Nonuniform Markov models

A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model must decide that each symbol in a string depends on at most a small, finite number of other symbols in the string. In this report we propose a new way to model conditional independence in Markov models. The central feature of our nonuniform Markov model is that it makes predictions of varying lengths using contexts of varying lengths. Experiments on the Wall Street Journal reveal that the nonuniform model performs slightly better than the classic interpolated Markov model. This result is somewhat remarkable because both models contain identical numbers of parameters whose values are estimated in a similar manner. The only difference between the two models is how they combine the statistics of longer and shorter strings. Keywords: nonuniform Markov model, interpolated Markov model, conditional independence, statistical language model, discrete time series.Comment: 17 page

Short course on principles and applications of beach nourishment

Covers the engineering aspects of beach nourishment. (Document is 192 pages

Partial Adjustment Without Apology

Many kinds of economic behavior appear to be governed by discrete and occasional individual choices. Despite this, econometric partial adjustment models perform relatively well at the aggregate level. Analyzing the classic employment adjustment problem, we show how discrete and occasional microeconomic adjustment is well described by a new form of partial adjustment model that aggregates the actions of a large number of heterogeneous producers. We begin by describing a basic model of discrete and occasional adjustment at the micro level, where production units are essentially restricted to either operate with a fixed number of workers or shut down. We show that this simple model is observationally equivalent at the market level to the standard rational expectations partial adjustment model. We then construct a related, but more realistic, model that incorporates the idea that increases or decreases in the size of an establishment’s workforce are subject to fixed adjustment costs. In the market equilibrium of this model, employment responses to aggregate disturbances include changes both in employment selected by individual establishments and in the measure of establishments actively undertaking adjustment. Yet the model retains a partial adjustment flavor in its aggregate responses. Moreover, in contrast to existing models of discrete adjustment, our generalized partial adjustment model is sufficiently tractable to allow extension to general equilibrium.

Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on $\mathbb{R}^{1,d-1}$. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.Comment: 40 pages, 5 figure

Stock return autocorrelations revisited: A quantile regression approach

The aim of this study is to provide a comprehensive description of the dependence pattern of stock returns by studying a range of quantiles of the conditional return distribution using quantile autoregression. This enables us in particular to study the behavior of extreme quantiles associated with large positive and negative returns in contrast to the central quantile which is closely related to the conditional mean in the least-squares regression framework. Our empirical results are based on 30 years of daily, weekly and monthly returns of the stocks comprised in the Dow Jones Stoxx 600 index. We find that lower quantiles exhibit positive dependence on past returns while upper quantiles are marked by negative dependence. This pattern holds when accounting for stock specific characteristics such as market capitalization, industry, or exposure to market risk. --stock return distribution,quantile autoregression,overreaction and underreaction

Union effects on health insurance provision and coverage in the United States

Since Freeman and Medoff's (1984) comprehensive review of what unions do, union density in the U.S. has fallen substantially. During the same period, employer provision of health insurance has undergone substantial changes in extent and form. Using individual data from various supplements to the Current Population Survey and establishment data from the 1993 Robert Wood Johnson Foundation survey, we investigate the effects of unionization on employer provision of health benefits. We find that in addition to increasing coverage by employer-provided health benefits, unions reduce employee cost sharing and substantially increase the probability that employer-provided health plans extend to retirees. The union effects on coverage for current employees and for retirees have risen over time, and our estimates suggest that declining unionization explains about 17-20 percent of the decrease in employer-provided health insurance between 1983 and 1997.Labor unions ; Insurance, Health