Posterior contraction for conditionally Gaussian priors

The goal of statistics is to draw sensible conclusions from data. In mathematical statistics, observed data is assumed to be generated according to some unknown probability distribution. The aim is to find the unknown probability distribution using the available observations. In parametric statistics this is typically done by considering a finite-dimensional parametric family of probability distributions and estimating a parameter using the data. On the other hand, in non-parametric statistics one deals with infinite dimensional statistical models. The model is then described by some non-parametric parameter such as a probability distribution or a regression function. In Bayesian statistics one makes inference by choosing a probability distribution on the statistical model. We distinguish between the prior distribution and the posterior distribution. These distributions represent the statistician’s belief about the parameter before and after the data has become available. In the frequentist’s setup however, the parameter is assumed to have some true value. An asymptotic analysis is then possible by considering the posterior measure of shrinking neighborhoods around the true parameter as the number of observations increases. We are interested in how fast the posterior concentrates around the true parameter. In this thesis we consider two examples of a conditionally Gaussian process for the construction of a prior distribution on certain statistical models indexed by a function. The two examples that we consider are defined by choosing the paths of the process to be either tensor-product spline functions or location-scale kernel mixtures. The use of log-spline models and kernel mixtures to construct priors on probability densities is well-established in Bayesian non-parametrics. The use of Gaussian priors provides a unified approach to obtain rates of posterior contraction in various statistical settings. We consider density estimation, classification and fixed design regression settings. If the true function is a function of d variables with smoothness level ?? in the sense of H¨older, then the optimal rate of posterior contraction is of the order n-d+2?? if n is the number of observations. We show that it is possible to construct Gaussian priors from either the spline functions or the kernel mixtures which actually achieve posterior contraction at a near optimal rate. These priors will however depend on ??, an unknown characteristic of the function to be estimated. We show that in both cases it is possible to define a new procedure, based on these Gaussian priors, which also achieves a near optimal rate of posterior contraction, but which itself does not depend on the level of smoothness of the function of interest. This procedure thus adapts to the smoothness level. In the last chapter of this thesis, we focus on posterior contraction in the setting of fixed design regression with Gaussian errors. In this setting, the variance of the errors is a finite dimensional nuisance parameter which we can equip with a prior as well. The posterior contraction results imply in particular the concentration of posterior mass around this finite dimensional parameter at a non-parametric rate. We however know that posterior contraction in the finite-dimensional parameter case is typically faster: the optimal rate is n-1/2. We show via a semi-parametric Bernstein-von Mises result that it is possible to achieve posterior contraction around the finite dimensional parameter at rate n-1/2 if we equip the infinite dimensional parameter, the regression function f, as before with a Gaussian prior distribution

Cellijnen en Salmonella

In human gastrointestinal disease caused by Salmonella, transepithelial migration of neutrophils follows the attachment of bacteria to epithelial tissue. This migration of neutrophils is stimulated by the release of chemokines, including interleukin-8 (Il -8), from the epithelial cells. We have developed an in vitro model system (human epithelial monolayers, among which Caco-2 cells grown on microtiter multiwell plates) for studying host-pathogen interactions. After infection with different pathogens we measured Il-8 production during time. Results showed that Il-8 release was time related and varied with the pathogen. Salmonella enteritidis (Se) did induce the highest response. Subsequently, three doses of this Se strain were used and the Il-8 response was measured at different time points. Caco-2 cells remained intact over a period of 24h, the production of Il-8 increased in time and was found to be Se dose-dependent. Other tested epithelial monolayers, such as HT29 colon cancer cells, gave similar results.Infectie met Salmonella kan gepaard gaan met de invasie van darmepitheelcellen. De aan de invasie voorafgaande aanhechting leidt reeds tot de transmigratie van witte bloedcellen (neutrofielen) vanuit de bloedbaan naar het epitheelweefsel. De migratie wordt gestimuleerd door de productie van chemokines, waaronder interleukine-8 (Il-8) door epitheelcellen. Wij hebben een in vitro model systeem ontwikkeld (humaan epitheelweefsel gekweekt in microtiterplaten) waarin gastheer - pathogeen interacties kunnen worden bestudeerd. Epitheelcellen zijn gedurende een uur blootgesteld aan verschillende pathogene micro-organismen, waarna de Il-8 response is gemeten. Als controle zijn meegenomen een Escherichia coli stam zonder LPS en een probiotische Lactobacillus. De resultaten laten zien dat de IL-8 productie per pathogeen varieert, waarbij Salmonella enteritidis de hoogste respons geeft. In vervolgexperimenten zijn drie concentraties S. enteritidis gebruikt, waarna de respons gedurende 24 uur is gemeten. De gebruikte cellijn bleek na 24 uur nog intact, de Il-8 productie correleerde met de doses, en nam toe in de tijd. Hieruit kan geconcludeerd worden dat het door ons ontwikkelde model gebruikt kan worden voor het bestuderen van factoren die van invloed zijn op dosis-respons relaties. De respons betreft dan prikkeling van het immuunsysteem ten gevolge van adhesie en invasie van darmepitheelcellen door salmonellae. Tenslotte wordt een benaderingwijze voorgesteld om resultaten van in vitro dosis-respons experimenten te vertalen naar de mens

Future challenges to microbial food safety

Despite significant efforts by all parties involved, there is still a considerable burden of foodborne illness, in which micro-organisms play a prominent role. Microbes can enter the food chain at different steps, are highly versatile and can adapt to the environment allowing survival, growth and production of toxic compounds. This sets them apart from chemical agents and thus their study from food toxicology. We summarize the discussions of a conference organized by the Dutch Food and Consumer Products Safety Authority and the European Food Safety Authority. The goal of the conference was to discuss new challenges to food safety that are caused by micro-organisms as well as strategies and methodologies to counter these. Management of food safety is based on generally accepted principles of Hazard Analysis Critical Control Points and of Good Manufacturing Practices. However, a more pro-active, science-based approach is required, starting with the ability to predict where problems might arise by applying the risk analysis framework. Developments that may influence food safety in the future occur on different scales (from global to molecular) and in different time frames (from decades to less than a minute). This necessitates development of new risk assessment approaches, taking the impact of different drivers of change into account. We provide an overview of drivers that may affect food safety and their potential impact on foodborne pathogens and human disease risks. We conclude that many drivers may result in increased food safety risks, requiring active governmental policy setting and anticipation by food industries whereas other drivers may decrease food safety risks. Monitoring of contamination in the food chain, combined with surveillance of human illness and epidemiological investigations of outbreaks and sporadic cases continue to be important sources of information. New approaches in human illness surveillance include the use of molecular markers for improved outbreak detection and source attribution, sero-epidemiology and disease burden estimation. Current developments in molecular techniques make it possible to rapidly assemble information on the genome of various isolates of microbial species of concern. Such information can be used to develop new tracking and tracing methods, and to investigate the behavior of micro-organisms under environmentally relevant stress conditions. These novel tools and insight need to be applied to objectives for food safety strategies, as well as to models that predict microbial behavior. In addition, the increasing complexity of the global food systems necessitates improved communication between all parties involved: scientists, risk assessors and risk managers, as well as consumer

The role and evolution of fungal effectors in plant pathogenesis

cum laude graduation (with distinction