Lectures and conferences on mathematical statistics and probability.

Original mimeographed ed. published in 1938 under title: Lectures and conferences on mathematical statistics.

Accounting for Fetal Death: Vital Statistics and the Medicalization of Pregnancy in the United States

Recent reports by the Centers for Disease Control and Prevention have decried the high rate of fetal mortality in the contemporary United States. Much of the data about fetal and infant deaths, as well as other poor pregnancy outcomes, are tabulated and tracked through vital statistics. In this article, I demonstrate how notions of fetal death became increasingly tied to the surveillance of maternal bodies through the tabulating and tracking of vital statistics in the middle part of the twentieth century. Using a historical analysis of the revisions to the United States Standard Certificate of Live Birth, and the United States Standard Report of Fetal Death, I examine how the categories of analysis utilized in these documents becomes integrally linked to contemporary ideas about fetal and perinatal death, gestational age, and prematurity. While it is evident that there are relationships between maternal behavior and birth outcomes, in this article I interrogate the ways in which the surveillance of maternal bodies through vital statistics has naturalized these relationships. Copyright 2013 Elsevier Ltd. All rights reserved.

Lecture notes on probability, statistics, and experimental errors; an elementary summary for students of experimental science.

Mode of access: Internet.

Relevant Aspects on Teaching Probability and Statistics in Basic General Education

Probability and Statistics were included in the Basic General Education curricula by the Ministry of Public Education (Costa Rica), since 1995. To analyze the teaching reality in these fields, a research was conducted in two educational regions of the country: Heredia and Pérez Zeledón. The survey included university training and updating processes of teachers teaching Statistics and Probability in the schools. The research demonstrated the limited university training in these fields, the dissatisfaction of teachers about it, and the poor support of training institutions to their professional exercise.

Forecast encompassing tests and probability forecasts

We consider tests of forecast encompassing for probability forecasts, for both quadratic and logarithmic scoring rules. We propose test statistics for the null of forecast encompassing, present the limiting distributions of the test statistics, and investigate the impact of estimating the forecasting models' parameters on these distributions. The small-sample performance is investigated, in terms of small numbers of forecasts and model estimation sample sizes. We show the usefulness of the tests for the evaluation of recession probability forecasts from logit models with different leading indicators as explanatory variables, and for evaluating survey-based probability forecasts.

Calculation of non-Gaussian statistics and bit error rate degradation due to pulse-to-pulse interaction

We develop a theoretical method to calculate jitter statistics of interacting solitons. Applying this approach, we have derived the non-Gaussian probability density function and calculated the bit-error rate as a function of noise level, initial separation and phase difference between solitons.

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.

Theoretical estimates of consumable food and probability of acquiring food in larvae of Chrysomya putoria (Diptera: Calliphoridae)

An indirect estimate of consumable food and probability of acquiring food in a blowfly species, Chrysomya putoria, is presented. This alternative procedure combines three distinct models to estimate consumable food in the context of the exploitative competition experienced by immature individuals in blowfly populations. The relevant parameters are derived from data for pupal weight and survival and estimates of density-independent larval mortality in twenty different larval densities. As part of this procedure, the probability of acquiring food per unit of time and the time taken to exhaust the food supply are also calculated. The procedure employed here may be valuable for estimations in insects whose immature stages develop inside the food substrate, where it is difficult to partial out confounding effects such as separation of faeces. This procedure also has the advantage of taking into account the population dynamics of immatures living under crowded conditions, which are particularly characteristic of blowflies and other insects as well.

Incongruence between test statistics and P values in medical papers

Given an observed test statistic and its degrees of freedom, one may compute the observed P value with most statistical packages. It is unknown to what extent test statistics and P values are congruent in published medical papers. Methods:We checked the congruence of statistical results reported in all the papers of volumes 409–412 of Nature (2001) and a random sample of 63 results from volumes 322–323 of BMJ (2001). We also tested whether the frequencies of the last digit of a sample of 610 test statistics deviated from a uniform distribution (i.e., equally probable digits).Results: 11.6% (21 of 181) and 11.1% (7 of 63) of the statistical results published in Nature and BMJ respectively during 2001 were incongruent, probably mostly due to rounding, transcription, or type-setting errors. At least one such error appeared in 38% and 25% of the papers of Nature and BMJ, respectively. In 12% of the cases, the significance level might change one or more orders of magnitude. The frequencies of the last digit of statistics deviated from the uniform distribution and suggested digit preference in rounding and reporting.Conclusions: this incongruence of test statistics and P values is another example that statistical practice is generally poor, even in the most renowned scientific journals, and that quality of papers should be more controlled and valued

Optimal magnitude and probability of fines

The economic literature on crime and punishment focuses on the trade-off between probability and severity of punishment, and suggests that detection probability and fines are substitutes. In this paper it is shown that, in presence of substantial underdeterrence caused by costly detection and punishment, these instruments may become complements. When offenders are poor, the deterrent value of monetary sanctions is low. Thus, the government does not invest a lot in detection. If offenders are rich, however, the deterrent value of monetary sanctions is high, so it is more profitable to prosecute them.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.