Catene di Markov Monte Carlo nei modelli di Ising

This study demonstrated the equivalence between the Rasch testlet model and the three‐level one‐parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE) with the expectation‐maximization algorithm in ConQuest and the sixth‐order Laplace approximation estimation in HLM6. The results indicated that the estimation methods had significant effects on the bias of the testlet variance and ability variance estimation, the random error in the ability parameter estimation, and the bias in the item difficulty parameter estimation. The Laplace method best recovered the testlet variance while the MMLE best recovered the ability variance. The Laplace method resulted in the smallest random error in the ability parameter estimation while the MCMC method produced the smallest bias in item parameter estimates. Analyses of three real tests generally supported the findings from the simulation and indicated that the estimates for item difficulty and ability parameters were highly correlated across estimation methods.

Multivariate allometric coefficients of red-spot prawn sampled from the adjacent waters of Tashi, Keelung, Taichung and Kaohsiung were estimated and compared to examine whether (1) allometry can be used to elucidate the genetic variation among groups and (2) the assumption that those groups compared share a common allometric pattern in some multivariate statistic method, e. g. Burnaby's method and shearing principal component analysis (PCA) for size correction, or common PCA and multiple-group PCA for multiple-group ordination, can be satisfied. The specimens were sampled during November and December in 1995. A total of 11 measurements was made for each individual. The first eigenvector extracted from the covariance matrix of log-transformed data was used to reflect the multivariate allometric coefficients. The bootstrap method was used to assess the accuracy of estimates. The dendrogram of four areas was constructed by unweighted pair-group method with arithmetic means (UPGMA) by using the angles between four first eigenvectors by sex. The results show that four areas were clustered into two distinct groups for each sex, one group included Tashi, Keelung and Kaohsiung; the other included Taichung. The hypothesis of one common multivariate allometric pattern was clearly rejected. This indicates that some multivariate statistic methods should not be used with out testing this assumption. The geographic clusters are different from the one derived from shape analysis, so the examination in genetic variation among populations by multivariate variate allometric comparison may be not suitable for this species. Different water masses in winter and flow patterns of coastal current around sampling areas may be the main factors to result in the differences of allometric coefficients between two clusters.

The particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to\nsample from the full posterior distribution of a state-space model. It does so\nby executing Gibbs sampling steps on an extended target distribution defined on\nthe space of the auxiliary variables generated by an interacting particle\nsystem. This paper makes the following contributions to the theoretical study\nof this algorithm. Firstly, we present a coupling construction between two\nparticle Gibbs updates from different starting points and we show that the\ncoupling probability may be made arbitrarily close to one by increasing the\nnumber of particles. We obtain as a direct corollary that the particle Gibbs\nkernel is uniformly ergodic. Secondly, we show how the inclusion of an\nadditional Gibbs sampling step that reselects the ancestors of the particle\nGibbs' extended target distribution, which is a popular approach in practice to\nimprove mixing, does indeed yield a theoretically more efficient algorithm as\nmeasured by the asymptotic variance. Thirdly, we extend particle Gibbs to work\nwith lower variance resampling schemes. A detailed numerical study is provided\nto demonstrate the efficiency of particle Gibbs and the proposed variants.\n

The launch of Roll Back Malaria (RBM) initiative in the early 2000s marked the first serious international efforts to control, prevent and treat malaria in endemic countries of sub-Sahara Africa unparalleled since the demise of the global malaria eradication campaign in the 1960s. These efforts have led to accelerated scale-up of highly proven malaria interventions, that is, insecticide-treated nets, indoor residual spraying, and case management with artemisinin-based combination therapies. This has been followed by a decline of malaria morbidity and mortality in high endemic countries including Uganda which is ranked in the top six high-burden countries. Despite these achievements, malaria remains a major global public health problem and a leading cause of hospitalization and death in Uganda. The RBM support in Uganda has been extended to malaria surveillance specifically to strengthen the national Health Management Information System (HMIS), and periodical implementation of nationally representative household surveys such as Malaria Indicator Survey (MIS) and Demographic Health Surveys (DHS), and facility assessment surveys. The availability of these large datasets notwithstanding, their utilization remains low and the information extracted is limited to national averages that neither take into account subnational heterogeneities and disparities nor evaluate the effects of interventions and other important confounders on malaria burden changes in space and time. In this thesis, we developed Bayesian hierarchical geostatistical and spatio-temporal models for malaria surveillance data collected in Uganda during 2009-2017 to estimate malaria burden, assess interventions and health system-related effects on its changes, and forecast malaria cases to support early warning systems. These models fitted via Markov Chain Monte Carlo (MCMC) simulations offer the flexibility to incorporate correlation of malaria in space and time and can easily be extended to capture complex relationships.

In-line inspection (ILI) data is commonly used in corrosion growth models (CGMs) to predict the corrosion growth in energy pipelines. A hierarchical stochastic corrosion growth model is considered in this paper which considers the variations in the corrosion growth, both spatially and temporally, the inherent measurement error of the ILI tools as well as the model uncertainties. These uncertainties are represented as unknown model variables and are often inferred using a Bayesian method [1], [2] and samples of the unknown parameters’ posterior probability density functions (PDFs) are obtained using Markov Chain Monte Carlo (MCMC) sampling techniques [3]. ILIs can result in massive data sets. In order for MCMC-based inference techniques to yield reasonably accurate results, many samples (approaching infinity) are required. This fact in addition to the massive data sets exponentially increases the scale of the inference problem from an attainable solution to a potentially impossible one that is limited by today’s computing power. For this reason, MCMC-based inference techniques can become inefficient in the cases where ILI datasets are large. The objective is to propose variational inference (VI) as an alternative to MCMC to determine a Bayesian solution for the unknown parameters in complex stochastic CGMs. VI produces approximations of the posterior PDFs by treating the inference as an optimization problem. Variational inference emerged from machine learning for Bayesian inference of large data sets; therefore, it is an appropriate tool to use in the analysis of mass pipeline inspection data[4]–[7]. This paper introduces VI to solve the inference problem and provide a solution for a hierarchical stochastic CGM to describe the defect-specific corrosion growth experienced in pipelines based on excessively large ILI datasets. To gauge the accuracy of the VI implementation in the model, the results are compared to a set of values generated using a stochastic gamma process that represents the corrosion growth process experienced by the pipe.

A new Monte Carlo sampling technique is used to study the spin-1/2 Heisenberg antiferromagnet on square lattices of up to 256 spins. The energy, specific heat, uniform and staggered susceptibilities, and correlation function are calculated. The correlation length as a function of temperature is deduced from correlation functions and is shown to be consistent with a quantum-renormalized classical approximation. Using the coupling constant provided by Raman scattering experiments, good agreement is found between the calculated and experimental correlation lengths in La/sub 2/CuO/sub 4/.

Schistosomiasis is a parasitic disease that is currently endemic in more than 70 countries with the bulk of infections concentrated in Africa. The interest in schistosomiasis has recently grown due to the commitment of substantial amounts of funding to the control of the so-called neglected tropical diseases. Targeting of interventions and allocation of financial resources should be driven by evidenced-based information on the spatial distribution and schistosomiasis burden estimates in order to increase cost-effectiveness and to meet local needs. Currently, decisions are mainly made based on crude schistosomiasis risk estimates which are largely obsolete due to ongoing control efforts, ecological transformations, demographic changes and improved hygiene, among other reasons. Schistosomiasis transmission depends on the distribution of intermediate host snail species. This distribution is determined by climatic and other environmental conditions, such as temperature, precipitation or water flow velocity. Statistical models can be used to establish the relation between the aforementioned factors and schistosomiasis risk and to predict the risk at unobserved locations. Empirical risk mapping requires observed prevalence data distributed within the area of interest, however contemporary large-scale surveys are not available. To address this issue, the European Union (EU)-funded CONTRAST project initiated the development of the Global Neglected Tropical Disease (GNTD) database. To-date, the GNTD database is the most comprehensive schistosomiasis database in Africa. Schistosomiasis prevalence data are spatially correlated, because locations in close proximity share common spatial exposures, which similarly influence transmission. Standard statistical models are not appropriate because they assume independence between locations, leading to imprecise parameter estimates and risk predictions. Geostatistical models assume take into account potential spatial correlation by introducing location-specific random effects. Bayesian model formulations, implemented via Markov chain Monte Carlo (MCMC) simulations methods, enable model fit overcoming the computational problems of likelihood-based methods. Geostatistical model fit requires the repeated inversion of the correlation matrix of the spatial process. The size of this matrix increases with the number of locations and, for very large number of locations, matrix inversion is infeasible. An important aspect of geostatistical model fit is the choice of predictors driving schistosomiasis transmission. There are a number of environmental factors which are correlated, complicating model fit. Rigorous geostatistical variable selection has not yet been applied in spatial schistosomiasis epidemiology. Data compilations contain heterogeneous surveys across locations in terms of age groups involved and diagnostic methods used. The lack of prevalence data reported in standard age groups complicates the estimation of age-adjusted schistosomiasis risk. A common assumption of geostatistical models is that of isotropy implying that spatial correlation is a function of distance between locations irrespective of direction or location. However in schistosomiasis risk mapping, spatial correlation is likely to be related to the direction of river flow due to water-dependent intermediate host snail species. This might introduce directional dependency (anisotropy). Schistosomiasis tends to be present in areas with other neglected diseases. Cost-effective interventions call for an integrated disease control, which requires estimating of the geographical distribution of high co-endemicity. The co-endemic diseases might be correlated, however surveys screening for multiple diseases are not available over large geographical areas. There rather exist data from independent surveys screening for single diseases on different sets of individuals. The main contributions of this thesis were (i) the development of Bayesian isotropic and anisotropic geostatistical models for high spatial resolution schistosomiasis risk mapping and prediction based on age-heterogeneous historical survey data collected over very large number of locations; (ii) the development of statistical methodology for assessing the geographical distribution of co-infection risk from independent single-disease surveys; and (iii) the estimation of location-specific schistosomiasis risk and number of infected people in 29 countries across West and eastern Africa. Hence, for first time, empirical model-based evidence of schistosomiasis risk and burden in those regions is provided. These estimates are of considerable importance for schistosomiasis control programs, as they indicate high-risk areas requiring interventions, allow calculations of the number of drugs required based on WHO guidelines, and provide baseline maps to assess effectiveness of interventions on the roadmap towards schistosomiasis elimination.

Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China

Multistate models, that is, models with more than two distributions, are preferred over single-state probability models in modeling the distribution of travel time. Literature review indicated that the finite multistate modeling of travel time using lognormal distribution is superior to other probability functions. In this study, we extend the finite multistate lognormal model of estimating the travel time distribution to unbounded lognormal distribution. In particular, a nonparametric Dirichlet Process Mixture Model (DPMM) with stick-breaking process representation was used. The strength of the DPMM is that it can choose the number of components dynamically as part of the algorithm during parameter estimation. To reduce computational complexity, the modeling process was limited to a maximum of six components. Then, the Markov Chain Monte Carlo (MCMC) sampling technique was employed to estimate the parameters’ posterior distribution. Speed data from nine links of a freeway corridor, aggregated on a 5-minute basis, were used to calculate the corridor travel time. The results demonstrated that this model offers significant flexibility in modeling to account for complex mixture distributions of the travel time without specifying the number of components. The DPMM modeling further revealed that freeway travel time is characterized by multistate or single-state models depending on the inclusion of onset and offset of congestion periods.

The development of adequate models for binary time series data with covariate adjustment has been an active research area in the last years. In the case, where interest is focused on marginal and association parameters, generalized estimating equations (GEE) (see for example Lipsitz, Laird and Harrington (1991) and Liang, Zeger and Qaqish (1992)) and likelihood (see for example Fitzmaurice and Laird (1993) and Molenberghs and Lesaffre (1994)) based methods have been proposed. The number of parameters required for the full specification of these models grows exponentially with the length of the binary time series. Therefore, the analysis is often focused on marginal and first order parameters. In this case, the multivariate probit model (Ashford and Sowden (1970)) becomes an attractive alternative to the above models. The application of the multivariate probit model has been hampered by the intractability of the maximum likelihood estimator, when the length of the binary time series is large. This paper shows that this difficulty can be overcome by the use of Markov Chain Monte Carlo methods. This analysis also allows for valid point and interval estimates of the parameters in small samples. In addition, the analysis is adopted to handle the case of missing at random responses. The approach is illustrated on data involving binary responses measured at unequally spaced time points. Finally, this data analysis is compared to a GEE analysis given in Fitzmaurice and Lipsitz (1995).

The Normal Inverse Gaussian (NIG) distribution recently introduced by Barndorff-Nielsen (1997) is a promising alternative for modelling financial data exhibiting skewness and fat tails. In this paper we explore the Bayesian estimation of NIG-parameters by Markov Chain Monte Carlo Methods.

The adoption of organic production has increased dramatically over recent years, especially in less developed countries. However, little information is available about who adopts, the difficulties they face in converting and how these factors vary over time. Using small-scale avocado producers (<15ha) from Michoacán, Mexico as a case study, this paper explores the factors affecting the time-to-adoption of organic production and certification, drawing from five parametric descriptions of the data. These models are implemented using a Bayesian approach and advances in Markov chain Monte Carlo methods. The results indicate that additional sources of income, together with membership of producers' associations, higher levels of education and experience of export markets, other than the US, have a positive effect on the adoption decision. Labour requirements and administrative capacity appear to be unimportant, while information sources and the frequency of contact with these sources have a varied, but largely negative effect on the probability of adoption. These findings raise a number of questions about the future of organic production in Mexico and the avocado zone, not least how to overcome credit and information constraints, but more importantly whether aiming for the organic market is a viable production strategy for small-scale producers.

In this paper, we offer generalized exponentiated gamma distribution. We consider the maximum likelihood and Bayesian estimators of unknown parameters and propose Markov chain Monte Carlo (MCMC) method to generate samples from the posterior distribution. The mean square error of estimations is computed and comparisons are made using Monte Carlo simulation. Key words: Maximum likelihood estimator, Bayesian estimator, squared error loss function, generalized exponentiated gamma distribution.

The epidemic of COVID-19 has been effectively controlled in China, which provides an empirical basis for intervention analysis. An extended SIR transmission model with heterogeneous force of infectiousness is presented including three fractals sub-models of Wuhan, Hubei and China. The model is built upon the data from January 20 to March 23, 2020. The Markov chain Monte Carlo (MCMC) Gibbs sampling and machine learning of Gaussian process regression are applied to solve the parameters estimation and the sensitivity analysis is used in various scenarios. The model has a breakthrough in parameter setting and accuracy optimization. It is found that contact reduction is the most effective core lever to control the epidemic, with 3.5 times or more sensitivity as much as other levers. The asymmetric marginal effect in strong and weak scenarios proves that Chinese controlling strategy is close to the Pareto Optimality. The intervention effectiveness of COVID-19 in China is evaluated by simulation analysis. The result provides valuable reference for China and other countries to judge the epidemic risk, control the intervention pace, and formulate prevention strategies in the future.

The Fiedler vector of a graph, namely the eigenvector corresponding to the second smallest eigenvalue of a graph Laplacian matrix, plays an important role in spectral graph theory with applications in problems such as graph bi-partitioning and envelope reduction. Algorithms designed to estimate this quantity usually rely on a priori knowledge of the entire graph, and employ techniques such as graph sparsification and power iterations, which have obvious shortcomings in cases where the graph is unknown, or changing dynamically. In this paper, we develop a framework in which we construct a stochastic process based on a set of interacting random walks on a graph and show that a suitably scaled version of our stochastic process converges to the Fiedler vector for a sufficiently large number of walks. Like other techniques based on exploratory random walks and on-the-fly computations, such as Markov Chain Monte Carlo (MCMC), our algorithm overcomes challenges typically faced by power iteration based approaches. But, unlike any existing random walk based method such as MCMCs where the focus is on the leading eigenvector, our framework with interacting random walks converges to the Fiedler vector (second eigenvector). We also provide numerical results to confirm our theoretical findings on different graphs, and show that our algorithm performs well over a wide range of parameters and the number of random walks. Simulations results over time varying dynamic graphs are also provided to show the efficacy of our random walk based technique in such settings. As an important contribution, we extend our results and show that our framework is applicable for approximating not just the Fiedler vector of graph Laplacians, but also the second eigenvector of any time reversible Markov Chain kernel via interacting random walks.