MCMC

Bayesowskie podejście rzadko omawiane jest w polskojęzycznej literaturze statystycznej (zob. Grzenda, 2012; Niemiro, 2013), mimo iż stanowi ważną gałąź statystyki. Możemy je stosować jako podstawową metodę estymacji, uzupełnienie metod częstościowych lub jako metodę używaną równolegle. (...) głównym zastosowaniem tego podejścia jest modelowanie statystyczne. Podejście Bayesowskie pozwala na bezpośrednie określenie modelu zgodnie z terminologią relacji stochastycznych między poszczególnymi zmiennymi ujętymi w modelu. Estymacja w tym ujęciu najczęściej opiera się na stosowaniu metod symulacyjnych, dzięki czemu w mniejszym stopniu ograniczeni jesteśmy wielkością próby w porównaniu do metod częstościowych. Z drugiej strony, badacz stosujący to podejście musi zaakceptować fakt, że uzyskany w ten sposób wynik może być obciążony założeniami a priori, jakie przyjął, definiując model statystyczny interesującego go zjawiska. (...)

We propose a new discrete-time model of returns in which jumps capture persistence in the conditional variance and higher-order moments. Jump arrival is governed by a heterogeneous Poisson process. The intensity is directed by a latent stochastic autoregressive process, while the jump-size distribution allows for conditional heteroskedasticity. Model evaluation focuses on the dynamics of the conditional distribution of returns using

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects  characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The
group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for
large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced.

The electric motor or compressor consists of set multiple mechanical parts and these parts are passing by some stages to reaches to the final image for the product to be ready for the assembly process. There is more than one stage that the parts of the motor passes by them and these stages as technical work shop, production department, quality department ,final test department. In these report we are show every thing of the motor and parts of them and every stage of every part in some chapters. In this report we are talking about the "Rotor" and the stage of it from the first stage to the final stage. We are talking about the "Stator" and the stages of it from the first stage to the final stage. We are talking about the most important department in the factory because of its importance in preparing every part in the motor like as crank case, crank shaft, piston, paella, valve, upper and the shell. Then they are passing to the collecting department we are install the piston, paella, upper, valve, crank shaft, in the crank case, we will put them in the motor body. We will paint the compressor from the outside and label the attachment of the model. II Acknowledgment

In this thesis, we address several problems related to modelling complex systems. The difficulty of modelling complex systems lies partly in their topology and how they form rather complex networks. From this perspective, our interest in networks (graphs) is part of a broader current of research on complex systems.
Graphical models provide powerful tools to model and make the statistical inference regarding complex relationships among variables. In this context, Gaussian graphical models are commonly used, since inference in such models is often tractable. In Chapter 2, we introduce a novel Bayesian framework for Gaussian graphical model determination.
We carry out the posterior inference by using an efficient sampling scheme which is a trans-dimensional MCMC approach based on birth-death process. In particular, we construct an efficient search algorithm which explores the graph space to detect the underlying graph with high accuracy. We cover the theory and computational details of the proposed method. We then apply the method to large-scale real applications from mammary gene expression studies to show its empirical usefulness.

In this paper, we address the problem of tracking an unknown and time varying number of targets and their states from noisy observations available at discrete intervals of time. Attention has recently focused on the role of simulation-based approaches, including Monte Carlo methods, in solving multitarget tracking problem, as these methods are able to perform well for nonlinear and non-Gaussian data models. In this paper, we present a comparative study of several Monte-Carlo methods in terms of estimation quality and complexity.

Teknik pengukuran geolistrik sounding (VES) dengan konfigurasi Schlumberger mampu menjangkau kedalaman cukup besar dan praktis dilakukan di lapangan dengan kondisi topografi yang sulit. Makalah ini membahas algoritma Markov Chain Monte Carlo (MCMC) untuk pemodelan inversi 1-D data VES. Model terdiri dari sejumlah lapisan dengan ketebalan tetap dengan resistivitas sebagai parameter model yang dicari. Pilihan harga resistivitas lapisan adalah harga-harga diskret yang dapat mewakili medium konduktif sampai resistif. Algortima MCMC didasarkan pada sampling ruang model secara lebih terarah dengan memanfaatkan probabilitas transisi rantai Markov. Harga resistivitas untuk satu lapisan tertentu memiliki probabilitas terpilih lebih besar jika menghasilkan misfit lebih kecil. Karena adanya ekivalensi, konfigurasi resistivitas lapisan yang bervariasi dapat menghasilkan misfit yang dekat dengan harga optimumnya. Oleh karena itu selain misfit kecil, model disebut optimum jika variasi resistivitasnya minimum (smooth). Penerapan inversi pada
data sintetik maupun data lapangan memberikan hasil yang memuaskan. Teknik inversi ini akan dikembangkan dengan menambahkan kriteria kesinambungan antara satu lapisan dengan lapisan yang sama dari titik sounding yang berdekatan untuk memudahkan korelasi dan interpretasi.

Vertical Electrical Sounding (VES) using Schlumberger electrode configuration has relatively deep investigation depth and is practical in the field with rough topography. This paper discusses the Markov Chain Monte Carlo (MCMC) algorithm for 1-D VES data inversion. Layered model is formed by a number of layers with fixed thickness and the model parameters are layers’ resistivities. The possible values for resistivities are discrete values representing conductive to resistive medium. MCMC algorithm is based on guided sampling of the model space employing transition probability of a Markov chain. A resisitivity value for a particular layer has higher probability if it is associated with lower misfit. Due to equivalence problems, models with high variation in resistivities may result in near-optimal misfit. Therefore, additional constrain other than misfit is introduced, i.e. model smoothness. Inversion results of synthetic and field data are encouraging. The inversion technique will be developed by adding constrains on lateral continuity of layers to facilitate correlation and interpretation.

What factors best explain the low incidence of skills training in a late industrial society like Russia? This research undertakes a multilevel analysis of the role of occupational structure against the probability of training. The explanatory power of occupation-specific determinants and skills polarisation are evaluated, using a representative 2012 sample from the Russian Longitudinal Monitoring Survey. Applying a two-level Bayesian logistic regression model, we show that the incidence of training in Russia is significantly contextualised within the structure of occupations and the inequalities between them. The study shows that extremely high wage gaps within managerial class jobs can discourage training, an unusual finding. Markets accumulating interchangeable and disposable labour best explain the low incidence of training; workers within generic labour are less likely to develop their skills formally, except in urban markets. Although we did not find strong evidence of skills polarisation, Russians are yet to live in a knowledge economy.

Mes travaux portent sur l'analyse de la dynamique cerebrale a partir de donnees de neuro-imagerie fonctionnelle issues d'examens d'Imagerie par Resonance Magnetique fonctionnelle (IRMf). Ils concernent aussi bien l'etude de la dynamique evoquee par un paradigme d'activation cerebrale et celle issue de l'activite spontanee ou de « fond » lorsque le sujet est au repos (resting state). Les algorithmes que j'ai developpes s'appuient pour une large partie sur une connaissance explicite du paradigme experimental mis au point par l'experimentateur mais aussi prennent place dans une moindre part au sein des methodes exploratoires, qui n'exploitant pas ces informations issues du paradigme. Ce theme de recherche embrasse a la fois des problemes bas niveau relatifs a la reconstruction d'images en IRM mais aussi des aspects plus haut niveau qui concernent l'estimation et la selection de modeles hemodynamiques regionaux non-parametriques, capables ...

Genome comparison has shed light on many fields of both basic and applied research, including the study of species phylogeny. Grass carp (Ctenopharyngodon idella) belongs to Cyprinidae, the largest freshwater fish family; but which subfamily it belongs to remains a controversial issue. In this study, the complete mitochondrial genome (mitogenome) sequence of grass carp was determined and phylogenetic analyses of all mitochondrial protein-coding genes and a nuclear gene (RAG 2) were conducted to explore the evolutionary relationship of grass carp with other cyprinid species. The mitogenome of grass carp is 16,609 bp in length. As with most other vertebrates, it contains the same gene order and an identical number of genes or regions, including 13 protein-coding genes, two rRNA genes, 22 tRNA genes and one putative control region. Phylogenetic analyses using two different datasets (mitochondrial and nuclear) and three different computational algorithms (Bayesian, MP and ML) all revealed two distinct groups with high statistical support, indicating that Cyprininae and Leuciscinae are two separate, valid subfamilies. Importantly, our phylogenetic result provides strong molecular evidence in support of the placement of Ctenopharyngodon in Leuciscinae rather than in Cyprininae.

Adaptive and interacting Markov Chains Monte Carlo (MCMC) algorithms are a novel class of non-Markovian algorithms aimed at improving the simulation efficiency for complicated target distributions. In this paper, we study a general (non-Markovian) simulation framework covering both the adaptive and interacting MCMC algorithms. We establish a Central Limit Theorem for additive functionals of unbounded functions under a set of

A two-phase Monte Carlo simulation (TPMCS) uncertainty analysis framework is used to analyze epistemic and aleatory uncertainty associated with simulated exceedances of an in-stream fecal coliform (FC) water quality criterion when using the Hydrological Simulation Program–FORTRAN (HSPF). The TPMCS framework is compared with a single-phase or standard Monte Carlo simulation (SPMCS) analysis. Both techniques are used to assess two total maximum daily load (TMDL) pollutant allocation scenarios. The application of TPMCS illustrates that cattle directly depositing FC in the stream is a greater source of epistemic uncertainty than FC loading from cropland overland runoff, the two sources specifically targeted for reduction in the allocation scenario. This distinction is not possible using SPMCS. Although applying the TPMCS framework involves subjective decisions about how selected model parameters are considered within the framework, this uncertainty analysis approach is transparent and the results provide information that can be used by decision makers when considering pollution control measure implementation alternatives, including quantifying the level of confidence in achieving applicable water quality standards.

—We propose a Bayesian multi-target batch processing algorithm capable of tracking an unknown number of targets that move close and/or cross each other in a dense clutter environment. The optimal Bayes multi-target tracking problem is formulated in the random finite set framework and a Particle Marginal Metropolis-Hastings (PMMH) technique which is a combination of Metropolis-Hastings (MH) algorithm and sequential Monte Carlo methods is applied to compute the multi-target posterior distribution. The PMMH technique is used to design a high dimensional proposal distributions for the MH algorithm and allows the proposed batch process multi-target tracker to handle a large number of tracks in a computationally feasible manner. Our simulations show that the proposed tracker reliably estimates the number of tracks and their trajectories in scenarios with a large number of closely spaced tracks in a dense clutter environment albeit, more expensive than on-line methods.

Within the Generalized Linear Latent Variable Models context (GLVM; Moustaki and Knott 2000) we discuss the implementation of Bayesian measures of model complexity such as the Bayes Factor (BF; Kass and Raftery, 1995).
Patz and Juncker (1999) initially proposed a Bayesian approach regarding the estimation of the parameters of a latent variable model with categorical responses. A-priori distributions are assigned to the model parameters as well as to the latent vector. A Markov chain, whose stationary distribution is the required posterior distribution P(α,β,z|x), is simulated via a Metropolis-Hastings within Gibbs algorithm (Chib and Greenberg, 1995). After a sufficiently log run of the chain, inference can be made about each parameter. We expand this work addressing the problem of approximating the marginal likelihood, over all parameters and for each competing model, involved in the calculation of the BF. Five methods proposed in the Bayesian literature are applied in the GLVM, namely:Harmonic mean estimator (Raftery et al, 2007), Importance sampling estimator (Newton and Raftery, 1994), Laplace estimator (Lewis and Raftery, 1997), Chib and Jeliazkov estimator (Chib and Jeliazkov, 2001), Power posterior estimator (Friel and Pettit, 2008).A comparison with respect to the accuracy and computational complexity of estimators is illustrated.

Abstract: Deterministic models have been used in the past to understand the epidemiology of infectious diseases, most importantly to estimate the basic reproduction number, Ro by using disease parameters. However, the approach overlooks variation on the disease parameter(s) which are function of Ro and can introduce random effect on Ro. In this paper, we estimate the Ro as a random variable by first developing and analyzing a deterministic model for transmission patterns of pneumonia, and then compute the probability distribution of Ro using Monte Carlo Markov Chain (MCMC) simulation approach. A detailed analysis of the simulated transmission data, leads to probability distribution of Ro as opposed to a single value in the convectional deterministic modeling approach. Results indicate that there is sufficient information generated when uncertainty is considered in the computation of Ro and can be used to describe the effect of parameter change in deterministic models.

Regression density estimation is the problem of
exibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses mixtures of experts models and our article considers flexible mixtures of heteroscedastic experts (MHE) regression models where the response distribution
is a normal mixture, with the component means, variances and mixture weights all varying as a function of covariates. Our article develops fast variational approximation methods for inference. Our motivation is that alternative computationally intensive MCMC methods for tting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three
contributions. First, a variational approximation for MHE models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation methods to perturb the initial solution to
attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared to MCMC based approaches are illustrated. These advantages are particularly compelling for time series data where repeated retting for one step ahead prediction in model choice and diagnostics and in rolling window computations is very common.