Markov chain Monte Carlo methods for high dimensional inversion in remote sensing

Summary.  We discuss the inversion of the gas profiles (ozone, NO₃, NO₂, aerosols and neutral density) in the upper atmosphere from the spectral occultation measurements. The data are produced by the 'Global ozone monitoring of occultation of stars' instrument on board the Envisat satellite that was launched in March 2002. The instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10–20 km. The new feature is that these data allow the inversion of the gas concentration height profiles. A short introduction is given to the present operational data management procedure with examples of the first real data inversion. Several solution options for a more comprehensive statistical inversion are presented. A direct inversion leads to a non-linear model with hundreds of parameters to be estimated. The problem is solved with an adaptive single-step Markov chain Monte Carlo algorithm. Another approach is to divide the problem into several non-linear smaller dimensional problems, to run parallel adaptive Markov chain Monte Carlo chains for them and to solve the gas profiles in repetitive linear steps. The effect of grid size is discussed, and we present how the prior regularization takes the grid size into account in a way that effectively leads to a grid-independent inversion.     

Goodness of fit for the inverse Gaussian distribution

For testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution-function statistic A² is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao-Blackwell distribution estimator. A table is given for the asymptotic critical points of A². These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for A². This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.     

Campus attitudes toward alcohol and drugs in a deep southern university.

In our zeal to deal with alcohol and drug abuse, we may have a distorted picture of what the majority of college students actually think about alcohol and drug use. Students in this study done at a public university located in the Deep South report being generally intolerant of substance abuse.     

The historical decline of fertility in Eastern Europe

I test the hypothesis that the growth of autonomy was the factor responsible for the decline of marital fertility in eight Eastern European countries. By growth of autonomy I mean increased control over one's political, personal, religious, economic and reproductive life. This increased control was manifested in revolutions, democratic political reforms, nationalist movements and declining marital fertility. The political reforms were the result of the growth of autonomy but they also accelerated the dissemination of these new ideas among the populace contributing to further growth of autonomy. My hypothesis is generally supported by the historical data.     

State of the unions: Assessment by elite American labor leaders

One hundred and sixty-four elite union leaders in the United States completed a survey to assess the condition of the American labor movement and the factors affecting it. The respondents included high-level international union and state federation officers, central labor presidents, and 58 shop stewards. This study compares the responses of these labor officials and finds that they have similar, negative assessments of the condition of the American labor movement. The study also finds that these leaders agree that the most important factors affecting the labor movement are collective bargaining rights, union leadership, union member solidarity, and the NLRB.     

Assessment of influence in non-linear measurement error models

We consider the assessment of outliers and influential observation in non-linear measurement error models. Residuals, leverage measures and case-deletiondiagonostics are examined. The method of local influence is also applied to the models. In particular, the perturbation of measurement error variances has been found useful in assessing the adequancy of the model assumptions. A numerical example is given to illustrate the application of the diagonostics.