()Tj 0.6389 0 TD /F6 1 Tf /F2 1 Tf Mathematical Theory of Bayesian Statistics introduces the mathematical foundation of Bayesian inference which is well-known to be more accurate in many real-world problems than the maximum likelihood method. 1Bayesian statistics has a way of creating extreme enthusiasm among its users. 0.7863 0 TD (observables)Tj HIGHLIGHTS THE USE OF BAYESIAN STATISTICS TO GAIN INSIGHTS FROM EMPIRICAL DATA Featuring an accessible … In this third Edition, four newly-added chapters address topics that reflect the rapid advances in the field of Bayesian statistics. 0.5555 0 TD I. Gelman, Andrew. 14.303 0 TD /F3 1 Tf 2The di erences are mostly cosmetic. [(Univer)9.9(sitat)-250.3(de)-250.1(V)110.8(alència,)-250.5(Spain)]TJ Bayesian Estimation For example, we might know that the normalized frequency f 0 of an observed sinusoid cannot be greater than 0.1. /F6 1 Tf >> library (tidyverse) library (ggplot2) library (dplyr) 1.1 Introduction. )]TJ ()Tj 4. /F7 1 Tf <>/XObject<>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
(. Introduction to Bayesian Analysis Lecture Notes for EEB 596z, °c B. Walsh 2002 As opposed to the point estimators (means, variances) used by classical statis- tics, Bayesian statistics is concerned with generating the posterior distribution of the unknown parameters … /F1 4 0 R 0.7862 0 TD Holes in Bayesian Statistics Andrew Gelmany Yuling Yao z 11 Feb 2020 Abstract Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Introduction to Risk Management and Business Intelligence Topic 9. 0.659 0 TD endobj /F6 1 Tf [(Uni)25(v)15(ersité)-250.4(de)-250.1(Neuchâtel,)-250.7(Switzerland)]TJ /F6 1 Tf A. Bayesian statistics uses more than just Bayes’ Theorem In addition to describing random variables, Bayesian statistics uses the ‘language’ of probability to describe what is known about unknown parameters. )]TJ 0.5031 0 TD 0.2502 Tc 7 • Interpretation and calibration of the intrinsic discrepancy Let {p1(x|θ1),θ1 ∈ Θ1} or {p2(x|θ2),θ2 ∈ Θ2} be two alternative statistical models for x ∈ X, one of which is assumed to be true.The intrinsic divergence δ{θ1,θ2} = δ{p1,p2} is then minimum expected log-likelihood ratio in favour of the true model. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. 2.139 0 TD /F5 1 Tf /F7 1 Tf 1. ‘An introduction to computational Bayesian statistics cooked to perfection, with the right mix of ingredients, from the spirited defense of the Bayesian approach, to the description of the tools of the Bayesian trade, to a definitely broad and very much up-to-date presentation of Monte Carlo and Laplace approximation methods, to a helpful description of the most common software. 0.5031 0 TD (C)Tj The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. 0.5555 0 TD 1.25 0 TD (quantities\),)Tj /F2 1 Tf >> [(“xed)-250.3(unknown)]TJ 0.3889 0 TD This course describes Bayesian statistics, in which one's inferences about parameters or hypotheses are updated as evidence accumulates. (\))Tj (,)Tj /F1 1 Tf An introduction to the concepts of Bayesian analysis using Stata 14. endobj
0 Tw /F5 1 Tf Bayesian frameworks have been used to deal with a wide variety of prob-lems in many scientiﬁc and engineering areas. (\()Tj << 5/37. Kapitel 37: Bayesian Inference and Sampling Theory. /F5 1 Tf (0)Tj /F2 1 Tf It can also be used as a reference work for statisticians who require a working knowledge of Bayesian statistics. 0.5937 0 TD (|)Tj /F5 1 Tf 1. >> (Notation)Tj 2 The Bayesian scan statistic Here we consider the natural Bayesian extension of Kulldorff’s scan statistic, moving from a Poisson to a conjugate Gamma-Poisson model. [(h)250.2(a)270(v)265.2(ea\()]TJ /F3 1 Tf /F2 1 Tf /F3 6 0 R Introduction to Bayesian Statistics - 6 Edoardo Milotti Università di Trieste and INFN-Sezione di Trieste Bayesian estimates often require the evaluation of complex integrals. /F7 1 Tf /F6 1 Tf (2004),Computational Bayesian ‘ Statistics’ by Bolstad (2009) and Handbook of Markov Chain Monte ‘ Carlo’ by Brooks et al. 0.7382 0 TD 0.5 0.8056 TD 1.5419 0 TD <>>>
(C)Tj (x)Tj 1.6111 0.8055 TD << )]TJ /F4 1 Tf f )]TJ 0.8333 -1.1667 TD In our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence. /F2 1 Tf 0 23.9103 -23.9103 0 157.1637 89.1736 Tm )]TJ /GS1 gs /F3 1 Tf /F5 1 Tf /F6 1 Tf )-361.1(Other)-250.2(e)14.8(xamples:)]TJ [(,B)250(i)]TJ (C)Tj (2011). 0 23.9103 -23.9103 0 176.6217 289.5363 Tm 0.3889 0 TD (|)Tj All of these aspects can be understood as part of a tangled workflow of applied Bayesian statistics. /F3 1 Tf -25.7581 -1.2852 TD 0.3889 0 TD Bayesian Models for Categorical Data (eBook, PDF) 91,99 € Ioannis Ntzoufras. ET 0.8715 0 TD /ProcSet [/PDF /Text ] T* (=1)Tj (|)Tj An introduction to the concepts of Bayesian analysis using Stata 14. 13.084 0 TD 90% of the content is the same. 0.4445 0 TD (4)Tj 0.3889 0 TD [(P)15.2(arameters)]TJ /F3 1 Tf Bayesian statistics mostly involves conditional probability, which is the the probability of an event A given event B, and it can be calculated using the Bayes rule. 0.5 0 TD BT /F5 1 Tf [(Infer)36.8(ence)-250.5(summaries. ({)Tj 0.5 0 TD 0.7382 0 TD 1.25 0 TD 0 Tc /F5 1 Tf f (3)Tj using p-values & con dence intervals, does not quantify what is known about parameters. [(scienti“c)-250(and)-250.2(industrial)-250.7(reporting,)-250.5(public)-250.5(decision)-250.5(making,)-250.5(...)]TJ Whenever a quantity is to be inferred, or some conclusion is to be drawn, from observed data, Bayesian principles and tools can be used. /F6 1 Tf (2)Tj /F5 1 Tf 145.061 77.228 13.549 -0.398 re [(Conclusions)-250.2(conditional)-251(on)-250(the)-250.3(assumption)-250.4(that)-250.5(model)-250.5(is)-250(correct)]TJ Using Bayesian inference to solve real-world problems requires not only statistical skills, subject matter knowledge, and programming, but also awareness of the decisions made in the process of data analysis. /F6 1 Tf /F3 1 Tf 145.011 76.83 0.399 -8.64 re f /F6 1 Tf (E)Tj 231.581 68.228 13.549 -0.398 re (|)Tj /F4 1 Tf >> /F7 1 Tf -13.0058 -1.2852 TD [(Special)-250.7(densities)-250.5(\(or)-250(mass\))-250(functions)-250.4(use)-250(speci“c)-250(notation,)-250.7(as)]TJ 4��p:��7ә��n�O���T�I3�� }���OT�X̋%�V��h�r�� Series. [(,)-163()]TJ 0.7863 0 TD /F2 1 Tf (Prior)Tj 0.0037 Tc While there is increasing interest in Bayesian statistics among scholars of different social science disciplines, I always looked for a text book which is accessible to a wide range of students who do not necessarily have extended knowledge of statistics. -7.5343 -1.6473 TD %PDF-1.5
/F2 1 Tf /F5 1 Tf To test the signiﬁcance of the result we asked what is the probability of measuring this value of r if there is no correlation? [(b)20(u)0(t)-250.2(a)-250.2(description)-250.7(of)-250(the)]TJ /F6 1 Tf Bayesian statistics mostly involves conditional probability, which is the the probability of an event A given event B, and it can be calculated using the Bayes rule. >> (x)Tj 0.2778 Tc f (\))Tj 1 0 0 rg 0 23.9103 -23.9103 0 49.5044 758.8633 Tm (x)Tj /F6 1 Tf 0 Tc endobj /Font << /F7 1 Tf (\()Tj Mathematical statistics uses two major paradigms, conventional (or frequentist), and Bayesian. [(Notation.)-361.6(Statistical)-251.2(models. /F3 1 Tf Prediction problems, which are often considered to be the primary objective of statistical analysis, are solved most naturally if one follows the Bayesian approach. /GS1 gs 0.8257 0 TD 1 0 0 rg 0.7222 0 TD 0.3889 0 TD ()Tj Bayesian methods provide a complete paradigm for both statistical inference and decision mak-ing under uncertainty. ()Tj 0.5 0 TD (,)Tj 4.617 0 TD /F5 1 Tf 158.212 76.83 0.398 -8.64 re 0.4444 0 TD [(Structur)36.8(e)-250.2(o)0(f)-250.2(a)-250(decision)-250.5(pr)45.2(oblem. Using Bayesian inference to solve real-world problems requires not only statistical skills, subject matter knowledge, and programming, but also awareness of the decisions made in the process of data analysis. /F4 1 Tf 0.611 0 TD [(1.1. 446.092 76.83 0.398 -8.64 re /F6 1 Tf ET /F3 1 Tf /F7 1 Tf /F6 1 Tf /F5 1 Tf 0.3889 0 TD /F3 1 Tf /F4 1 Tf 0.7604 0 TD Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, Understanding Computational Bayesian Statistics successfully guides readers through this new, cutting-edge approach. /F2 1 Tf 0.7863 0 TD /F4 1 Tf Praktische Bedeutung in der Statistik ... insb. 0.25 Tc 0 0 0 rg (,)Tj 12.804 0 TD [(pr)45.2(obability)]TJ 0.3889 0 TD /F2 1 Tf In disease mapping, the effect of the … 0 20.9215 -20.9215 0 215.7041 579.3246 Tm (and)Tj ()Tj I use Bayesian methods in my research at Lund University where I also run a network for people interested in Bayes. /Length 2845 f 0.2778 Tc )]TJ /F2 5 0 R 1.0556 0 TD Bayesian methodology. Bayesian Statistics (eBook, PDF) 42,99 € Bayesian Inference in the Social Sciences (eBook, PDF) 103,99 € Peter Congdon. /F2 1 Tf )]TJ 0.6059 0 TD Bayesian statistics naturally allows for combination with previous measurements, via the prior • In Lecture 2 we measured the correlation coefﬁcient of two variables. BT /F3 1 Tf /F3 1 Tf 0.4444 0 TD (p)Tj Note: Frequentist statistics , e.g. (,)Tj 11 0 obj 5.999 0 TD 0.2778 Tc 0.5833 0 TD (|)Tj (2. https://www.quantstart.com/articles/Bayesian-Statistics-A-Beginners-Guide /F2 1 Tf 0 23.9103 -23.9103 0 207.3524 288.7193 Tm Interdisciplinary Bayesian Statistics, eBook pdf (pdf eBook) bei hugendubel.de als Download für Tolino, eBook-Reader, PC, Tablet und Smartphone. [(Summar)-9.7(y)]TJ /F5 1 Tf Introduction to Bayesian Statistics, Third Edition is a textbook for upper-undergraduate or first-year graduate level courses on introductory statistics course with a Bayesian emphasis. [(Objective)-251(Bayesian)-250.5(Statistics)]TJ (x)Tj 0.3889 0 TD /F7 1 Tf /F6 1 Tf /F2 1 Tf Produktinformationen zu „Introduction to Bayesian Statistics (PDF) “ The Introduction to Bayesian Statistics (2nd edition) presents Bayes' theorem, the estimation of unknown parameters, the determination of confidence regions and the derivation of tests of hypotheses for the unknown parameters, in a manner that is simple, intuitive and easy to comprehend. %PDF-1.3 endobj
/F4 1 Tf 0.5031 0 TD /F6 1 Tf 0.4445 0 TD 244.732 76.83 0.398 -8.64 re 0.4445 0 TD /F2 1 Tf (. 0 23.9103 -23.9103 0 255.0227 89.1736 Tm /F5 1 Tf 1.5555 0 TD 8.682 0 TD (|)Tj /F6 1 Tf 1.6543 0 TD The Bayesian approach to statistics considers parameters as random variables that are characterised by a prior distribution which is combined with the traditional likelihood to obtain the posterior distribution of the parameter of interest on which the statistical inference is based. (x)Tj /F2 1 Tf )]TJ 2 The Bayesian scan statistic Here we consider the natural Bayesian extension of Kulldorff’s scan statistic, moving from a Poisson to a conjugate Gamma-Poisson model. )]TJ (\()Tj 0.5 0 TD II. How does it differ from the frequentist approach? )]TJ /F6 1 Tf /F6 1 Tf /F3 1 Tf 0.722 0 TD /F7 1 Tf /F3 1 Tf 0.5 0.8055 TD /F1 4 0 R 0 0 0 rg 8.879 0 TD /ExtGState << The concept of conditional probability is widely used in medical testing, in which false positives and false negatives may occur. 0 31.8805 -31.8805 0 296.2621 275.8615 Tm (must)Tj 0.9368 0 TD f /Font << ()Tj /F6 1 Tf f (|)Tj 0.4445 0 TD (\))Tj Recent research has uncovered several mathematical laws in Bayesian statistics, by which both the generalization loss and the marginal likelihood are estimated … Bayesian Statistics (a very brief introduction) Ken Rice Epi 516, Biost 520 1.30pm, T478, April 4, 2018 (=1)Tj /F7 1 Tf (|)Tj /F6 1 Tf /F4 1 Tf – David Hume 254. 0.7382 0 TD Bayesian statistics has many important advantages that students should learn about if they are going into fields where statistics will be used. 0 23.9103 -23.9103 0 118.0832 39.3604 Tm /F3 1 Tf )-278(Intr)19.9(oduction)]TJ Firstly, we need to dispel the myth that a Bayesian probability, the plausibility of a hypothe-sis given incomplete knowledge, is in some sense a more vague concept than a frequentist proba- 0.7604 0 TD 0 23.9103 -23.9103 0 49.5044 758.8633 Tm (0)Tj /F7 1 Tf /F4 1 Tf 0.4445 0 TD Statistical Association and the Journal of the Royal Statistical Society). )]TJ 0.3889 0 TD 0 0 0 rg 6.948 0 TD ()Tj [(Intrinsic)-250.5(con)39.8(v)15(e)0(r)17.8(gence)-250.5(of)-250(distrib)19.6(utions. ()Tj ET 0 31.8805 -31.8805 0 78.6949 226.2715 Tm 103.061 77.228 13.549 -0.398 re Statistical Association and the Journal of the Royal Statistical Society). [(Exchangeability)63.5(. (x)Tj 4.805 0 TD Bayesian Statistics: Background In the frequency interpretation of probability, the probability of an event is limiting proportion of times the event occurs in an inﬁnite sequence of independent repetitions of the experiment. [(\))-250(distrib)19.6(ution)-250.4(describing)-250.5(a)19.8(v)25(ailable)]TJ (Beta)Tj /F8 1 Tf (Not)Tj ET (\))Tj [(José)-277.8(M.)-278.2(Bernar)20.5(do)]TJ <>
Nature of Bayesian Inference Standard Normal Theory Inference Problems Bayesian Assessment of Assumptions: Effect of Non-Normality on Inferences About a Population Mean with Generalizations Bayesian Assessment of Assumptions: Comparison of Variances Random Effect Models Analysis of Cross Classification Designs Inference About Means with Information from More than One … (3. ET BT /Length 2158 2 0 obj Bayesian Statistics for Beginners is an entry-level book on Bayesian statistics. /F2 1 Tf f 0.8257 0 TD /F3 1 Tf [(Important)-205.3(particular)-205.5(case:)-338.9(no)-204.5(rele)24.5(v)25(ant)-204.9(\(or)-204.6(subjecti)24.3(v)15(e)0(\))-204.7(initial)-205.6(information:)]TJ (\))Tj stream
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well-documented data:Objective Bayesian Statistics. 2 Bayesian statistics represents a powerful alternative to frequentist (classical) statistics, and is therefore, controversial. /F7 1 Tf [(Refer)36.5(ence)-250.5(analysis. f /F7 1 Tf 0.6059 0 TD endstream %âãÏÓ
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[(An)-278(Intr)19.9(oduction)-278.7(to)]TJ The software packages which feature in this book are R and WinBUGS. Data Analysis’ by Gelman et al. f [()]TJ (d)Tj 8.879 0 TD /F3 1 Tf 1.445 0 TD 0.8257 0 TD /F5 1 Tf 0 23.9103 -23.9103 0 176.6217 604.8379 Tm (\))Tj (\))Tj /F5 1 Tf In Bayesian statistics or inference, we estimate a distribution (see resource “Probability Distribution Functions”) for that parameter rather than just a single point estimate. -2.155 -3.5404 TD )Tj /F1 1 Tf /F6 1 Tf <>
2.056 0 TD 1.2972 -1.2852 TD (|)Tj endstream /F2 1 Tf [(1. [(µ,)-166.7()]TJ T* (\()Tj 0 Tw [(Probability)-250.7(as)-250(a)-250.2(rational)-250.8(de)14.8(gree)-250.3(of)-250(belief. (\()Tj [(axiomatic)-250.7(foundations)]TJ ()Tj 11.538 0 TD 7.166 0 TD (,)Tj 0 0 0 rg PROLOGUE 5 Figure 1.1: An ad for the original … 14 0 obj Bayesian methods may be derived from an axiomatic system, and hence provideageneral, coherentmethodology. /Length 729 /F8 1 Tf -9.8128 -1.2852 TD )]TJ /F2 1 Tf /F6 1 Tf [(Hypothesis)-250.2(testing)14.5(. )]TJ (C)Tj (N)Tj -11.1697 -1.2853 TD 5.451 0 TD [(Intrinsic)-250.4(discr)37(epancy)54.5(. /F3 1 Tf 0.5556 0 TD /F3 1 Tf ET 9.451 0 TD 0.0845 -1 TD /F2 1 Tf 7.846 0 TD 0.3889 0 TD (C)Tj (x)Tj /F1 4 0 R (2011). )Tj (x)Tj (\))Tj ET (\()Tj Book Description. 0.5 0 TD /F6 1 Tf 2.639 0 TD What is Bayesian statistics and why everything else is wrong Michael Lavine ISDS, Duke University, Durham, North Carolina Abstract We use a single example to explain (1), the Likelihood Principle, (2) Bayesian statistics, and (3) why classical statistics cannot be used to compare hypotheses. 242.811 76.83 0.399 -8.64 re (x)Tj 10 0 obj ()Tj 0.2778 0 TD (x)Tj 2.25 0 TD 0.6667 0 TD [(Under)-250(conditions)]TJ (,)Tj [(Basics)-250.2(of)-250.2(Bayesian)-250.5(Analysis)]TJ /F3 1 Tf /F4 1 Tf 1.7062 0 TD The fundamental objections to Bayesian methods are twofold: on one hand, Bayesian methods are presented as an automatic inference engine, and this raises suspicion in anyone with applied experience. Bayesian inference is one of the more controversial approaches to statistics. (|)Tj [(T)69.8(entati)24.2(v)15(ely)-250.3(accept)-250.8(a)]TJ 231.652 76.83 0.399 -8.64 re /F3 1 Tf ()Tj 0.7604 0 TD ()Tj enter the Monte Carlo methods! 0 Tc 301.251 702.507 0.399 -576.597 re 0 Tc Bayesian Analysis (2008) 3, Number 3, pp. [(statistical)-251.2(model)]TJ >y����LV{v�Np ��i5yƇ�f����l��[��'�,�f["m���*�:�e^\2�Ea�X��S�6,�01�^��VWv��(-3��,��_�=yuI��~>,�3=94��U�g��11�w���.7O�-�}F����.���$g) Bayesian Gamma-Poisson models are a common representation for count data in epidemiology, and have been used in disease (d)Tj Objections to Bayesian statistics Andrew Gelman Abstract. 0 Tw 0.7222 0 TD 0 23.9103 -23.9103 0 243.7519 89.1736 Tm (]=)Tj 103.061 68.228 13.549 -0.398 re -7.989 -1.1667 TD /F5 1 Tf -8.822 -1.1667 TD [(Point)-250.2(and)-250.2(re)14.9(gion)-250.2(estimation. 231.581 77.228 13.549 -0.398 re [(about)-250.3(their)-250.5(true)-250.3(v)25(alues. /F7 1 Tf ()Tj /F6 1 Tf (|)Tj (C)Tj 0.8257 0 TD /ProcSet [/PDF /Text ] 0.4445 0 TD (\()Tj [(F)104.8(oundations. 3 0 obj This is ensured by choosing p(f 0) = 10, if 0 6 f 0 6 0.1 0, otherwise as the prior PDF in the Bayesian framework. 0.8333 -1.1667 TD A wise man, therefore, proportions his belief to the evidence. Bayesian analysis Class Notes Manuel Arellano March 8, 2016 1 Introduction Bayesian methods have traditionally had limited in⁄uence in empirical economics, but they have become increasingly important with the popularization of computer-intensive stochastic simulation algorithms in the 1990s. /F5 1 Tf (X)Tj (d)Tj /F4 1 Tf /F6 1 Tf A hands-on introduction to computational statistics from a Bayesian point of view. stream
Bayesian Gamma-Poisson models are a common representation for count data in epidemiology, and have been used in disease mapping by Clayton and Kaldor [7], Molli´e [8], and others. (0)Tj BT 0 0 0 rg enter the Monte Carlo methods! >> The concept of conditional probability is widely used in medical testing, in which false positives and false negatives may occur. 242.861 77.228 13.549 -0.398 re 0 Tc In Bayesian statistics or inference, we estimate a distribution (see resource “Probability Distribution Functions”) for that parameter rather than /F2 5 0 R /F4 1 Tf 9.4981 0 TD (E)Tj 1.111 0 TD )]TJ 0.25 Tc /F3 1 Tf 0 0 1 rg [(information)-250.9(about)-250.3(their)-250.5(v)25(alues)]TJ /F4 1 Tf /F2 1 Tf Bayesian Statistics Explained in Simple English For Beginners.pdf - Free download as PDF File (.pdf), Text File (.txt) or read online for free. f /F3 1 Tf This interpretation assumes that an experiment can … 0 Tc 0.5 0 TD /F5 1 Tf 0.4444 0 TD ת�i��S� L���f��C]����@��?�����0���a"~�HMo��)�)�>0�!�ca��4���a (\()Tj )]TJ 1. 0.7778 0 TD /F5 1 Tf 242.861 68.228 13.549 -0.398 re /F2 1 Tf /F3 1 Tf /F3 1 Tf (|)Tj )]TJ /F5 1 Tf /F5 1 Tf Bayesian methodology. )]TJ Sivia: Data Analysis: A Bayesian Tutorial, Oxford Science Publications, 2006, ISBN 0-19-856831-2, besonders für Probleme aus der Physik zu empfehlen. 0.3889 0 TD 1.3125 -1.3049 TD 0.6059 0 TD [(n,)-166.7()]TJ (C)Tj 3.833 0 TD 0.7604 0 TD /F4 1 Tf Bayesian statistical decision theory. 0.5031 0 TD /F3 1 Tf /F3 1 Tf CHAPTER 1. The first edition of Peter Lees book appeared in1989, but the subject has moved ever onwards, with increasingemphasis on Monte Carlo based techniques. [(. BT [(Bayesian)-250.5(approach)-250.5(“rmly)-250.2(based)-250.2(on)]TJ 1.2972 -1.2852 TD /F3 1 Tf Lee (1997), ‘Bayesian Methods: An Analysis for Statisticians and Interdisciplinary Researchers’ by Leonard and Hsu (1999), Bayesian ‘ Data Analysis’ by Gelman et al. << BT [(are,)-250.3(respecti)24.3(v)15(ely)64.7(,)]TJ f [(Decision)-250.4(Making)]TJ 2 0 obj
/ProcSet [/PDF /Text ] /F5 1 Tf Bayesian Modeling Using WinBUGS (eBook, PDF) 128,99 € Produktbeschreibung. [(,o)250(rP)250(n)]TJ 3 0 obj
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