José A. Moler

Minimal quasi-stationary distributions under nullR-recurrence

The existence of quasi-stationary distributions (QSD) in an absorbing Markov chain entails a stationary behaviour before absorption. In general, depending on the initial distribution, several QSDs may exist. Under some conditions upon the transition matrix between non-absorbing states, we prove that the QSD associated with any Dirac initial distribution, when it exists, is unique, and is the minimal QSD. In other words, if we take this QSD as an initial distribution, the process has the smallest probability of not being absorbed in the first jump.

On Testing Hypotheses in Response-Adaptive Designs Targeting the Best Treatment

We considerer a sequential, response-adaptive design for clinical trials which is characterized by the fact that it assigns patients to the best treatment with a probability converging to one. This property is optimal from an ethical point of view; in this paper we analyze some inferential problems related to the design. In particular, we want to establish, by means of a test of hypothesis, which treatment is superior, in the sense that it has greater mean response. Together with the natural generalization of the classical t-statistic, we introduce a statistic based on the probability of assigning patients to a treatment conditional on past observations. Theoretical properties of the tests are studied, together with numerical evaluations of the power for dichotomous responses.

Effects of reduced levels of sulfite in wine production using mixtures with lysozyme and dimethyl dicarbonate on levels of volatile and biogenic amines

ABSTRACT Sulphur dioxide (SO2) is an important preservative for wine, but its presence in foods can cause allergies and this has given impetus to the research for alternatives. The aim of this study was to reduce levels of sulfite in wine production using mixtures with lysozyme and dimethyl dicarbonate and examine the influence on levels of volatile and biogenic amines. To do so, vinifications were carried out using lysozyme, dimethyl dicarbonate (DMDC) and mixtures of these with SO2 in different concentrations (25 and 50 mg l−1). Results were compared with a control vinification with only SO2 (50 mg l−1). Mixing low concentrations of SO2 with lysozyme and DMDC reduced the concentration of biogenic amines (histamine, tyramine, putrescine, cadaverine, phenylethylamine + spermidine and spermine). In general, the total concentration of volatile amines (dimethylamine, isopropylamine, isobutylamine, pyrrolidine, ethylamine, diethylamine, amylamine and hexylamine) was higher in the sample fermented only with SO2. The concentrations of amines with secondary amino groups (dimethylamine, diethylamine, pyrrolidine) were higher in the sample only fermented with SO2 than those fermented with DMDC and lysozyme or with a mixture of preservatives. When SO2 was the only preservative in wine, total amine concentration (biogenic and volatile amines) was higher than for the rest of the treatments. Lysozyme by itself, and lysozyme mixed with SO2, both reduced the formation of biogenic amines but given the antioxidant activity of SO2 the use of the preservative mixture seems more advisable.

Randomization Based Inference for the Drop-The-Loser Rule

In the framework of clinical trials, legal and ethical restrictions make a population model unrealistic for sampling. Randomization tests are a viable alternative to classical inference. Their theoretical properties depend heavily on the random rule used to allocate patients to treatments, so that Ad-Hoc theoretical studies are necessary for each allocation design. In this paper, we obtain theoretical results for randomization tests when the drop-the-loser rule is used.

Oak wood extracts applied to the grapevine. An alternative to obtain quality Garnacha wines

Stomata in leaves regulate gas interchange and transpiration in the grapevine and through these pores both the penetration of aqueous solutions with nutrients as well as the excretion of products take place. The aim of this work was to study the influence of spraying the vineyard with toasted and untoasted oak extracts on the volatile composition and on the organoleptic quality of wine made from Garnacha grapes. The results were compared with a Garnacha control wine obtained with grapes sprayed with distilled water. The absorption of the compounds from the oak wood extracts was irregular and some of these compounds were modified by the yeast during fermentation so as to prevent fermentation problems. This was observed particularly in the case of furfural which were transformed into furfuryl alcohol by yeast in order to avoid irreversible cellular damage. On applying a discriminant analysis to the concentration of volatile compounds in the wines, the three treatments (control, toasted and untoasted oak extracts) were differentiate. The wine obtained from grapes treated with toasted oak extract showed a more intense wood aroma after 18months of bottle aging than the other wines. Likewise, spicy aromas were found to be more intense in the samples treated with some type of oak wood extracts.

Simulation of household electricity consumption by using Functional Data Analysis

Obtaining patterns for electricity consumption in a particular household is a key issue to simulate and dimension the electricity supply needed in an isolated house. The electricity consumption profile (load curve) of a user is a function that indicates the electrical consumption in a dwelling over a period of time, usually one day. When this function is considered as a datum and several days are observed, a sample of functions is obtained. Functional Data Analysis (FDA) provides procedures and techniques to analyze this kind of data. Specifically, functional linear regression is used to estimate the average daily consumption of electricity for a given household type. Classification of households is carried out by using characteristics of the dwellings and their inhabitants. Nevertheless, the electricity consumption is very variable among different households, even those belonging to the same type. Inhabitant behavior strongly influences energy consumption patterns and is an important factor that accounts for a major share of the observed variability in the household consumption. The error term of the regression model captures this specific variability. In this paper we propose a method for its modeling based on a functional principal component analysis, which captures the homoscedasticity and main variability patterns, followed by fitting a sinusoidal function series to the error remainder. This statistical modeling facilitates the simulation of new individual load curves for any household, depending on the profile of the dwelling and its inhabitants. We illustrate this methodology with a real data set of household consumptions.

Asymptotic Behavior of a Randomization Test for a Response-Adaptive Design

Abstract Response-adaptive designs allow the incorporation of ethical goals in the performance of a clinical trial, and they have been thoroughly studied assuming that treatment responses follow a population model. However, in some clinical trials, population models are not appropriate and randomization tests appear as a plausible alternative to make inference. Randomization-based tests can be devised but the calculation of their exact p-values when a response-adaptive design is used to allocate patients is either time consuming or not feasible for moderate to large sample sizes and so asymptotic results become helpful. Nevertheless, these asymptotic results are not available for response-adaptive designs with good properties. The Klein allocation rule is a response-adaptive design, with good ethical and inferential properties, that generalizes the classical Ehrenfest urn design by making the replacement policy dependent on the response of the last patient. The goal of this article is to study the asymptotic distribution of a test statistic under a randomization-based approach when patients are allocated by using the Klein allocation rule.

A New Tool for Comparing Adaptive Designs; a Posteriori Efficiency

In this work, we consider an adaptive linear regression model designed to explain the patient’s response in a clinical trial. Patients are assumed to arrive sequentially. The adaptive nature of this statistical model allows the error terms to depend on the past which has not been permitted in other adaptive models in the literature.