods and offers a wider range of opportunities. In particular, since it does not corrupt second-order properties then it may be used in a double-bootstrap form, with the second bootstrap application being employed to calibrate a basic percentile method confidence interval. This approach confers second-order accuracy without the need to estimate variance. That offers substantial benefits, since variances of statistics based on time series can be difficult to estimate reliably, and—partly because of the relatively small amount of information contained in a dependent process—are notorious for causing problems when used to Studentize. Other advantages of the sieve bootstrap include considerably greater robustness against variations in the choice of the tuning parameter, here equal to the autoregressive order, and the fact that, in contradistinction to the case of the block bootstrap, the percentile t version of the sieve bootstrap may be based on the 'raw' estimator of standard error. In the process of establishing these properties we show that the sieve bootstrap is second order correct.     

Increasing Returns and Social Contagion in Cultural Industries

A formal definition of cultural industries is developed following four distinct features of cultural goods: (a) oversupply, (b) quality uncertainty, (c) network effects and (d) demand reversal. Drawing on economic and socio-psychological notions of ‘network’, increasing returns and social contagion effects are distinguished. Increasing returns may govern the adoption of standards when choices are binary, social contagion explains the diffusion of cultural goods when choices are multiple. Together, the four structural features delineating cultural industries account for curious competitive dynamics prevalent in cultural markets, such as the notorious 10 : 90 proportionality (under which 10% of cultural goods account for 90% of the market), causal ambiguity about the reasons for success, and the formation of fashions. Six managerial recommendations are advanced, focusing on a criticial circulation point triggering self-sustaining diffusion patterns. Finally ‘project-based enterprises’ and ‘network forms of governance’ are identified as the organizational forms most suited to the dynamics of the cultural markets.