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Background: Identifying effective treatments and policies early in a pandemic is challenging because only limited and noisy data are available, and biological processes are unknown or uncertain. Consequently, classical statistical procedures may not work or require strong structural assumptions. An information-theoretic approach can overcome these problems and identify effective treatments and policies. The efficacy of this approach is illustrated using a study conducted at the beginning of the COVID-19 pandemic.Methods: An information-theoretic inferential approach with and without prior information was applied to the limited data available in the second month (April 24, 2020) of the COVID-19 pandemic. For comparison, a second statistical analysis used a large sample with millions of observations available at the end of the pandemic’s pre-vaccination period (mid-December 2020).Results: Even with limited data, the information-theoretic estimates performed well in identifying influential factors and helped explain why death rates varied across nations. Later experiments and statistical analyses based on more recent, richer data confirm that these factors contribute to survival.Conclusions: An information-theoretic statistical technique is a robust method that can overcome the challenges of under-identified estimation problems in the early stages of medical emergencies. It can easily incorporate prior information from theory, logic, or previously observed emergencies.

Modeling and inference are central to most areas of science and especially to evolving and complex systems. Critically, the information we have is often uncertain and insufficient, resulting in an underdetermined inference problem; multiple inferences, models, and theories are consistent with available information. Information theory (in particular, the maximum information entropy formalism) provides a way to deal with such complexity. It has been applied to numerous problems, within and across many disciplines, over the last few decades. In this perspective, we review the historical development of this procedure, provide an overview of the many applications of maximum entropy and its extensions to complex systems, and discuss in more detail some recent advances in constructing comprehensive theory based on this inference procedure. We also discuss efforts at the frontier of information-theoretic inference: application to complex dynamic systems with time-varying constraints, such as highly disturbed ecosystems or rapidly changing economies.

To prevent discrimination, the U.S. Navy enlisted-personnel promotion process relies primarily on objective measures. However, it also uses the subjective opinion of a sailor's superior. The Navy's promotion and retention process involves two successive decisions: The Navy decides whether to promote an individual, and conditional on that decision, the sailor decides whether to stay. Using estimates of these correlated decision-making processes, we find that during 1997-2008, Blacks and Hispanics were less likely to be promoted than Whites, especially during wartime. The Navy's decision-making affects Blacks' differential promotion rates by twice as much as differences in the groups' characteristics. However, Nonwhite retention probabilities, even when not promoted, are higher than for Whites, in part because they have fewer opportunities in the civilian market. Females have lower promotion rates than males and slightly lower retention rates during wartime.

We present a new, information-theoretic approach for estimating a system of many demand equations where the unobserved reservation or choke prices vary across consumers. We illustrate this method by estimating a nonlinear, almost ideal demand system (AIDS) for four types of meat using cross-sectional data from Mexico, where most households did not buy at least one type of meat during the survey week. The system of de­mand curves vary across demo­graphic groups.

The Navy’s promotion-retention process involves two successive decisions: The Navy decides whether an individual is selected for promotion, and then, conditional on the Navy’s decision, the sailor decides whether to reenlist or leave the Navy. Rates of promotion and retention depend on individuals’ demographic and other characteristics, wars and economic conditions and factors that the Navy policy makers can control. Using estimates of these decision-making processes, we examine two important public policy questions: Do Navy promotion and retention rates differ across race and sex? Can the Navy alter its promotion and other policies to better retain sailors, or do war and civilian labor market conditions determine retention?

We develop a generalized maximum entropy estimator that can estimate pure and mixed strategies subject to restrictions from game theory. This method avoids distributional assumptions and is consistent and efficient. We demonstrate this method by estimating the mixed strategies of duopolistic airlines.

A variety of parametric and semiparametric models produce qualitatively similar estimates of government policies’ effects on income distribution and welfare (as measured by the Gini, standard deviation of logarithms, relative mean deviation, coefficient of variation, and various Atkinson indexes). Taxes and the Earned Income Tax Credit are an effective way to redistribute income to the poor and raise welfare. The minimum wage lowers welfare. Social insurance programs have little effect except for Supplemental Security Income, which raises welfare. Transfer programs (AFDC/TANF and food stamps) either have no statistically significant effect or lower welfare.

We use a nonlinear, nonparametric method to forecast the unemployment rates. We compare these forecasts to several linear and nonlinear parametric methods based on the work of Montgomery et al. (1998) and Carruth et al. (1998). Our main result is that, due to the nonlin-earity in the data generating process, the nonparametric method outperforms many other well-known models, even when these models use more information. This result holds for forecasts based on quarterly and on monthly data.

A semiparametric estimator for evaluating the parameters of data generated under a sample selection process is developed. This estimator is based on the generalized maximum entropy estimator and performs well for small and ill-posed samples. Theoretical and sampling comparisons with parametric and semiparametric estimators are given. This method and standard ones are applied to three small-sample empirical applications of the wage-participation model for female teenage heads of households, immigrants, and Native Americans.

The minimum wage, unlike most government transfer programs, lowered welfare in the 1980s and 1990s as measured by all commonly used welfare or inequality measures, including various Atkinson indexes, the Gini index, standard deviation of logarithms, and others. The effects of most government programs, macroeconomic variables, and aggregate demographic characteristics were qualitatively the same for all the inequality measures.

This paper presents a new generalized maximum entropy (GME) approach to estimation of sample-selection models with small data sets, such as are found in many empirical agricultural economic analysis. For small samples, the GME approach produces more stable estimates and has smaller mean square error measures than other well-known estimators such as ordinary least squares, Heckman's two-step method, full-information maximum likelihood, and Ahn and Powell's method. The technique is used to analyze whether hired agricultural workers will work in piece-rate or time-rate jobs and to compare female-male wage differentials for both types of jobs.

A semi-parametric, information-based estimator is used to estimate strategies in prices and advertising for Coca-Cola and Pepsi-Cola. Separate strategies for each firm are estimated with and without restrictions from game theory. These information/entropy estimators are consistent, are efficient, and do not require distributional assumptions. These estimates are used to test theories about the strategies of firms and to see how changes in incomes or factor prices affect these strategies.

We develop a generalized maximum entropy estimator that can estimate pure and mixed strategies subject to restrictions from game theory. This method avoids distributional assumptions and is consistent and efficient. We demonstrate this method by estimating the mixed strategies of duopolistic airlines.

Generalized maximum entropy may be used to estimate mixed strategies subject to restrictions from game theory. This method avoids distributional assumptions and is consistent and efficient. We use this method to estimate the mixed strategies of duopolistic airlines.

Using a maximum entropy technique, we estimate the market shares of each firm in an industry using the available government summary statistics such as the four-firm concentration ratio (C4) and the Herfindahl-Hirschmann Index (HHI). We show that our technique is very effective in estimating the distribution of market shares in 20 industries. Our results provide support for the recent practice of using HHI rather than C4 as the key explanatory variable in many market power studies, if only one measure is to be used.