Natural gene-expression variation in Down syndrome modulates the outcome of gene-dosage imbalance.

Down syndrome (DS) is characterized by extensive phenotypic variability, with most traits occurring in only a fraction of affected individuals. Substantial gene-expression variation is present among unaffected individuals, and this variation has a strong genetic component. Since DS is caused by genomic-dosage imbalance, we hypothesize that gene-expression variation of human chromosome 21 (HSA21) genes in individuals with DS has an impact on the phenotypic variability among affected individuals. We studied gene-expression variation in 14 lymphoblastoid and 17 fibroblast cell lines from individuals with DS and an equal number of controls. Gene expression was assayed using quantitative real-time polymerase chain reaction on 100 and 106 HSA21 genes and 23 and 26 non-HSA21 genes in lymphoblastoid and fibroblast cell lines, respectively. Surprisingly, only 39% and 62% of HSA21 genes in lymphoblastoid and fibroblast cells, respectively, showed a statistically significant difference between DS and normal samples, although the average up-regulation of HSA21 genes was close to the expected 1.5-fold in both cell types. Gene-expression variation in DS and normal samples was evaluated using the Kolmogorov-Smirnov test. According to the degree of overlap in expression levels, we classified all genes into 3 groups: (A) nonoverlapping, (B) partially overlapping, and (C) extensively overlapping expression distributions between normal and DS samples. We hypothesize that, in each cell type, group A genes are the most dosage sensitive and are most likely involved in the constant DS traits, group B genes might be involved in variable DS traits, and group C genes are not dosage sensitive and are least likely to participate in DS pathological phenotypes. This study provides the first extensive data set on HSA21 gene-expression variation in DS and underscores its role in modulating the outcome of gene-dosage imbalance.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.

Expression of somatostatin receptors in human melanoma cell lines: effect of two different somatostatin analogues, octreotide and SOM230, on cell proliferation

Somatostatin analogues (SAs) are potential anticancer agents. This study was designed to investigate the expression of somatostatin receptors (SSTRs) in melanoma cells and the effect of two SAs on cell proliferation and viability. Eighteen primary and metastatic human cutaneous melanoma cell lines were treated with octreotide and SOM230. Expression of SSTR1, SSTR2, SSTR3 and SSTR5 was assessed by real-time polymerase chain reaction. Proliferation, viability and cell death were assessed using standard assays. Inhibition was modelled by mixed-effect regression. Melanoma cells expressed one or more SSTR. Both SAs inhibited proliferation of most melanoma cell lines, but inhibition was less than 50%. Neither SA affected cell viability or induced cell death. The results suggest that melanoma cell lines express SSTRs. The SAs investigated, under the conditions used in this study, did not, however, significantly inhibit melanoma growth or induce cell death. Novel SAs, combination therapy with SAs and their anti-angiogenic properties should be further investigated.

Expression and functional role of the prorenin receptor in the human adrenocortical zona glomerulosa and in primary aldosteronism.

OBJECTIVES: Prorenin can be detected in plasma of hypertensive patients. If detected in patients with primary aldosteronism could implicate prorenin in the development of primary aldosteronism. To address this issue, we measured the plasma prorenin levels in primary aldosteronism patients, the expression of the prorenin receptor (PRR) in the normal human adrenocortical zona glomerulosa and aldosterone-producing adenoma (APA), and we investigated the functional effects of PRR activation in human adrenocortical cells. METHOD: Plasma renin activity, aldosterone, and active and total trypsin-activated renin were measured in primary aldosteronism patients, essential hypertensive patients, and healthy individuals, and then prorenin levels were calculated. Localization and functional role of PRR were investigated in human and rat tissues, and aldosterone-producing cells. RESULTS: Primary aldosteronism patients had detectable plasma levels of prorenin. Using digital-droplet real-time PCR, we found a high PRR-to-porphobilinogen deaminase ratio in both the normal adrenal cortex and APAs. Marked expression of the PRR gene and protein was also found in HAC15 cells. Immunoblotting, confocal, and immunogold electron microscopy demonstrated PRR at the cell membrane and intracellularly. Renin and prorenin significantly triggered both CYP11B2 expression (aldosterone synthase) and ERK1/2 phosphorylation, but only CYP11B2 transcription was prevented by aliskiren. CONCLUSION: The presence of detectable plasma prorenin in primary aldosteronism patients, and the high expression of PRR in the normal human adrenal cortex, APA tissue, CD56+ aldosterone-producing cells, along with activation of CYP11B2 synthesis and ERK1/2 phosphorylation, suggest that the circulating and locally produced prorenin may contribute to the development or maintenance of human primary aldosteronism.

Renewal equations for option pricing

In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

Moottorimalliton skalaarisäätö

Työssä tutkitaan nopeusanturittoman vaihtovirtakäytön skalaarisia ohjaus- ja säätömenetelmiä. Työn alussa esitetään perusteoriat taajuusmuuttajista ja oikosulkumoottoreista. Tämän jälkeen esitellään yleisimmin kirjallisuudessa esiintyneet skalaariohjaukset ja –säädöt. Vektorisäätöä ja erityisesti moottoriparametrien vaikutusta säädön toimivuuteen esitellään lyhyesti. Työn tavoitteena on ACS800 taajuusmuuttajan skalaarisäädön tutkiminen. ACS800:n nykyinen skalaarisäätö on liian sidoksissa vektorisäätöön, joten simulointien ja kirjallisuustutkimuksen tarkoituksena on täysin vektorisäädöstä eriytetyn skalaarisäädön kehitysmahdollisuuksien tutkiminen. Kirjallisuudessa esiintyneiden säätöjen avulla muodostetaan diskreettiaikainen toteutus skalaarisäädölle vaihtovirtakäytössä, jossa on käytössä virran ja välipiirijännitteen takaisinkytkentä. Säädettävää moottoria mallinnetaan jatkuvaaikaisella L-sijaiskytkennällä. Välipiirin mallinnus toimii myös jatkuva-aikaisena lukuun ottamatta välipiirin tasavirtakomponenttia, joka muodostetaan virran takaisinkytkennän ja PWM-modulaattorin kytkinasentojen avulla. Simuloinnin tarkoituksena on mallintaa skalaarisäädön suurimpia ongelmia, kuten virta- ja välijännitesäätöä. Tuloksista voidaan päätellä, että perussäädöt toimivat moitteettomasti, mutta erityisesti virtasäätöä tulisi kehittää.

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

Spectral Analysis of Buffers in Communication Systems

Muokatun matriisi-geometrian tekniikan kehitys yleimmäksi jonoksi on esitelty tässä työssä. Jonotus systeemi koostuu useista jonoista joilla on rajatut kapasiteetit. Tässä työssä on myös tutkittu PH-tyypin jakautumista kun ne jaetaan. Rakenne joka vastaa lopullista Markovin ketjua jossa on itsenäisiä matriiseja joilla on QBD rakenne. Myös eräitä rajallisia olotiloja on käsitelty tässä työssä. Sen esitteleminen matriisi-geometrisessä muodossa, muokkaamalla matriisi-geometristä ratkaisua on tämän opinnäytetyön tulos.

Cdk5 controls lymphatic vessel development and function by phosphorylation of Foxc2.

The lymphatic system maintains tissue fluid balance, and dysfunction of lymphatic vessels and valves causes human lymphedema syndromes. Yet, our knowledge of the molecular mechanisms underlying lymphatic vessel development is still limited. Here, we show that cyclin-dependent kinase 5 (Cdk5) is an essential regulator of lymphatic vessel development. Endothelial-specific Cdk5 knockdown causes congenital lymphatic dysfunction and lymphedema due to defective lymphatic vessel patterning and valve formation. We identify the transcription factor Foxc2 as a key substrate of Cdk5 in the lymphatic vasculature, mechanistically linking Cdk5 to lymphatic development and valve morphogenesis. Collectively, our findings show that Cdk5-Foxc2 interaction represents a critical regulator of lymphatic vessel development and the transcriptional network underlying lymphatic vascular remodeling.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Consumption, investment and life insurance strategies with heterogeneous discounting

[cat] En aquest treball s'analitza l'efecte que comporta l'introducció de preferències inconsistents temporalment sobre les decisions òptimes de consum, inversió i compra d'assegurança de vida. En concret, es pretén recollir la creixent importància que un individu dóna a la herència que deixa i a la riquesa disponible per a la seva jubilació al llarg de la seva vida laboral. Amb aquesta finalitat, es parteix d'un model estocàstic en temps continu amb temps final aleatori, i s'introdueix el descompte heterogeni, considerant un agent amb una distribució de vida residual coneguda. Per tal d'obtenir solucions consistents temporalment es resol una equació de programació dinàmica no estàndard. Per al cas de funcions d'utilitat del tipus CRRA i CARA es troben solucions explícites. Finalment, els resultats obtinguts s'il·lustren numèricament.

Disentangling the formation of contrasting tree line physiognomies combining model selection and Bayesian parameterization for simulation models.

Alpine tree-line ecotones are characterized by marked changes at small spatial scales that may result in a variety of physiognomies. A set of alternative individual-based models was tested with data from four contrasting Pinus uncinata ecotones in the central Spanish Pyrenees to reveal the minimal subset of processes required for tree-line formation. A Bayesian approach combined with Markov chain Monte Carlo methods was employed to obtain the posterior distribution of model parameters, allowing the use of model selection procedures. The main features of real tree lines emerged only in models considering nonlinear responses in individual rates of growth or mortality with respect to the altitudinal gradient. Variation in tree-line physiognomy reflected mainly changes in the relative importance of these nonlinear responses, while other processes, such as dispersal limitation and facilitation, played a secondary role. Different nonlinear responses also determined the presence or absence of krummholz, in agreement with recent findings highlighting a different response of diffuse and abrupt or krummholz tree lines to climate change. The method presented here can be widely applied in individual-based simulation models and will turn model selection and evaluation in this type of models into a more transparent, effective, and efficient exercise.

Tavaratalokaupan strategiset menestystekijät

Tutkimuksen tavoitteena oli analysoida tavaratalokaupan strategisia menestystekijöitä, erityisesti tavarataloliiketoiminnan johtamisen merkitystä strategisena menestystekijänä. Empiirinen sovellus suunnattiin Sokos-tavarataloketjuun. Tutkimuksen osatavoitteena oli kuvata ja analysoida Sokos-tavarataloketjun liiketoiminnan kehittymistä 1970 - 1990 välisellä ajanjaksolla sekä pohtia syitä, miksi Sokos-liiketoiminta ajautui kriisiin 1990-luvun aikana. Vertailuksi otettiin Stockmann-tavarataloketjun menestyminen vastaavalla ajanjaksolla Tarkastelun kohteena oli johtamisen muuttuminen, liikeideamuutokset, ketjutoiminnan sekä hankinnan roolin muutokset Sokos-ketjussa. Lopuksi tavoitteena oli arvioida strategisen johtamisen onnistumista Sokos-ketjussa peilaten strategisten menesty stekij öiden viitekehykseen. Tutkimus on luonteeltaan toiminta-analyyttinenja sen aineistonkeruumenetelmänä käytettiin puolistrukturoitua haastattelua. Haastatteluja suoritettiin yhteensä kahdeksan.Empiirinen osa koostuu S-ryhmääja erityisesti Sokos-tavaratalokauppaa käsittelevästä materiaalista, kilpailustrategioiden kuvauksista, vuosikertomuksista ja kokousmuistioista sekä kahdeksan Sokos-ketjussa 90-luvulla johtavassa asemassa toimineen henkilön haastatteluista. Empiiristä aineistoa on kerätty myös yleisistä vähittäiskauppaa koskevista alan lehdistä ja artikkeleista sekä Stockmann- tavarataloketjun vuosikertomuksista. Tutkimuksessa todettiin kohdeyrityksen vaikeuksiin ajautumisen taustalta löytyvän voimakkaan talouslaman lisäksi kilpailutilanteen voimakas muuttuminen, johon ei kyetty riittävästi vastaamaan. Suunnanmuutoksia kilpailustrategiaan tehtiin useaan otteeseen, mutta kaikissa vaiheissa käytännön toteutus jäi puolinaiseksi. Ylivoimaisten kilpailuetujen rakentaminen onnistui heikosti.

Error models in hydrogeology applications

Notre consommation en eau souterraine, en particulier comme eau potable ou pour l'irrigation, a considérablement augmenté au cours des années. De nombreux problèmes font alors leur apparition, allant de la prospection de nouvelles ressources à la remédiation des aquifères pollués. Indépendamment du problème hydrogéologique considéré, le principal défi reste la caractérisation des propriétés du sous-sol. Une approche stochastique est alors nécessaire afin de représenter cette incertitude en considérant de multiples scénarios géologiques et en générant un grand nombre de réalisations géostatistiques. Nous rencontrons alors la principale limitation de ces approches qui est le coût de calcul dû à la simulation des processus d'écoulements complexes pour chacune de ces réalisations. Dans la première partie de la thèse, ce problème est investigué dans le contexte de propagation de l'incertitude, oú un ensemble de réalisations est identifié comme représentant les propriétés du sous-sol. Afin de propager cette incertitude à la quantité d'intérêt tout en limitant le coût de calcul, les méthodes actuelles font appel à des modèles d'écoulement approximés. Cela permet l'identification d'un sous-ensemble de réalisations représentant la variabilité de l'ensemble initial. Le modèle complexe d'écoulement est alors évalué uniquement pour ce sousensemble, et, sur la base de ces réponses complexes, l'inférence est faite. Notre objectif est d'améliorer la performance de cette approche en utilisant toute l'information à disposition. Pour cela, le sous-ensemble de réponses approximées et exactes est utilisé afin de construire un modèle d'erreur, qui sert ensuite à corriger le reste des réponses approximées et prédire la réponse du modèle complexe. Cette méthode permet de maximiser l'utilisation de l'information à disposition sans augmentation perceptible du temps de calcul. La propagation de l'incertitude est alors plus précise et plus robuste. La stratégie explorée dans le premier chapitre consiste à apprendre d'un sous-ensemble de réalisations la relation entre les modèles d'écoulement approximé et complexe. Dans la seconde partie de la thèse, cette méthodologie est formalisée mathématiquement en introduisant un modèle de régression entre les réponses fonctionnelles. Comme ce problème est mal posé, il est nécessaire d'en réduire la dimensionnalité. Dans cette optique, l'innovation du travail présenté provient de l'utilisation de l'analyse en composantes principales fonctionnelles (ACPF), qui non seulement effectue la réduction de dimensionnalités tout en maximisant l'information retenue, mais permet aussi de diagnostiquer la qualité du modèle d'erreur dans cet espace fonctionnel. La méthodologie proposée est appliquée à un problème de pollution par une phase liquide nonaqueuse et les résultats obtenus montrent que le modèle d'erreur permet une forte réduction du temps de calcul tout en estimant correctement l'incertitude. De plus, pour chaque réponse approximée, une prédiction de la réponse complexe est fournie par le modèle d'erreur. Le concept de modèle d'erreur fonctionnel est donc pertinent pour la propagation de l'incertitude, mais aussi pour les problèmes d'inférence bayésienne. Les méthodes de Monte Carlo par chaîne de Markov (MCMC) sont les algorithmes les plus communément utilisés afin de générer des réalisations géostatistiques en accord avec les observations. Cependant, ces méthodes souffrent d'un taux d'acceptation très bas pour les problèmes de grande dimensionnalité, résultant en un grand nombre de simulations d'écoulement gaspillées. Une approche en deux temps, le "MCMC en deux étapes", a été introduite afin d'éviter les simulations du modèle complexe inutiles par une évaluation préliminaire de la réalisation. Dans la troisième partie de la thèse, le modèle d'écoulement approximé couplé à un modèle d'erreur sert d'évaluation préliminaire pour le "MCMC en deux étapes". Nous démontrons une augmentation du taux d'acceptation par un facteur de 1.5 à 3 en comparaison avec une implémentation classique de MCMC. Une question reste sans réponse : comment choisir la taille de l'ensemble d'entrainement et comment identifier les réalisations permettant d'optimiser la construction du modèle d'erreur. Cela requiert une stratégie itérative afin que, à chaque nouvelle simulation d'écoulement, le modèle d'erreur soit amélioré en incorporant les nouvelles informations. Ceci est développé dans la quatrième partie de la thèse, oú cette méthodologie est appliquée à un problème d'intrusion saline dans un aquifère côtier. -- Our consumption of groundwater, in particular as drinking water and for irrigation, has considerably increased over the years and groundwater is becoming an increasingly scarce and endangered resource. Nofadays, we are facing many problems ranging from water prospection to sustainable management and remediation of polluted aquifers. Independently of the hydrogeological problem, the main challenge remains dealing with the incomplete knofledge of the underground properties. Stochastic approaches have been developed to represent this uncertainty by considering multiple geological scenarios and generating a large number of realizations. The main limitation of this approach is the computational cost associated with performing complex of simulations in each realization. In the first part of the thesis, we explore this issue in the context of uncertainty propagation, where an ensemble of geostatistical realizations is identified as representative of the subsurface uncertainty. To propagate this lack of knofledge to the quantity of interest (e.g., the concentration of pollutant in extracted water), it is necessary to evaluate the of response of each realization. Due to computational constraints, state-of-the-art methods make use of approximate of simulation, to identify a subset of realizations that represents the variability of the ensemble. The complex and computationally heavy of model is then run for this subset based on which inference is made. Our objective is to increase the performance of this approach by using all of the available information and not solely the subset of exact responses. Two error models are proposed to correct the approximate responses follofing a machine learning approach. For the subset identified by a classical approach (here the distance kernel method) both the approximate and the exact responses are knofn. This information is used to construct an error model and correct the ensemble of approximate responses to predict the "expected" responses of the exact model. The proposed methodology makes use of all the available information without perceptible additional computational costs and leads to an increase in accuracy and robustness of the uncertainty propagation. The strategy explored in the first chapter consists in learning from a subset of realizations the relationship between proxy and exact curves. In the second part of this thesis, the strategy is formalized in a rigorous mathematical framework by defining a regression model between functions. As this problem is ill-posed, it is necessary to reduce its dimensionality. The novelty of the work comes from the use of functional principal component analysis (FPCA), which not only performs the dimensionality reduction while maximizing the retained information, but also allofs a diagnostic of the quality of the error model in the functional space. The proposed methodology is applied to a pollution problem by a non-aqueous phase-liquid. The error model allofs a strong reduction of the computational cost while providing a good estimate of the uncertainty. The individual correction of the proxy response by the error model leads to an excellent prediction of the exact response, opening the door to many applications. The concept of functional error model is useful not only in the context of uncertainty propagation, but also, and maybe even more so, to perform Bayesian inference. Monte Carlo Markov Chain (MCMC) algorithms are the most common choice to ensure that the generated realizations are sampled in accordance with the observations. Hofever, this approach suffers from lof acceptance rate in high dimensional problems, resulting in a large number of wasted of simulations. This led to the introduction of two-stage MCMC, where the computational cost is decreased by avoiding unnecessary simulation of the exact of thanks to a preliminary evaluation of the proposal. In the third part of the thesis, a proxy is coupled to an error model to provide an approximate response for the two-stage MCMC set-up. We demonstrate an increase in acceptance rate by a factor three with respect to one-stage MCMC results. An open question remains: hof do we choose the size of the learning set and identify the realizations to optimize the construction of the error model. This requires devising an iterative strategy to construct the error model, such that, as new of simulations are performed, the error model is iteratively improved by incorporating the new information. This is discussed in the fourth part of the thesis, in which we apply this methodology to a problem of saline intrusion in a coastal aquifer.