Entropic Priors for Discrete Probabilistic Networks and for Mixtures of Gaussians Models

The ongoing unprecedented exponential explosion of available computing power, has radically transformed the methods of statistical inference. What used to be a small minority of statisticians advocating for the use of priors and a strict adherence to bayes theorem, it is now becoming the norm across disciplines. The evolutionary direction is now clear. The trend is towards more realistic, flexible and complex likelihoods characterized by an ever increasing number of parameters. This makes the old question of: What should the prior be? to acquire a new central importance in the modern bayesian theory of inference. Entropic priors provide one answer to the problem of prior selection. The general definition of an entropic prior has existed since 1988, but it was not until 1998 that it was found that they provide a new notion of complete ignorance. This paper re-introduces the family of entropic priors as minimizers of mutual information between the data and the parameters, as in [rodriguez98b], but with a small change and a correction. The general formalism is then applied to two large classes of models: Discrete probabilistic networks and univariate finite mixtures of gaussians. It is also shown how to perform inference by efficiently sampling the corresponding posterior distributions.Comment: 24 pages, 3 figures, Presented at MaxEnt2001, APL Johns Hopkins University, August 4-9 2001. See also http://omega.albany.edu:8008

Optimal Recovery of Local Truth

Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z, from n independent observations. It is shown that, the fastest possible estimators (like the k-nearest neighbor and kernel) have minimum asymptotic mean square errors when the space of observations is thought as conformally curved. The optimal metric is shown to be generated by the Hessian of f in the regions where the Hessian is definite. Thus, the peaks and valleys of f are surrounded by singular horizons when the Hessian changes signature from Riemannian to pseudo-Riemannian. Adaptive estimators based on the optimal variable metric show considerable theoretical and practical improvements over traditional methods. The formulas simplify dramatically when the dimension of the data space is 4. The similarities with General Relativity are striking but possibly illusory at this point. However, these results suggest that nonparametric density estimation may have something new to say about current physical theory.Comment: To appear in Proceedings of Maximum Entropy and Bayesian Methods 1999. Check also: http://omega.albany.edu:8008

Macroeconomic policies for structural adjustment

Structural adjustment is an economy wide adjustment effort aimed at allocating resources better. The author contends that functioning markets and a low, stable inflation rate are two macroeconomic preconditions for implementing structural adjustment. He further concludes that in highly distorted economies the market system must be restored before adjustment efforts are undertaken. Fiscal deficits are probably a key determinant of trade deficits - particularly when the fiscal deficit is financed abroad. This paper is concerned with the identification of macroeconomic policies consistent with the long run sustainability of a stable market framework or with changes that may be required as a consequence of the implementation of the structural adjustment program. It is not directly concerned with issues of short run stabilization, although those issues, particularly that of the timing of policies are mentioned whenever relevant.Economic Stabilization,Environmental Economics&Policies,Economic Theory&Research,Macroeconomic Management,Banks&Banking Reform

The external effects of public sector deficits

This paper develops a two equation model for measuring how public sector deficits - and the way that they are financed - affect the real exchange rate, the trade balance, the current account and the level of external indebtedness. One equation relates the real exchange rate to the trade surplus and the other describes the trade surplus as a function of structural parameters, the fiscal deficit, and the stock of foreign assets. To make the model dynamic, one must allow for the fact that the level of foreign assets - one determinant of the trade surplus and current account - changes over time. The trade surplus, plus foreign internest earned, determines the evolution over time of the stock of foreign assets. Using this model, the paper makes the following conclusions. The level and composition of government spending affects the real exchange rate because of the effect of spending on nontraded goods. Changes in the trade balance are also bound to affect the real exchange rate. How much depends on how much expenditure must be switched to make the trade balance compatible with the change in aggregate spending.Economic Theory&Research,Economic Stabilization,Environmental Economics&Policies,Macroeconomic Management,Public Sector Economics&Finance

FISCAL FEDERALISM WITH A SINGLE INSTRUMENT TO FINANCE GOVERNMENT

The structure of each level of government in the United States has changed over the last 200 years. Wallis (2000) has presented empirical evidence that relates the dominance of each level not to the functions government decides to undertake (the expenditures it commits to), but to the costs and benefits of the financial instruments each level has available (the way each level extracts revenues). In this paper we provide theoretical evidence for this hypothesis. We show why two different levels of government (e.g. state and federal) would not want to use a common instrument to finance the same good.