Tools in pharmacovigilance in psychiatry: therapeutic drug monitoring, pharmacogenetic tests and drug-drug interactions databases

SUMMARYIn order to increase drug safety we must better understand how medication interacts with the body of our patients and this knowledge should be made easily available for the clinicians prescribing the medication. This thesis contributes to how the knowledge of some drug properties can increase and how to make information readily accessible for the medical professionals. Furthermore it investigates the use of Therapeutic drug monitoring, drug interaction databases and pharmacogenetic tests in pharmacovigilance.Two pharmacogenetic studies in the naturalistic setting of psychiatric in-patients clinics have been performed; one with the antidepressant mirtazapine, the other with the antipsychotic clozapine. Forty-five depressed patients have been treated with mirtazapine and were followed for 8 weeks. The therapeutic effect was as seen in other previous studies. Enantioselective analyses could confirm an influence of age, gender and smoking in the pharmacokinetics of mirtazapine; it showed a significant influence of the CYP2D6 genotype on the antidepressant effective S-enantiomer, and for the first time an influence of the CYP2B6 genotype on the plasma concentrations of the 8-OH metabolite was found. The CYP2B6*/*6 genotype was associated to better treatment response. A detailed hypothesis of the metabolic pathways of mirtazapine is proposed. In the second pharmacogenetic study, analyses of 75 schizophrenic patients treated with clozapine showed the influence of CYP450 and ABCB1 genotypes on its pharmacokinetics. For the first time we could demonstrate an in vivo effect of the CYP2C19 genotype and an influence of P-glycoprotein on the plasma concentrations of clozapine. Further we confirmed in vivo the prominent role of CYP1A2 in the metabolism of clozapine.Identifying risk factors for the occurrence of serious adverse drug reactions (SADR) would allow a more individualized and safer drug therapy. SADR are rare events and therefore difficult to study. We tested the feasibility of a nested matched case-control study to examine the influence of high drug plasma levels and CYP2D6 genotypes on the risk to experience an SADR. In our sample we compared 62 SADR cases with 82 controls; both groups were psychiatric patients from the in-patient clinic Königsfelden. Drug plasma levels of >120% of the upper recommended references could be identified as a risk factor with a statistically significant odds ratio of 3.5, a similar trend could be seen for CYP2D6 poor metaboliser. Although a matched case-control design seems a valid method, 100% matching is not easy to perform in a relative small cohort of one in-patient clinic. However, a nested case-control study is feasible.On the base of the experience gained in the AMSP+ study and the fact that we have today only sparse data indicating that routine drug plasma concentration monitoring and/or pharmacogenetic testing in psychiatry are justified to minimize the risk for ADR, we developed a test algorithm named "TDM plus" (TDM plus interaction checks plus pharmacogenetic testing).Pharmacovigilance programs such as the AMSP project (AMSP = Arzneimittelsicherheit in der Psychiatrie) survey psychiatric in-patients in order to collect SADR and to detect new safety signals. Case reports of such SADR are, although anecdotal, valuable to illustrate rare clinical events and sometimes confirm theoretical assumptions of e.g. drug interactions. Seven pharmacovigilance case reports are summarized in this thesis.To provide clinicians with meaningful information on the risk of drug combinations, during the course of this thesis the internet based drug interaction program mediQ.ch (in German) has been developed. Risk estimation is based on published clinical and pharmacological information of single drugs and alimentary products, including adverse drug reaction profiles. Information on risk factors such as renal and hepatic insufficiency and specific genotypes are given. More than 20'000 drug pairs have been described in detail. Over 2000 substances with their metabolic and transport pathways are included and all information is referenced with links to the published scientific literature or other information sources. Medical professionals of more than 100 hospitals and 300 individual practitioners do consult mediQ.ch regularly. Validations with comparisons to other drug interaction programs show good results.Finally, therapeutic drug monitoring, drug interaction programs and pharmacogenetic tests are helpful tools in pharmacovigilance and should, in absence of sufficient routine tests supporting data, be used as proposed in our TDM plus algorithm.RESUMEPour améliorer la sécurité d'emploi des médicaments il est important de mieux comprendre leurs interactions dans le corps des patients. Ensuite le clinicien qui prescrit une pharmacothérapie doit avoir un accès simple à ces informations. Entre autres, cette thèse contribue à mieux connaître les caractéristiques pharmacocinétiques de deux médicaments. Elle examine aussi l'utilisation de trois outils en pharmacovigilance : le monitorage thérapeutique des taux plasmatiques des médicaments (« therapeutic drug monitoring »), un programme informatisé d'estimation du risque de combinaisons médicamenteuses, et enfin des tests pharmacogénétiques.Deux études cliniques pharmacogénétiques ont été conduites dans le cadre habituel de clinique psychiatrique : l'une avec la mirtazapine (antidépresseur), l'autre avec la clozapine (antipsychotique). On a traité 45 patients dépressifs avec de la mirtazapine pendant 8 semaines. L'effet thérapeutique était semblable à celui des études précédentes. Nous avons confirmé l'influence de l'âge et du sexe sur la pharmacocinétique de la mirtazapine et la différence dans les concentrations plasmatiques entre fumeurs et non-fumeurs. Au moyen d'analyses énantiomères sélectives, nous avons pu montrer une influence significative du génotype CYP2D6 sur l'énantiomère S+, principalement responsable de l'effet antidépresseur. Pour la première fois, nous avons trouvé une influence du génotype CYP2B6 sur les taux plasmatiques de la 8-OH-mirtazapine. Par ailleurs, le génotype CYP2B6*6/*6 était associé à une meilleure réponse thérapeutique. Une hypothèse sur les voies métaboliques détaillées de la mirtazapine est proposée. Dans la deuxième étude, 75 patients schizophrènes traités avec de la clozapine ont été examinés pour étudier l'influence des génotypes des iso-enzymes CYP450 et de la protéine de transport ABCB1 sur la pharmacocinétique de cet antipsychotique. Pour la première fois, on a montré in vivo un effet des génotypes CYP2C19 et ABCB1 sur les taux plasmatiques de la clozapine. L'importance du CYP1A2 dans le métabolisme de la clozapine a été confirmée.L'identification de facteurs de risques dans la survenue d'effets secondaire graves permettrait une thérapie plus individualisée et plus sûre. Les effets secondaires graves sont rares. Dans une étude de faisabilité (« nested matched case-control design » = étude avec appariement) nous avons comparé des patients avec effets secondaires graves à des patients-contrôles prenant le même type de médicaments mais sans effets secondaires graves. Des taux plasmatiques supérieurs à 120% de la valeur de référence haute sont associés à un risque avec « odds ratio » significatif de 3.5. Une tendance similaire est apparue pour le génotype du CYP2D6. Le « nested matched case-control design » semble une méthode valide qui présente cependant une difficulté : trouver des patients-contrôles dans le cadre d'une seule clinique psychiatrique. Par contre la conduite d'une « nested case-control study » sans appariement est recommandable.Sur la base de notre expérience de l'étude AMSP+ et le fait que nous disposons que de peux de données justifiant des monitorings de taux plasmatiques et/ou de tests pharmacogénétiques de routine, nous avons développé un test algorithme nommé « TDMplus » (TDM + vérification d'interactions médicamenteuses + tests pharmacogénétique).Des programmes de pharmacovigilances comme celui de l'AMSP (Arzneimittelsicherheit in der Psychiatrie = pharmacovigilance en psychiatrie) collectent les effets secondaires graves chez les patients psychiatriques hospitalisés pour identifier des signaux d'alertes. La publication de certains de ces cas même anecdotiques est précieuse. Elle décrit des événements rares et quelques fois une hypothèse sur le potentiel d'une interaction médicamenteuse peut ainsi être confirmée. Sept publications de cas sont résumées ici.Dans le cadre de cette thèse, on a développé un programme informatisé sur internet (en allemand) - mediQ.ch - pour estimer le potentiel de risques d'une interaction médicamenteuse afin d'offrir en ligne ces informations utiles aux cliniciens. Les estimations de risques sont fondées sur des informations cliniques (y compris les profils d'effets secondaires) et pharmacologiques pour chaque médicament ou substance combinés. Le programme donne aussi des informations sur les facteurs de risques comme l'insuffisance rénale et hépatique et certains génotypes. Actuellement il décrit en détail les interactions potentielles de plus de 20'000 paires de médicaments, et celles de 2000 substances actives avec leurs voies de métabolisation et de transport. Chaque information mentionne sa source d'origine; un lien hypertexte permet d'y accéder. Le programme mediQ.ch est régulièrement consulté par les cliniciens de 100 hôpitaux et par 300 praticiens indépendants. Les premières validations et comparaisons avec d'autres programmes sur les interactions médicamenteuses montrent de bons résultats.En conclusion : le monitorage thérapeutique des médicaments, les programmes informatisés contenant l'information sur le potentiel d'interaction médicamenteuse et les tests pharmacogénétiques sont de précieux outils en pharmacovigilance. Nous proposons de les utiliser en respectant l'algorithme « TDM plus » que nous avons développé.

Using qualia information to identify lexical semantic classes in an unsupervised clustering task

Acquiring lexical information is a complex problem, typically approached by relying on a number of contexts to contribute information for classification. One of the first issues to address in this domain is the determination of such contexts. The work presented here proposes the use of automatically obtained FORMAL role descriptors as features used to draw nouns from the same lexical semantic class together in an unsupervised clustering task. We have dealt with three lexical semantic classes (HUMAN, LOCATION and EVENT) in English. The results obtained show that it is possible to discriminate between elements from different lexical semantic classes using only FORMAL role information, hence validating our initial hypothesis. Also, iterating our method accurately accounts for fine-grained distinctions within lexical classes, namely distinctions involving ambiguous expressions. Moreover, a filtering and bootstrapping strategy employed in extracting FORMAL role descriptors proved to minimize effects of sparse data and noise in our task.

Evaluation of statistical and geostatistical models of digital soil properties mapping in tropical mountain regions

Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR) and geostatistical (ordinary kriging and co-kriging). The study was conducted in the municipality of Bom Jardim, RJ, using a soil database with 208 sampling points. Predictive models were evaluated for sand, silt and clay fractions, pH in water and organic carbon at six depths according to the specifications of the consortium of digital soil mapping at the global level (GlobalSoilMap). Continuous covariates and categorical predictors were used and their contributions to the model assessed. Only the environmental covariates elevation, aspect, stream power index (SPI), soil wetness index (SWI), normalized difference vegetation index (NDVI), and b3/b2 band ratio were significantly correlated with soil properties. The predictive models had a mean coefficient of determination of 0.21. Best results were obtained with the geostatistical predictive models, where the highest coefficient of determination 0.43 was associated with sand properties between 60 to 100 cm deep. The use of a sparse data set of soil properties for digital mapping can explain only part of the spatial variation of these properties. The results may be related to the sampling density and the quantity and quality of the environmental covariates and predictive models used.

The problem of nitrogen disposal in the obese

Amino-N is preserved because of the scarcity and nutritional importance of protein. Excretion requires its conversion to ammonia, later incorporated into urea. Under conditions of excess dietary energy, the body cannot easily dispose of the excess amino-N against the evolutively adapted schemes that prevent its wastage; thus ammonia and glutamine formation (and urea excretion) are decreased. High lipid (and energy) availability limits the utilisation of glucose, and high glucose spares the production of ammonium from amino acids, limiting the synthesis of glutamine and its utilisation by the intestine and kidney. The amino acid composition of the diet affects the production of ammonium depending on its composition and the individual amino acid catabolic pathways. Surplus amino acids enhance protein synthesis and growth, and the synthesis of non-protein-N-containing compounds. But these outlets are not enough; consequently, less-conventional mechanisms are activated, such as increased synthesis of NO∙ followed by higher nitrite (and nitrate) excretion and changes in the microbiota. There is also a significant production of N(2) gas, through unknown mechanisms. Health consequences of amino-N surplus are difficult to fathom because of the sparse data available, but it can be speculated that the effects may be negative, largely because the fundamental N homeostasis is stretched out of normalcy, forcing the N removal through pathways unprepared for that task. The unreliable results of hyperproteic diets, and part of the dysregulation found in the metabolic syndrome may be an unwanted consequence of this N disposal conflict.

A Unified Framework for Regularization Networks and Support Vector Machines

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples -- in particular the regression problem of approximating a multivariate function from sparse data. We present both formulations in a unified framework, namely in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics.

Upper-mantle seismic anisotropy from SKS splitting in the South American stable platform: A test of asthenospheric flow models beneath the lithosphere

Upper-mantle seismic anisotropy has been extensively used to infer both present and past deformation processes at lithospheric and asthenospheric depths. Analysis of shear-wave splitting (mainly from core-refracted SKS phases) provides information regarding upper-mantle anisotropy. We present average measurements of fast-polarization directions at 21 new sites in poorly sampled regions of intra-plate South America, such as northern and northeastern Brazil. Despite sparse data coverage for the South American stable platform, consistent orientations are observed over hundreds of kilometers. Over most of the continent, the fast-polarization direction tends to be close to the absolute plate motion direction given by the hotspot reference model HS3-NUVEL-1A. A previous global comparison of the SKS fast-polarization directions with flow models of the upper mantle showed relatively poor correlation on the continents, which was interpreted as evidence for a large contribution of ""frozen"" anisotropy in the lithosphere. For the South American plate, our data indicate that one of the reasons for the poor correlation may have been the relatively coarse model of lithospheric thicknesses. We suggest that improved models of upper-mantle flow that are based on more detailed lithospheric thicknesses in South America may help to explain most of the observed anisotropy patterns.

Upper-mantle seismic anisotropy from SKS splitting in the South American stable platform: A test of asthenospheric flow models beneath the lithosphere

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Influence of sedation on morbidity and mortality in the intensive care unit

CONTEXTO: Embora cerca de 30% a 50% dos pacientes hospitalizados em unidades de terapia intensiva (UTI) recebam algum tipo de sedativo, existe escassez de informações sobre efeitos adversos desta prática, especialmente no Brasil. Estes efeitos podem ser significantes e o uso de sedativos é associado a elevação de infecção e mortalidade, mesmo sendo difícil avaliar o impacto clínico deste procedimento. OBJETIVO: Avaliar o impacto da sedação sobre incidência de complicações e mortalidade em doentes graves durante internação em unidade de terapia intensiva. TIPO DE ESTUDO: Estudo prospectivo. LOCAL: Unidade de Terapia Intensiva Cirúrgica da Universidade Federal de São Paulo (UNIFESP) - Escola Paulista de Medicina. PARTICIPANTES: Após excluídos pacientes que permaneceram menos de 24 horas ou sem exames indispensáveis para o cálculo do índice de gravidade (APACHE II), restaram 307 pacientes. Estes foram divididos em dois grupos: Grupo Sedado e Grupo Não Sedado. Constatada heterogeneidade com relação ao APACHE II, foram pareados 97 sedados e 97 não sedados com idênticos índices de gravidade. VARIÁVEIS ESTUDADAS: Impacto da sedação e das técnicas sobre a mortalidade, tempo de internação, além da incidência de escara de decúbito ou pressão, trombose venosa profunda e infecção. RESULTADOS: Não houve diferença na incidência de trombose venosa profunda, entre os grupos Sedado e Não Sedado, enquanto que escara de decúbito foi significativamente maior nos sedados (p = 0,03). Infecção foi detectada em 45,4% dos pacientes com sedação e em 21,6% dos pacientes sem sedação (p = 0,006). A mortalidade para os pacientes que não receberam qualquer tipo de sedativo foi de 20,6% e, para aqueles que foram sedados durante a internação, foi de 52,6% (p < 0,0001). CONCLUSÕES: Conclui-se que a sedação está associada a maior duração da internação, morbidade e mortalidade significativas. Apesar da intensidade das associações encontradas, não é possível estabelecer relação causal entre sedação e mortalidade.

Suitability of distance metrics as indexes of home-range size in tropical rodent species

Estimators of home-range size require a large number of observations for estimation and sparse data typical of tropical studies often prohibit the use of such estimators. An alternative may be use of distance metrics as indexes of home range. However, tests of correlation between distance metrics and home-range estimators only exist for North American rodents. We evaluated the suitability of 3 distance metrics (mean distance between successive captures [SD], observed range length [ORL], and mean distance between all capture points [AD]) as indexes for home range for 2 Brazilian Atlantic forest rodents, Akodon montensis (montane grass mouse) and Delomys sublineatus (pallid Atlantic forest rat). Further, we investigated the robustness of distance metrics to low numbers of individuals and captures per individual. We observed a strong correlation between distance metrics and the home-range estimator. None of the metrics was influenced by the number of individuals. ORL presented a strong dependence on the number of captures per individual. Accuracy of SD and AD was not dependent on number of captures per individual, but precision of both metrics was low with numbers of captures below 10. We recommend the use of SD and AD instead of ORL and use of caution in interpretation of results based on trapping data with low captures per individual.

Bayesian generalized linear models for meta-analysis of diagnostic tests

With the recognition of the importance of evidence-based medicine, there is an emerging need for methods to systematically synthesize available data. Specifically, methods to provide accurate estimates of test characteristics for diagnostic tests are needed to help physicians make better clinical decisions. To provide more flexible approaches for meta-analysis of diagnostic tests, we developed three Bayesian generalized linear models. Two of these models, a bivariate normal and a binomial model, analyzed pairs of sensitivity and specificity values while incorporating the correlation between these two outcome variables. Noninformative independent uniform priors were used for the variance of sensitivity, specificity and correlation. We also applied an inverse Wishart prior to check the sensitivity of the results. The third model was a multinomial model where the test results were modeled as multinomial random variables. All three models can include specific imaging techniques as covariates in order to compare performance. Vague normal priors were assigned to the coefficients of the covariates. The computations were carried out using the 'Bayesian inference using Gibbs sampling' implementation of Markov chain Monte Carlo techniques. We investigated the properties of the three proposed models through extensive simulation studies. We also applied these models to a previously published meta-analysis dataset on cervical cancer as well as to an unpublished melanoma dataset. In general, our findings show that the point estimates of sensitivity and specificity were consistent among Bayesian and frequentist bivariate normal and binomial models. However, in the simulation studies, the estimates of the correlation coefficient from Bayesian bivariate models are not as good as those obtained from frequentist estimation regardless of which prior distribution was used for the covariance matrix. The Bayesian multinomial model consistently underestimated the sensitivity and specificity regardless of the sample size and correlation coefficient. In conclusion, the Bayesian bivariate binomial model provides the most flexible framework for future applications because of its following strengths: (1) it facilitates direct comparison between different tests; (2) it captures the variability in both sensitivity and specificity simultaneously as well as the intercorrelation between the two; and (3) it can be directly applied to sparse data without ad hoc correction. ^

Model results of ocean physical field of the reference state and the targets in NetCDF format

In a feasibility study, the potential of proxy data for the temperature and salinity during the Last Glacial Maximum (LGM, about 19 000 to 23 000 years before present) in constraining the strength of the Atlantic meridional overturning circulation (AMOC) with a general ocean circulation model was explored. The proxy data were simulated by drawing data from four different model simulations at the ocean sediment core locations of the Multiproxy Approach for the Reconstruction of the Glacial Ocean surface (MARGO) project, and perturbing these data with realistic noise estimates. The results suggest that our method has the potential to provide estimates of the past strength of the AMOC even from sparse data, but in general, paleo-sea-surface temperature data without additional prior knowledge about the ocean state during the LGM is not adequate to constrain the model. On the one hand, additional data in the deep-ocean and salinity data are shown to be highly important in estimating the LGM circulation. On the other hand, increasing the amount of surface data alone does not appear to be enough for better estimates. Finally, better initial guesses to start the state estimation procedure would greatly improve the performance of the method. Indeed, with a sufficiently good first guess, just the sea-surface temperature data from the MARGO project promise to be sufficient for reliable estimates of the strength of the AMOC.

Biologic therapies and non-melanoma skin cancer rates in three chronic immune-mediated diseases

Trabalho Final do Curso de Mestrado Integrado em Medicina, Faculdade de Medicina, Universidade de Lisboa, 2014

Bayesian population pharmacokinetic analysis of sirolimus

Objective: It is usual that data collected from routine clinical care is sparse and unable to support the more complex pharmacokinetic (PK) models that may have been reported in previous rich data studies. Informative priors may be a pre-requisite for model development. The aim of this study was to estimate the population PK parameters of sirolimus using a fully Bayesian approach with informative priors. Methods: Informative priors including prior mean and precision of the prior mean were elicited from previous published studies using a meta-analytic technique. Precision of between-subject variability was determined by simulations from a Wishart distribution using MATLAB (version 6.5). Concentration-time data of sirolimus retrospectively collected from kidney transplant patients were analysed using WinBUGS (version 1.3). The candidate models were either one- or two-compartment with first order absorption and first order elimination. Model discrimination was based on computation of the posterior odds supporting the model. Results: A total of 315 concentration-time points were obtained from 25 patients. Most data were clustered at trough concentrations with range of 1.6 to 77 hours post-dose. Using informative priors, either a one- or two-compartment model could be used to describe the data. When a one-compartment model was applied, information was gained from the data for the value of apparent clearance (CL/F = 18.5 L/h), and apparent volume of distribution (V/F = 1406 L) but no information was gained about the absorption rate constant (ka). When a two-compartment model was fitted to the data, the data were informative about CL/F, apparent inter-compartmental clearance, and apparent volume of distribution of the peripheral compartment (13.2 L/h, 20.8 L/h, and 579 L, respectively). The posterior distribution of the volume distribution of central compartment and ka were the same as priors. The posterior odds for the two-compartment model was 8.1, indicating the data supported the two-compartment model. Conclusion: The use of informative priors supported the choice of a more complex and informative model that would otherwise have not been supported by the sparse data.

Can restricting calories help you to live longer?

Excess calorie consumption is associated with metabolic disorders and increased incidence of morbidity. Restricting calorie content, either by daily calorie restriction or intermittent fasting periods, has multiple benefits including weight loss and improved body composition. Previous research has shown that restricting calories in this way can increase longevity and slow the ageing process in laboratory animals, although only sparse data exist in human populations. This review critically evaluates the benefits of these dietary interventions on age-related decline and longevity.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.