Approximate Bayesian Computation Methods Research Articles

Testing hypotheses for genealogical discordance in a rainforest lizard

Genealogical discordance, or when different genes tell distinct stories although they evolved under a shared history, often emerges from either coalescent stochasticity or introgression. In this study, we present a strong case of mito-nuclear genealogical discordance in the Australian rainforest lizard species complex of Saproscincus basiliscus and S. lewisi. One of the lineages that comprises this complex, the Southern S. basiliscus lineage, is deeply divergent at the mitochondrial genome but shows markedly less divergence at the nuclear genome. By placing our results in a comparative context and reconstructing the lineages' demography via multilocus and coalescent-based approximate Bayesian computation methods, we test hypotheses for how coalescent variance and introgression contribute to this pattern. These analyses suggest that the observed genealogical discordance likely results from introgression. Further, to generate such strong discordance, introgression probably acted in concert with other factors promoting asymmetric gene flow between the mitochondrial and nuclear genomes, such as selection or sex-biased dispersal. This study offers a framework for testing sources of genealogical discordance and suggests that historical introgression can be an important force shaping the genetic diversity of species and their populations.

Approximate Bayesian computation methods

Occasionally, Statistics and Computing is publishing Special Issues on topics of potential interests. The most recent published Special Issues were concerned with “Adaptive Methods in Bayesian Computation”, Guest Editor Paul Fearnhead, Volume 18 Issue 4 (2008), “Regularisation Methods in Classification and Regression”, Guest Editor Gerhard Tutz, Volume 20 Issue 2 (2009), and “Modeling of Computer Experiments for Uncertainty Propagation and Sensitivity Analysis”, Guest Editors Anestis Antoniadis and Alberto Pasanisi, Volume 22 Issue 3 (2012). Usually, those special issues are started with a “Call for papers” giving their purpose and specifying their desired subjects. This issue is proposing a Special Issue on Approximate Bayesian Computation (ABC) methods, which has not been conceived according to this scheme. Actually, ABC methodology is an emerging domain of computational statistics and there was no need to prepare a formal “Call for papers” for this special issue. The project of this special issue simply rises because, since early 2010, Statistics and Computing has received a lot of submissions on this new topic of computational statistics. And ABC methodology is typically a good material for Statistics and Computing. Roughly speaking each ten years, a new methodology of computational statistics appears and dominates the scene for a while, it was the bootstrap, Efron (1979), and the algorithms related to the EM algorithm of Dempster et al. (1977) in the eighties, Monte Carlo Markov Chains for Bayesian analysis in the nineties (Gelfand and Smith 1990), regularization methods derived from the Lasso (Tibshirani 1996)

Approximate Bayesian computation with differential evolution

Approximate Bayesian computation (ABC) is a simulation-based method for estimating the posterior distribution of the parameters of a model. The ABC approach is instrumental when a likelihood function for a model cannot be mathematically specified, or has a complicated form. Although difficulty in calculating a model’s likelihood is extremely common, current ABC methods suffer from two problems that have largely prevented their mainstream adoption: long computation time and an inability to scale beyond a few parameters. We introduce differential evolution as a computationally efficient genetic algorithm for proposal generation in our ABC sampler. We show how using this method allows our new ABC algorithm, called ABCDE, to obtain accurate posterior estimates in fewer iterations than kernel-based ABC algorithms and to scale to high-dimensional parameter spaces that have proven difficult for current ABC methods.

A Comparative Review of Dimension Reduction Methods in Approximate Bayesian Computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Understanding the recent colonization history of a plant pathogenic fungus using population genetic tools and Approximate Bayesian Computation.

Understanding the processes by which new diseases are introduced in previously healthy areas is of major interest in elaborating prevention and management policies, as well as in understanding the dynamics of pathogen diversity at large spatial scale. In this study, we aimed to decipher the dispersal processes that have led to the emergence of the plant pathogenic fungus Microcyclus ulei, which is responsible for the South American Leaf Blight (SALB). This fungus has devastated rubber tree plantations across Latin America since the beginning of the twentieth century. As only imprecise historical information is available, the study of population evolutionary history based on population genetics appeared most appropriate. The distribution of genetic diversity in a continental sampling of four countries (Brazil, Ecuador, Guatemala and French Guiana) was studied using a set of 16 microsatellite markers developed specifically for this purpose. A very strong genetic structure was found (F(st)=0.70), demonstrating that there has been no regular gene flow between Latin American M. ulei populations. Strong bottlenecks probably occurred at the foundation of each population. The most likely scenario of colonization identified by the Approximate Bayesian Computation (ABC) method implemented in DIYABC suggested two independent sources from the Amazonian endemic area. The Brazilian, Ecuadorian and Guatemalan populations might stem from serial introductions through human-mediated movement of infected plant material from an unsampled source population, whereas the French Guiana population seems to have arisen from an independent colonization event through spore dispersal.

Sequence variation patterns along a latitudinal cline in Scots pine (Pinus sylvestris): signs of clinal adaptation?

Adaptive clinal variation is abundant in nature, and its genetic basis is of great interest. The polygenic nature of this variation poses a challenge for identifying the causative loci underlying these adaptations. Here, we have examined the patterns of sequence variation in ten candidate genes for timing of bud set and cold tolerance, traits that form strong latitudinal clines in Scots pine (Pinus sylvestris). A set of reference genes was used for comparison and to infer a simplified demographic background model with approximate Bayesian computation methods. Against the resulting bottleneck model, the neutrality tests show little signs for local adaptation, but species-wide selection is suggested in some of the studied genes. In line with the theoretical expectations, we see little evidence for adaptive differentiation with F ST methods. Instead, allele frequency clines were found in three genes (dhn1, ftl2, and prr1). Our results add to the discussion on which molecular signals best characterize a gene subject to clinally varying selection. This will be especially relevant when these kinds of observations can be examined in parallel with association study results.

Tracking Invasion Histories in the Sea: Facing Complex Scenarios Using Multilocus Data

In recent years, new analytical tools have allowed researchers to extract historical information contained in molecular data, which has fundamentally transformed our understanding of processes ruling biological invasions. However, the use of these new analytical tools has been largely restricted to studies of terrestrial organisms despite the growing recognition that the sea contains ecosystems that are amongst the most heavily affected by biological invasions, and that marine invasion histories are often remarkably complex. Here, we studied the routes of invasion and colonisation histories of an invasive marine invertebrate Microcosmus squamiger (Ascidiacea) using microsatellite loci, mitochondrial DNA sequence data and 11 worldwide populations. Discriminant analysis of principal components, clustering methods and approximate Bayesian computation (ABC) methods showed that the most likely source of the introduced populations was a single admixture event that involved populations from two genetically differentiated ancestral regions - the western and eastern coasts of Australia. The ABC analyses revealed that colonisation of the introduced range of M. squamiger consisted of a series of non-independent introductions along the coastlines of Africa, North America and Europe. Furthermore, we inferred that the sequence of colonisation across continents was in line with historical taxonomic records - first the Mediterranean Sea and South Africa from an unsampled ancestral population, followed by sequential introductions in California and, more recently, the NE Atlantic Ocean. We revealed the most likely invasion history for world populations of M. squamiger, which is broadly characterized by the presence of multiple ancestral sources and non-independent introductions within the introduced range. The results presented here illustrate the complexity of marine invasion routes and identify a cause-effect relationship between human-mediated transport and the success of widespread marine non-indigenous species, which benefit from stepping-stone invasions and admixture processes involving different sources for the spread and expansion of their range.

Test of colonisation scenarios reveals complex invasion history of the red tomato spider mite Tetranychus evansi.

The spider mite Tetranychus evansi is an emerging pest of solanaceous crops worldwide. Like many other emerging pests, its small size, confusing taxonomy, complex history of associations with humans, and propensity to start new populations from small inocula, make the study of its invasion biology difficult. Here, we use recent developments in Approximate Bayesian Computation (ABC) and variation in multi-locus genetic markers to reconstruct the complex historical demography of this cryptic invasive pest. By distinguishing among multiple pathways and timing of introductions, we find evidence for the “bridgehead effect”, in which one invasion serves as source for subsequent invasions. Tetranychus evansi populations in Europe and Africa resulted from at least three independent introductions from South America and involved mites from two distinct sources in Brazil, corresponding to highly divergent mitochondrial DNA lineages. Mites from southwest Brazil (BR-SW) colonized the African continent, and from there Europe through two pathways in a “bridgehead” type pattern. One pathway resulted in a widespread invasion, not only to Europe, but also to other regions in Africa, southern Europe and eastern Asia. The second pathway involved the mixture with a second introduction from BR-SW leading to an admixed population in southern Spain. Admixture was also detected between invasive populations in Portugal. A third introduction from the Brazilian Atlantic region resulted in only a limited invasion in Europe. This study illustrates that ABC methods can provide insights into, and distinguish among, complex invasion scenarios. These processes are critical not only in understanding the biology of invasions, but also in refining management strategies for invasive species. For example, while reported observations of the mite and outbreaks in the invaded areas were largely consistent with estimates of geographical expansion from the ABC approach, historical observations failed to recognize the complex pathways involved and the corresponding effects on genetic diversity.

Likelihood-free parallel tempering

Approximate Bayesian Computational (ABC) methods, or likelihood-free methods, have appeared in the past fifteen years as useful methods to perform Bayesian analysis when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: MCMC methods have been developed by Marjoram et al. (2003) and by Bortot et al. (2007) for instance, and sequential methods have been proposed among others by Sisson et al. (2007), Beaumont et al. (2009) and Del Moral et al. (2012). Recently, sequential ABC methods have appeared as an alternative to ABC-PMC methods (see for instance McKinley et al., 2009; Sisson et al., 2007). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the parallel tempering algorithm (Geyer 1991). Performance is compared with existing ABC algorithms on simulations and on a real example.

A tutorial on approximate Bayesian computation

This tutorial explains the foundation of approximate Bayesian computation (ABC), an approach to Bayesian inference that does not require the specification of a likelihood function, and hence that can be used to estimate posterior distributions of parameters for simulation-based models. We discuss briefly the philosophy of Bayesian inference and then present several algorithms for ABC. We then apply these algorithms in a number of examples. For most of these examples, the posterior distributions are known, and so we can compare the estimated posteriors derived from ABC to the true posteriors and verify that the algorithms recover the true posteriors accurately. We also consider a popular simulation-based model of recognition memory (REM) for which the true posteriors are unknown. We conclude with a number of recommendations for applying ABC methods to solve real-world problems.

Extremely Low Genetic Diversity Indicating the Endangered Status of Ranodon sibiricus (Amphibia: Caudata) and Implications for Phylogeography

BackgroundThe Siberian salamander (Ranodon sibiricus), distributed in geographically isolated areas of Central Asia, is an ideal alpine species for studies of conservation and phylogeography. However, there are few data regarding the genetic diversity in R. sibiricus populations.Methodology/Principal FindingsWe used two genetic markers (mtDNA and microsatellites) to survey all six populations of R. sibiricus in China. Both of the markers revealed extreme genetic uniformity among these populations. There were only three haplotypes in the mtDNA, and the overall nucleotide diversity in the mtDNA was 0.00064, ranging from 0.00000 to 0.00091 for the six populations. Although we recovered 70 sequences containing microsatellite repeats, there were only two loci that displayed polymorphism. We used the approximate Bayesian computation (ABC) method to study the demographic history of the populations. This analysis suggested that the extant populations diverged from the ancestral population approximately 120 years ago and that the historical population size was much larger than the present population size; i.e., R. sibiricus has experienced dramatic population declines.Conclusion/SignificanceOur findings suggest that the genetic diversity in the R. sibiricus populations is the lowest among all investigated amphibians. We conclude that the isolation of R. sibiricus populations occurred recently and was a result of recent human activity and/or climatic changes. The Pleistocene glaciation oscillations may have facilitated intraspecies genetic homogeneity rather than enhanced divergence. A low genomic evolutionary rate and elevated inbreeding frequency may have also contributed to the low genetic variation observed in this species. Our findings indicate the urgency of implementing a protection plan for this endangered species.

Monitoring the effective population size of a brown bear (Ursus arctos) population using new single‐sample approaches

The effective population size (N(e) ) could be the ideal parameter for monitoring populations of conservation concern as it conveniently summarizes both the evolutionary potential of the population and its sensitivity to genetic stochasticity. However, tracing its change through time is difficult in natural populations. We applied four new methods for estimating N(e) from a single sample of genotypes to trace temporal change in N(e) for bears in the Northern Dinaric Mountains. We genotyped 510 bears using 20 microsatellite loci and determined their age. The samples were organized into cohorts with regard to the year when the animals were born and yearly samples with age categories for every year when they were alive. We used the Estimator by Parentage Assignment (EPA) to directly estimate both N(e) and generation interval for each yearly sample. For cohorts, we estimated the effective number of breeders (N(b) ) using linkage disequilibrium, sibship assignment and approximate Bayesian computation methods and extrapolated these estimates to N(e) using the generation interval. The N(e) estimate by EPA is 276 (183-350 95% CI), meeting the inbreeding-avoidance criterion of N(e) > 50 but short of the long-term minimum viable population goal of N(e) > 500. The results obtained by the other methods are highly consistent with this result, and all indicate a rapid increase in N(e) probably in the late 1990s and early 2000s. The new single-sample approaches to the estimation of N(e) provide efficient means for including N(e) in monitoring frameworks and will be of great importance for future management and conservation.

A species assemblage approach to comparative phylogeography of birds in southern Australia

We present a novel approach to investigating the divergence history of biomes and their component species using single-locus data prior to investing in multilocus data. We use coalescent-based hierarchical approximate Bayesian computation (HABC) methods (MsBayes) to estimate the number and timing of discrete divergences across a putative barrier and to assign species to their appropriate period of co-divergence. We then apply a coalescent-based full Bayesian model of divergence (IMa) to suites of species shown to have simultaneously diverged. The full Bayesian model results in reduced credibility intervals around divergence times and allows other parameters associated with divergence to be summarized across species assemblages. We apply this approach to 10 bird species that are wholly or patchily discontinuous in semi-arid habitats between Australia's southwest (SW) and southeast (SE) mesic zones. There was substantial support for up to three discrete periods of divergence. HABC indicates that two species wholly restricted to more mesic habitats diverged earliest, between 594,382 and 3,417,699 years ago, three species from semi-arid habitats diverged between 0 and 1,508,049 years ago, and four diverged more recently, between 0 and 396,843 years ago. Eight species were assigned to three periods of co-divergence with confidence. For full Bayesian analyses, we accounted for uncertainty in the two remaining species by analyzing all possible suites of species. Estimates of divergence times from full Bayesian divergence models ranged between 429,105 and 2,006,355; 67,172 and 663,837; and 24,607 and 171,085 for the earliest, middle, and most recent periods of co-divergence, respectively. This single-locus approach uses the power of multitaxa coalescent analyses as an efficient means of generating a foundation for further, targeted research using multilocus and genomic tools applied to an understudied biome.

Multiple independent introductions of Plasmodium falciparum in South America.

The origin of Plasmodium falciparum in South America is controversial. Some studies suggest a recent introduction during the European colonizations and the transatlantic slave trade. Other evidence--archeological and genetic--suggests a much older origin. We collected and analyzed P. falciparum isolates from different regions of the world, encompassing the distribution range of the parasite, including populations from sub-Saharan Africa, the Middle East, Southeast Asia, and South America. Analyses of microsatellite and SNP polymorphisms show that the populations of P. falciparum in South America are subdivided in two main genetic clusters (northern and southern). Phylogenetic analyses, as well as Approximate Bayesian Computation methods suggest independent introductions of the two clusters from African sources. Our estimates of divergence time between the South American populations and their likely sources favor a likely introduction from Africa during the transatlantic slave trade.

The ensemble Kalman filter is an ABC algorithm

The ensemble Kalman filter is the method of choice for many difficult high-dimensional filtering problems in meteorology, oceanography, hydrology and other fields. In this note we show that a common variant of the ensemble Kalman filter is an approximate Bayesian computation (ABC) algorithm. This is of interest for a number of reasons. First, the ensemble Kalman filter is an example of an ABC algorithm that predates the development of ABC algorithms. Second, the ensemble Kalman filter is used for very high-dimensional problems, whereas ABC methods are normally applied only in very low-dimensional problems. Third, recent state of the art extensions of the ensemble Kalman filter can also be understood within the ABC framework.

Approximate Bayesian computational methods

Approximate Bayesian Computation (ABC) methods, also known as likelihood-free techniques, have appeared in the past ten years as the most satisfactory approach to intractable likelihood problems, first in genetics then in a broader spectrum of applications. However, these methods suffer to some degree from calibration difficulties that make them rather volatile in their implementation and thus render them suspicious to the users of more traditional Monte Carlo methods. In this survey, we study the various improvements and extensions brought on the original ABC algorithm in recent years.

Interview with Sarah Tishkoff: Perspectives for Genetic Research in African Populations

Interview with Sarah Tishkoff:Perspectives for Genetic Research in African Populations Giovanni Destro-Bisol Keywords Sub-Saharan Africa, genetic variation, human origins, genetic epidimiology, African ancestry, natural selection, genetic studies of functional variants, unilinearly transmitted polymorphisms, phylogeography, approximate Bayesian computation methods, next generation sequencing technologies Sarah Tishkoff is the David and Lyn Silfen University Associate Professor in Genetics and Biology at the University of Pennsylvania, holding appointments in the Perelman School of Medicine and the School of Arts and Sciences. Dr. Tishkoff studies genetic variation in ethnically diverse Africans in order to reconstruct modern human origins, African population history, and processes of adaptation. Her research examines how genetic variation influences normal variable traits as well as disease susceptibility and drug response. Dr. Tishkoff has long been an advocate for the need for populations in Africa to be represented in human genetic studies so that they may benefit from knowledge about their population history and development of more effective medical treatments. Dr. Tishkoff received her bachelor's degree in anthropology and genetics from the University of California at Berkeley, and her masters of philosophy and doctorate in genetics from Yale School of Medicine. She taught in the Department of Biology at the University of Maryland at College Park from 2000-2007 and became a faculty member at the University of Pennsylvania in 2008. Dr. Tishkoff is a recipient of an NIH Pioneer Award, a Packard Career Award, and a Burroughs/Wellcome Fund Career Award. She is currently a member of the editorial boards of Genome Research Journal and G3: Genes Genomes Genetics and is an associate editor of Molecular Biology and Evolution Journal and The Quarterly Review of Biology. Her research is supported by grants from the National Institutes of Health and the National Science Foundation. Giovanni Destro-Bisol: Sarah, a significant part of your research work focuses on the genetics of human populations living south of the Sahara desert. Therefore, you can probably explain, better than anyone else, why sub-Saharan Africa is such an important and attractive area for researchers studying human molecular evolution. [End Page 637] Click for larger view View full resolution Figure 1. Sarah Tishkoff is the David and Lyn Silfen Univerity Associate Professor in Genetics and Biology at the University of Pennsylvania. Photo courtesy of Sadie Robinson. Sarah Tishkoff: Africa is an important region to study for genetic variation for a number of reasons. First is that Africa is thought to be the homeland of all modern humans. If we want to learn more about human origins (e.g., when and where did modern humans evolve and how did they adapt to shifting environments?) then we need to study diversity in Africa. Secondly, Africa is the recent homeland of millions of people whose ancestors were brought to the Americas and elsewhere as slaves. Knowledge of genetic diversity across ethnically diverse Africans will be important for reconstructing ancestry in individuals of recent African descent. Thirdly, study of genetic, phenotypic, and environmental variation in Africa will be important for identifying the genetic and environmental factors that play a role in both normal phenotypic variation as well as in diseases common in Africa and in people of recent African descent (e.g., infectious diseases such as malaria, TB, and HIV and other diseases such as hypertension and prostate cancer). Additionally, little is currently known about genetic variation at genes that play a role in drug response across ethnically diverse Africans. Such knowledge will be important for the development of more effective treatments in these populations. Lastly, because of high levels of genetic, cultural, and climatic diversity in Africa there has likely been local adaptation within populations from different regions practicing diverse lifestyles. Therefore, the possibility of geographically restricted rare, as well as common, functional variants requires the inclusion of a broad range of geographically and ethnically diverse African populations in human genetic studies. [End Page 638] GD-B: There have been a number of studies of DNA polymorphisms published in the literature which offer contrasting hypotheses regarding the geographic origin of anatomically modern humans. For example, your Science 2009 paper provides compelling evidence that modern human migration originated in southwestern Africa (Tishkoff et al. 2010). However, a recent...

Molecular data reveal isolation by distance and past population expansion for the shea tree (Vitellaria paradoxa C.F. Gaertn) in West Africa

While the genetic structure of many tree species in temperate, American and Asian regions is largely explained by climatic oscillations and subsequent habitat contractions and expansions, little is known about Africa. We investigated the genetic diversity and structure of shea tree (Vitellaria paradoxa,) in Western Africa, an economically important tree species in the Sudano-Sahelian zone. Eleven nuclear microsatellites (nuc) were used to genotype 673 trees selected in 38 populations. They revealed moderate to high within-population diversity: allelic richness ranged from R(nuc) = 3.99 to 5.63. This diversity was evenly distributed across West Africa. Populations were weakly differentiated (F(STnuc) = 0.085; P < 0.0001) and a pattern of isolation by distance was noted. No phylogeographic signal could be detected across the studied sample. Additionally, two chloroplast microsatellite loci, leading to 11 chlorotypes, were used to analyse a sub-set of 370 individuals. Some variation in chloroplast allelic richness among populations could be detected (R(cp) = 0.00 to 4.36), but these differences were not significant. No trend with latitude and longitude were observed. Differentiation was marked (G(STcp) = 0.553; P < 0.0001), but without a significant phylogeographical signal. Population expansion was detected considering the total population using approximate Bayesian computation (nuclear microsatellites) and mismatch distribution (chloroplast microsatellites) methods. This expansion signal and the isolation by distance pattern could be linked to the past climatic conditions in West Africa during the Pleistocene and Holocene which should have been favourable to shea tree development. In addition, human activities through agroforestry and domestication (started 10,000 bp) have probably enhanced gene flow and population expansion.

Approximate Bayesian computation reveals the factors that influence genetic diversity and population structure of foxsnakes

Contemporary geographical range and patterns of genetic diversity within species reflect complex interactions between multiple factors acting across spatial and temporal scales, and it is notoriously difficult to disentangle causation. Here, we quantify patterns of genetic diversity and genetic population structure using mitochondrial DNA sequences (101 individuals, cytochrome b) and microsatellites (816 individuals, 12 loci) and use Approximate Bayesian computation methods to test competing models of the demographic history of eastern and western foxsnakes. Our analyses indicate that post-glacial colonization and past population declines, probably caused by the infilling of deciduous forest and cooler temperatures since the mid-Holocene, largely underpin large-scale genetic patterns for foxsnakes. At finer geographical scales, our results point to more recent anthropogenic habitat loss as having accentuated genetic population structure by causing further declines and fragmentation.

Assessing Wastewater Micropollutant Loads with Approximate Bayesian Computations

Wastewater production, like many other engineered and environmental processes, is inherent stochastic in nature and requires the use of complex stochastic models, for example, to predict realistic patterns of down-the-drain chemicals or pharmaceuticals and personal care products. Up until now, a formal method of statistical inference has been lacking for many of those models, where explicit likelihood functions were intractable. In this Article, we investigate Approximate Bayesian Computation (ABC) methods to infer important parameters of stochastic environmental models. ABC methods have been recently suggested to perform model-based inference in a Bayesian setting when model likelihoods are analytically or computationally intractable and have not been applied to environmental systems analysis or water quality modeling before. In a case study, we investigate the performance of three different algorithms to infer the number of wastewater pulses contained in three high-resolution data series of benzotriazole and total nitrogen loads in sewers. We find that all algorithms perform well and that the uncertainty in the inferred number of corresponding wastewater pulses varies between 6% and 28%. In our case, the results are more sensitive to substance characteristics than to catchment properties. Although the application of ABC methods requires careful tuning and attention to detail, they have a great general potential to update stochastic model parameters with monitoring data and improve their predictive capabilities.