BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

The Effects of Culture on the Meaning of Loneliness

The present study examined the influence of culturalbackground on the experience of loneliness. Threehundred and seventy five participants from NorthAmerica and 375 from Croatia volunteered to answer an82 item questionnaire which examined the quality oftheir loneliness experiences. The factors whichcomprise the experience of loneliness are Emotionaldistress, Social inadequacy and alienation, Growth anddiscovery, Interpersonal isolation, andSelf-alienation. Results indicated that culturalbackground, indeed, affects the experience ofloneliness. North Americans scored higher on all fivefactors, and a similar trend was evident when men andwomen were compared across cultures.     

Parsimonious Estimation of the Covariance Matrix in Multinomial Probit Models

This article presents a Bayesian analysis of a multinomial probit model by building on previous work that specified priors on identified parameters. The main contribution of our article is to propose a prior on the covariance matrix of the latent utilities that permits elements of the inverse of the covariance matrix to be identically zero. This allows a parsimonious representation of the covariance matrix when such parsimony exists. The methodology is applied to both simulated and real data, and its ability to obtain more efficient estimators of the covariance matrix and regression coefficients is assessed using simulated data.     

Roadmap to recovery: Reporting on a research taskforce supporting Indigenous responses to COVID‐19 in Australia

In April 2020 a Group of Eight Taskforce was convened, consisting of over 100 researchers, to provide independent, research‐based recommendations to the Commonwealth Government on a “Roadmap to Recovery” from COVID‐19. The report covered issues ranging from pandemic control and relaxation of social distancing measures, to well‐being and special considerations for vulnerable populations. Our work focused on the critical needs of Aboriginal and Torres Strait Islander communities; this paper presents an overview of our recommendations to the Roadmap report. In addressing the global challenges posed by pandemics for citizens around the world, Indigenous people are recognised as highly vulnerable. At the time of writing Australia's First Nations Peoples have been largely spared from COVID‐19 in comparison to other Indigenous populations globally. Our recommendations emphasise self‐determination and equitable needs‐based funding to support Indigenous communities to recover from COVID‐19, addressing persistent overcrowded housing, and a focus on workforce, especially for regional and remote communities. These latter two issues have been highlighted as major issues of risk for Indigenous communities in Australia It remains to be seen how governments across Australia take up these recommendations to support Indigenous peoples' health and healing journey through yet another, potentially catastrophic, health crisis.     

Efficiency of Large Double Auctions

We consider large double auctions with private values. Values need be neither symmetric nor independent. Multiple units may be owned or desired. Participation may be stochastic. We introduce a very mild notion of “a little independence.” We prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient. For any α>0, inefficiency disappears at rate 1/n^2‐α.     

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.     

Strategic Experimentation with Exponential Bandits

We analyze a game of strategic experimentation with two‐armed bandits whose risky arm might yield payoffs after exponentially distributed random times. Free‐riding causes an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with beliefs as the state variable. We construct the unique symmetric Markovian equilibrium of the game, followed by various asymmetric ones. There is no equilibrium where all players use simple cut‐off strategies. Equilibria where players switch finitely often between experimenting and free‐riding all yield a similar pattern of information acquisition, greater efficiency being achieved when the players share the burden of experimentation more equitably. When players switch roles infinitely often, they can acquire an approximately efficient amount of information, but still at an inefficient rate. In terms of aggregate payoffs, all these asymmetric equilibria dominate the symmetric one wherever the latter prescribes simultaneous use of both arms.     

Imperfect Monitoring and Impermanent Reputations

We study the long‐run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for noncredible behavior in the presence of imperfect monitoring.