TY - JOUR A1 - Reich, Sebastian T1 - A nonparametric ensemble transform method for bayesian inference JF - SIAM journal on scientific computing N2 - Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. KW - Bayesian inference KW - Monte Carlo method KW - sequential data assimilation KW - linear programming KW - resampling Y1 - 2013 U6 - https://doi.org/10.1137/130907367 SN - 1064-8275 VL - 35 IS - 4 SP - A2013 EP - A2024 PB - Society for Industrial and Applied Mathematics CY - Philadelphia ER - TY - JOUR A1 - Groth, Detlef T1 - Modeling a secular trend by Monte Carlo simulation of height biased migration in a spatial network JF - Anthropologischer Anzeiger : journal of biological and clinical anthropology ; Mitteilungsorgan der Gesellschaft für Anthropologie N2 - Background: In a recent Monte Carlo simulation, the clustering of body height of Swiss military conscripts within a spatial network with characteristic features of the natural Swiss geography was investigated. In this study I examined the effect of migration of tall individuals into network hubs on the dynamics of body height within the whole spatial network. The aim of this study was to simulate height trends. Material and methods: Three networks were used for modeling, a regular rectangular fishing net like network, a real world example based on the geographic map of Switzerland, and a random network. All networks contained between 144 and 148 districts and between 265-307 road connections. Around 100,000 agents were initially released with average height of 170 cm, and height standard deviation of 6.5 cm. The simulation was started with the a priori assumption that height variation within a district is limited and also depends on height of neighboring districts (community effect on height). In addition to a neighborhood influence factor, which simulates a community effect, body height dependent migration of conscripts between adjacent districts in each Monte Carlo simulation was used to re-calculate next generation body heights. In order to determine the direction of migration for taller individuals, various centrality measures for the evaluation of district importance within the spatial network were applied. Taller individuals were favored to migrate more into network hubs, backward migration using the same number of individuals was random, not biased towards body height. Network hubs were defined by the importance of a district within the spatial network. The importance of a district was evaluated by various centrality measures. In the null model there were no road connections, height information could not be delivered between the districts. Results: Due to the favored migration of tall individuals into network hubs, average body height of the hubs, and later, of the whole network increased by up to 0.1 cm per iteration depending on the network model. The general increase in height within the network depended on connectedness and on the amount of height information that was exchanged between neighboring districts. If higher amounts of neighborhood height information were exchanged, the general increase in height within the network was large (strong secular trend). The trend in the homogeneous fishnet like network was lowest, the trend in the random network was highest. Yet, some network properties, such as the heteroscedasticity and autocorrelations of the migration simulation models differed greatly from the natural features observed in Swiss military conscript networks. Autocorrelations of district heights for instance, were much higher in the migration models. Conclusion: This study confirmed that secular height trends can be modeled by preferred migration of tall individuals into network hubs. However, basic network properties of the migration simulation models differed greatly from the natural features observed in Swiss military conscripts. Similar network-based data from other countries should be explored to better investigate height trends with Monte Carlo migration approach. KW - secular trend KW - body height KW - simulation KW - community effect KW - Monte Carlo method KW - network Y1 - 2017 U6 - https://doi.org/10.1127/anthranz/2017/0703 SN - 0003-5548 SN - 2363-7099 VL - 74 IS - 1 SP - 81 EP - 88 PB - Schweizerbart CY - Stuttgart ER - TY - JOUR A1 - Fritz, Amelie A1 - Makeyeva, Angelina A1 - Staub, Kaspar A1 - Groth, Detlef T1 - Influence of network properties on a migration induced secular height trend by Monte Carlo simulation JF - Journal of biological and clinical anthropology : Anthropologischer Anzeiger ; Mitteilungsorgan der Gesellschaft für Anthropologie N2 - Background: Recent research reported height biased migration of taller individuals and a Monte Carlo simulation showed that such preferential migration of taller individuals into network hubs can induce a secular trend of height. In the simulation model taller agents in the hubs raise the overall height of all individuals in the network by a community effect. However, it could be seen that the actual network structure influences the strength of this effect. In this paper the background and the influence of the network structure on the strength of the secular trend by migration is investigated. Material and methods: Three principal network types are analyzed: networks derived from street connections in Switzerland, more regular fishing net like networks and randomly generated ones. Our networks have between 10 and 152 nodes and between 20 and 307 edges connecting the nodes. Depending on the network size between 5.000 and 90.000 agents with an average height of 170 cm (SD 6.5 cm) are initially released into the network. In each iteration new agents are regenerated based on the actual average body height of the previous iteration and, to a certain proportion, corrected by body heights in the neighboring nodes. After generating new agents, a certain number of them migrated into neighbor nodes, the model let preferentially taller agents migrate into network hubs. Migration is balanced by back migration of the same number of agents from nodes with high centrality measures to less connected nodes. The latter is random as well, but not biased by the agents height. Furthermore the distribution of agents per node and their correlation to the centrality of the nodes is varied in a systematic manner. After 100 iterations, the secular trend, i.e. the gain in body height for the different networks, is investigated in relation to the network properties. Results: We observe an increase of average agent body height after 100 iterations if height biased migration is enabled. The increase rate depends on the height of the neighboring factor, the population distribution, the relationship between population in the nodes and their centrality as well as on the network topology. Networks with uniform like distributions of the agents in the nodes, uncorrelated associations between node centrality and agent number per node, as well as very heterogeneous networks with very different node centralities lead to biggest gains in average body height. Conclusion: Our simulations show, that height biased migration into network hubs can possibly contribute to the secular trend of height increase in the human population. The strength of this "tall by migration" event depends on the actual properties of the underlying network. There is a possible significance of this mechanism for social networks, when hubs are represented by individuals and edges as their personal relationships. However, the required high number of iterations to achieve significant effects in more natural network structures in our models requires further studies to test the relevance and real effect sizes in real world scenarios. KW - secular trend KW - body height KW - simulation KW - community effect KW - Monte Carlo method KW - network KW - centrality measures Y1 - 2019 U6 - https://doi.org/10.1127/anthranz/2019/1032 SN - 0003-5548 VL - 76 IS - 5 SP - 433 EP - 443 PB - Schweizerbart CY - Stuttgart ER - TY - JOUR A1 - Novine, Masiar A1 - Mattsson, Cecilie Cordua A1 - Groth, Detlef T1 - Network reconstruction based on synthetic data generated by a Monte Carlo approach JF - Human biology and public health N2 - Background: Network models are useful tools for researchers to simplify and understand investigated systems. Yet, the assessment of methods for network construction is often uncertain. Random resampling simulations can aid to assess methods, provided synthetic data exists for reliable network construction. Objectives: We implemented a new Monte Carlo algorithm to create simulated data for network reconstruction, tested the influence of adjusted parameters and used simulations to select a method for network model estimation based on real-world data. We hypothesized, that reconstructs based on Monte Carlo data are scored at least as good compared to a benchmark. Methods: Simulated data was generated in R using the Monte Carlo algorithm of the mcgraph package. Benchmark data was created by the huge package. Networks were reconstructed using six estimator functions and scored by four classification metrics. For compatibility tests of mean score differences, Welch’s t-test was used. Network model estimation based on real-world data was done by stepwise selection. Samples: Simulated data was generated based on 640 input graphs of various types and sizes. The real-world dataset consisted of 67 medieval skeletons of females and males from the region of Refshale (Lolland) and Nordby (Jutland) in Denmark. Results: Results after t-tests and determining confidence intervals (CI95%) show, that evaluation scores for network reconstructs based on the mcgraph package were at least as good compared to the benchmark huge. The results even indicate slightly better scores on average for the mcgraph package. Conclusion: The results confirmed our objective and suggested that Monte Carlo data can keep up with the benchmark in the applied test framework. The algorithm offers the feature to use (weighted) un- and directed graphs and might be useful for assessing methods for network construction. KW - Monte Carlo method KW - network reconstruction KW - mcgraph KW - random sampling KW - linear enamel hypoplasia Y1 - 2022 U6 - https://doi.org/10.52905/hbph2021.3.26 SN - 2748-9957 VL - 2021 IS - 3, Summer School Supplement PB - Universitätsverlag Potsdam CY - Potsdam ER -