Bayesian statistics

We consider the problem of combining opinions from different experts in an explicitly model-based way to construct a valid subjective prior in a Bayesian statistical approach. We propose a generic approach by considering a hierarchical model accounting for various sources of variation as well as accounting for potential dependence between experts. We apply this approach to two problems. The first problem deals with a food risk assessment problem involving modelling dose-response for Listeria monocytogenes contamination of mice. Two hierarchical levels of variation are considered (between and within experts) with a complex mathematical situation due to the use of an indirect probit regression. The second concerns the time taken by PhD students to submit their thesis in a particular school. It illustrates a complex situation where three hierarchical levels of variation are modelled but with a simpler underlying probability distribution (log-Normal).

There exists a considerable literature on reliability growth modelling. Recently somecommon models have been extended to encompass innovation. They assume the time of aninnovation is known and that there is a coincidental improvement in performance. However,despite such developments, it remains that most models do not fully address the engineeringconcerns as they do not capture the underlying physical processes and they

The advances in computing and information storage have provided vast amounts of data. The challenge has been to extract knowledge from this raw data that has lead to new methods and techniques such as data mining that can bridge the knowledge gap. This research aimed to assess these new data mining techniques and apply them to a soil science database to establish if meaningful relationships can be found. A large data set of Soil database is extracted from the Department of Soil Sciences and Agricultural Chemistry, S V Agricultural College, Tirupati, The database contains measurements of soil profile data from various locations of Chandragiri Mandal, Chittoor District. The research establishes whether Soils are Classified Using various data mining techniques. In addition, comparison was made between Naive bayes classification and analyse the most effective technique. The outcome of the research may have many benefits, t o agriculture, soil management and environmental.

In the aftermath of the 2001 anthrax letters, researchers have been exploring ways to predict the production environment of unknown-source microorganisms. Culture medium, presence of agar, culturing temperature, and drying method are just some of the broad spectrum of characteristics an investigator might like to infer. The effects of many of these factors on microorganisms are not well understood, but the complex way in which microbes interact with their environments suggests that numerous analytical techniques measuring different properties will eventually be needed for complete characterization. In this work, we present a Bayesian statistical framework for integrating disparate analytical measurements. We illustrate its application to the problem of characterizing the culture medium of Bacillus spores using three different mass spectral techniques. The results of our study suggest that integrating data in this way significantly improves the accuracy and robustness of the analyses.

1] One challenge that faces hydrologists in water resources planning is to predict the catchment's response to a given rainfall. Estimation of parameter uncertainty (and model uncertainty) allows assessment of the risk in likely applications of hydrological models. Bayesian statistical inference provides an ideal means of assessing parameter uncertainty, whereby prior knowledge about the parameter is combined with information from the available data to produce a probability distribution (the posterior distribution) that describes uncertainty about the parameter and serves as a basis for selecting appropriate values for use in modeling applications. Widespread use of Bayesian techniques in hydrology has been hindered by difficulties in summarizing and exploring the posterior distribution. These difficulties have been largely overcome by recent advances in Markov chain Monte Carlo (MCMC) methods that involve Monte Carlo sampling of the posterior distribution. This study compares four MCMC sampling algorithms in the context of rainfall-runoff modeling. The algorithms compared include a conventional Metropolis-Hastings algorithm used previously in hydrological applications which uses a combination of block and single-site updating and an adaptive Metropolis algorithm that has characteristics that are well suited to model parameters with a high degree of correlation and interdependence, as is often evident in hydrological models. In addition to these, two other algorithms are evaluated to clarify the relative importance of updating all model parameters as a block versus updating each parameter one at a time. The MCMC techniques are compared for simplicity, ease of use, statistical efficiency in exploration of the parameter space, and speed of implementation, using 11 years of daily rainfall-runoff data from the Bass river catchment in Australia. The results show that the adaptive Metropolis algorithm is superior in many respects and can offer a relatively simple basis for assessing parameter uncertainty in hydrological modeling studies and that the efficiency of the adaptive algorithm is not solely attributed to the blockupdating element of the algorithm.

Methods for Bayesian statistical analysis of stratigraphically related radiocarbon dates have been in use for over a decade. This paper extends these techniques to stratigraphically related ESR dates, allowing estimation of the dates of events not directly dated. A hierarchical model of the uncertainties in ESR dating is developed, to account for the correlation of error terms between samples. Using the new method, an analysis is made of the dating at Border Cave, Kwa Zulu Natal, South Africa. The results for individual dates and the dating of layer boundaries are more precise than previously obtained. The hominid fossils BC1 and BC2 are placed at either 71–91 ka (95% highest posterior density—hpd) or 152–171 ka (95% hpd) depending on the stratigraphic provenance assigned. BC3 is dated to 66–90 ka and BC5 to 61–72 ka (both 95% hpd). The estimated duration of the Howieson's Poort industry at Border Cave is demonstrated to have significant uncertainty, and the ESR dates, even with the increased precision of this analysis, are unable to decide between hypotheses that the industry lasted 10 ka and that it lasted 20 ka.

Many people has contributed to the completion of this dissertation and I am grateful to all of them. First and foremost, I would like to thank my advisor, Kenneth Barner, for providing the encouragement, supervision and support needed during my Ph.D. studies. His optimistic look into life and positive thinking always inspired me. He gave me the freedom to pick the topic I wanted and always pushed me to think outside the box. I would like to thank my committee members, Gonzalo Arce, Javier Garcia-Frias and Can Aysal for dedicating their time to read my thesis and providing useful perspectives and comments to the work presented to them. A special thanks goes to Can Aysal for helping me out along the way with many obstacles I faced. I also want to thank the people from my lab for providing such a great working

The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different types of prior distributions are used to investigate the sensitivity of a prior distribution onto the Bayesian PCC estimation. In this simulation study, it appears that the MAP would be the estimator of choice for the PCC. The performance of the MAP is not only better than the ML but also appears to overcome the limitations of the EAP (i.e., the shrinkage effect).

The theory of dual numerical means of random and experienced variables is briefly described in the framework of the new theory of experience and the chance that arises as an axiomatic synthesis of two dual theories — the Kolmogorov theory of probability and the theory of believability. A new term is introduced for the numerical mean of the experienced variable — mathematical reflection, which is dual to the mathematical expectation of a random variable within the framework of the new theory. The basic properties and examples of dual numerical means are considered.

Using social information processing theory, we examined the congruence between employee and customer assessments of organizations' service quality. The setting was a public health care delivery system. Contrary to expectations, employee assessments of service quality were lower than those of their customers. Also unexpectedly, employees with professional training had less congruent assessments than other employees. As expected, employees with longer

Road accident remedial work can be effected in many cases by implementing low cost engineering measures. These are intended to restore the safety performance of sites to which they are applied to prevailing levels according to their kind, traf®c¯ows and design. This approach is, therefore, appropriate to sites where the mean accident frequency exceeds a standard value for that site. In this paper, we present several analyses that provide quantitative but uncertain indications of which sites should be considered for this kind of treatment according to their accident record. We describe four measures that are informative in this respect Ð the count of accidents, an estimate of the mean accident frequency, the amount by which this estimate exceeds a standard value, and the probability that it does so. We illustrate the use of these analyses by applying them to a dataset of accident records of priority controlled road junctions and compare the results of using the different measures.

We discuss epistemological and methodological aspects of the Bayesian approach in astrophysics and cosmology. The introduction to the Bayesian framework is given for a further discussion concerning the Bayesian inference in physics. The interplay between the modern cosmology, Bayesian statistics, and philosophy of science is presented. We consider paradoxes of confirmation, like Goodman's paradox, appearing in the Bayesian theory of confirmation. As in Goodman's paradox the Bayesian inference is susceptible to some epistemic limitations in the logic of induction. However Goodman's paradox applied to cosmological hypotheses seems to be resolved due to the evolutionary character of cosmology and accumulation new empirical evidences. We argue that the Bayesian framework is useful in the context of falsificability of quantum cosmological models, as well as contemporary dark energy and dark matter problem.

Freestanding and bound morphemes differ in many (psycho)linguistic aspects. Some theorists have claimed that the representation and retrieval of freestanding and bound morphemes in the course of language production are governed by similar processing mechanisms. Alternatively, it has been proposed that both types of morphemes may be selected for production in different ways. In this article, the authors first review the available experimental evidence related to this topic and then present new experimental data pointing to the notion that freestanding and bound morphemes are retrieved following distinct processing principles: freestanding morphemes are subject to competition, bound morphemes not.

Bayesci istatistik, özellikle psikoloji alanında, tekrarlanabilirlik krizi denilen, gerçekleştirilen çoğu araştırmanın sonuçlarının tekrarlanabilir olmaması nedeniyle Frekansçı yaklaşıma alternatif olarak sık kullanılır hale gelmiştir. Bilgi teknolojilerinin gelişmesi ile gerekli hesaplamaların kısa sürede yapılabilir hale gelmesi, Bayesci istatistiğin uygulamalarının yaygınlaşmasını sağlamıştır. Bu çalışma, Akdeniz Üniversitesi Veri Analitiği ve Yönetimi Tezsiz Yüksek Lisans Dönem Projesi çalışmanın bir kısmını oluşturmakta ve Bayesci yöntemleri araştırmacılara ve bu konuya meraklı/ilgili kişilere tanıtmayı amaçlamaktadır.

Data in many practical problems are acquired according to decisions or actions made by users or experts to achieve specific goals. For instance, policies in the mind of biologists during the intervention process in genomics and metagenomics are often reflected in available data in these domains, or data in cyber-physical systems are often acquired according to actions/decisions made by experts/engineers for purposes such as control or stabilization. Quantification of experts' policies through available data, which is also known as reward function learning, has been discussed extensively in literature in the context of inverse reinforcement learning (IRL). However, most of the available techniques come short to deal with practical problems due to the following main reasons: 1) Lack of scalability: arising from incapability or poor performance of existing techniques in dealing with large systems; 2) Lack of reliability: coming from the incapability of the existing techniques to properly learn the optimal reward function during the learning process. Toward this, in this paper, we propose a multi-fidelity Bayesian optimization (MFBO) framework that significantly scales the learning process of a wide range of existing inverse reinforcement learning techniques. The proposed framework enables the incorporation of multiple approximators and efficiently takes their uncertainty and computational costs into account to balance exploration and exploitation during the learning process. The proposed framework's high performance is demonstrated through genomics, metagenomics, and sets of random simulated problems.

This paper explores how the remaining useful life (RUL) can be assessed for complex systems whose internal state variables are either inaccessible to sensors or hard to measure under operational conditions. Consequently, inference and estimation techniques need to be applied on indirect measurements, anticipated operational conditions, and historical data for which a Bayesian statistical approach is suitable. Models of electrochemical processes in the form of equivalent electric circuit parameters were combined with statistical models of state transitions, aging processes, and measurement fidelity in a formal framework. Relevance vector machines (RVMs) and several different particle filters (PFs) are examined for remaining life prediction and for providing uncertainty bounds. Results are shown on battery data. 1

Although the statistical tools most often used by researchers in the field of psychology over the last 25 years are based on frequentist statistics, it is often claimed that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n ϭ 1,579). We aim to provide a thorough presentation of the role Bayesian statistics plays in psychology. This historical assessment allows us to identify trends and see how Bayesian methods have been integrated into psychological research in the context of different statistical frameworks (e.g., hypothesis testing, cognitive models, IRT, SEM, etc.). We also describe take-home messages and provide "big-picture" recommendations to the field as Bayesian statistics becomes more popular. Our review indicated that Bayesian statistics is used in a variety of contexts across subfields of psychology and related disciplines. There are many different reasons why one might choose to use Bayes (e.g., the use of priors, estimating otherwise intractable models, modeling uncertainty, etc.). We found in this review that the use of Bayes has increased and broadened in the sense that this methodology can be used in a flexible manner to tackle many different forms of questions. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends. Translational Abstract Over 250 years ago, Bayes (or Price, or Laplace) introduced a method to take prior knowledge into account in data analysis. Although these ideas and Bayes's theorem have been longstanding within the fields of mathematics and statistics, these tools have not been at the forefront of modern-day applied psychological research. It was frequentist statistics (i.e., p values and null hypothesis testing; developed by Fisher, Neyman, and Pearson long after Bayes's theorem), which has dominated the field of Psychology throughout the 21st century. However, it is often claimed by 'Bayesians' that the alternative Bayesian approach to statistics is gaining in popularity. In the current article, we investigated this claim by performing the very first systematic review of Bayesian psychological articles published between 1990 and 2015 (n ϭ 1,579). Our findings showed that there was some merit in this thought. In fact, the use of Bayesian methods in applied Psychological work has steadily increased since the nineties and is currently taking flight. It was clear in this review that Bayesian statistics is used in a variety of contexts across subfields of Psychology and related disciplines. This is an exciting time, where we can watch the field of applied statistics change more than ever before. The way in which researchers think about and answer substantive inquiries is slowly taking on a new philosophical meaning that now incorporates previous knowledge and opinions into the estimation process. We hope this presentation opens the door for a larger discussion regarding the current state of Bayesian statistics, as well as future trends.

B ayesian methods have become widespread in marketing literature. We review the essence of the Bayesian approach and explain why it is particularly useful for marketing problems. While the appeal of the Bayesian approach has long been noted by researchers, recent developments in computational methods and expanded availability of detailed marketplace data has fueled the growth in application of Bayesian methods in marketing. We emphasize the modularity and flexibility of modern Bayesian approaches. The usefulness of Bayesian methods in situations in which there is limited information about a large number of units or where the information comes from different sources is noted. We include an extensive discussion of open issues and directions for future research.

Bayesian methods have become widespread in the marketing literature. We review the essence of the Bayesian approach and explain why it is particularly useful for marketing problems. While the appeal of the Bayesian approach has long been noted by researchers, recent developments in computational methods and expanded availability of detailed marketplace data has fueled the Bayesian growth in marketing. We emphasize the modularity and flexibility of modern Bayesian approaches. Finally, the usefulness of Bayesian methods in situations in which there is limited information about a large number of units or where the information comes from different sources is noted

Multilevel structural equation modeling (MSEM) is gaining popularity in the social sciences as a framework for estimating latent variable models in the presence of hierarchical data. In addition, we believe that MSEMs are quite helpful to psychological and educational inquiries. Many research papers have been published on technical developments in MSEM; however, we are not aware of any tutorials on how to properly implement these complex models. In addition, applied researchers may be unfamiliar with how to implement a Bayesian estimation approach to MSEM, despite the fact that it has distinct advantages in this modeling context (Depaoli and Clifton, 2015; Hox, van de Schoot, and Matthijsse, 2012). To that end, this paper serves as a nontechnical tutorial on the implementation and application of MSEM using both frequentist and Bayesian estimation methods. We demonstrate the implementation of MSEM with three motivating examples using data from the Program for International Student Assessment (PISA). In addition, we present a small Monte Carlo study to show how the estimation of MSEM is impacted by different types of priors for data structures similar to those presented in the PISA examples. We conclude with recommendations for applied researchers based on findings from the empirical examples and the simulation study. We also outline future methodological considerations in the context of Bayesian MSEM.

Previous research showed that employing results from meta-analyses of relevant previous fMRI studies can improve the performance of voxelwise Bayesian second-level fMRI analysis. In this process, prior distributions for Bayesian analysis can be determined by information acquired from the meta-analyses. However, only image-based meta-analysis, which is not widely accessible to fMRI researchers due to the lack of shared statistical images, was tested in the previous study, so the applicability of the prior determination method proposed by the previous study might be limited. In the present study, whether determining prior distributions based on coordinate-based meta-analysis, which is widely accessible to researchers, can also improve the performance of Bayesian analysis, was examined. Three different types of coordinate-based meta-analyses, BrainMap and Ginger ALE, and NeuroQuery, were tested as information sources for prior determination. Five different datasets addressing three task conditions, i.e., working memory, speech, and face processing, were analyzed via Bayesian analysis with a meta-analysis informed prior distribution, Bayesian analysis with a default Cauchy prior adjusted for multiple comparisons, and frequentist analysis with familywise error correction. The findings from the aforementioned analyses suggest that use of coordinate-based meta-analysis also significantly enhanced performance of Bayesian analysis as did image-based meta-analysis.

Forensic scientists are often expected to present the likelihood of DNA identifications in US courts based on comparative population data, yet forensic anthropologists tend not to quantify the strength of an osteological identification. Because forensic anthropologists are trained first and foremost as physical anthropologists, they emphasize estimation problems at the expense of evidentiary problems, but this approach must be reexamined. In this paper, the statistical bases for presenting osteological and dental evidence are outlined, using a forensic case as a motivating example. A brief overview of Bayesian statistics is provided, and methods to calculate likelihood ratios for five aspects of the biological profile are demonstrated. This paper emphasizes the definition of appropriate reference samples and of the “population at large,” and points out the conceptual differences between them. Several databases are introduced for both reference information and to characterize the “population at large,” and new data are compiled to calculate the frequency of specific characters, such as age or fractures, within the “population at large.” Despite small individual likelihood ratios for age, sex, and stature in the case example, the power of this approach is that, assuming each likelihood ratio is independent, the product rule can be applied. In this particular example, it is over three million times more likely to obtain the observed osteological and dental data if the identification is correct than if the identification is incorrect. This likelihood ratio is a convincing statistic that can support the forensic anthropologist's opinion on personal identity in court. Am J Phys Anthropol, 2006. © 2006 Wiley-Liss, Inc.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

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. (...)

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

Money illusion has been defined as a tendency to think in terms of nominal rather than real monetary values, and understood as a cognitive bias. Overcoming money illusion would lead individuals to the preferable decisions, and consequently, the market would become more efficient. In this paper, we focused on the role of emotions that are evoked by the numerical information and investigated whether money illusion would be alleviated or become more serious depending on individuals' differences in numerical abilities and depending on how information is presented to investors. Our results showed that people in the high numeracy group could correctly answer regardless of how nominal value is expressed when the questions required a rational decision. However, they suffered from strong money illusion when answering questions that induced an emotional reaction, especially in the situations where nominal value was expressed in the balance of assets. High numeracy individuals tend to extract more emotional meaning from numerical information and consequently, they selected the irrational choices even though they know the rational one. It seems that the subjects were not able to control the impulsive emotion that came from their aversion to nominal losses. These uncontrollable emotions lead to the irrational decision-making (named "Id effect ") which may be one of the triggers of money illusion. To overcoming money illusion, it requires the sufficient ability not only to find rational choice but also to maintain rational ideas.

Introduction: Despite the current enthusiasms in applying the concept of microfinance as a poverty alleviation tool in many countries, the risk management aspects of micro-financing should not be overlooked. Ethiopia is also one of the countries where microfinance has been given due consideration as a safety net for the poor to help them overcome the adversities of poverty.
Objectives: The objective of this study is to analysis a credit risk of Microfinance loan repayment on the Microcredit and Savings Institution in Gambella town, Ethiopia.
Methodology: A study was conducted on 457 people who took loans from microfinance institutions in Gambella town, Gambella region, Ethiopia in 60 months starting January 2014 and ending December 2018. The data used in this study was the secondary data from GMCSI. We have applied Cox regression model and weibull parametric regression model after purposeful selection covariates, checking for the linearity of covariates in the model and assessment of model adequacy to diagnosis the model from semi parametric model for analyzing the loan repayment performance data on eighteen explanatory variables that would be included in the study. Loan repayment status is dependent variable, while eighteen borrower’s characteristics, institutional characteristics and firm characteristics are considered as explanatory variables. In this case the value of the dependent variable (loan repayment performance) is 0 and 1, if borrowers defaulted it takes 1 and otherwise 0.
Results: So, the outcome revealed that depicts from the total of 457 borrowers 256 (56.0%) of them are defaulted (unpaid on due) and 201 (44.0%) of them repaid their loan on due. The median of survival time is 41 months, which mean the survival curve reaches the 50% line before the end of the study by probability 0.499 which is approximation to 0.5. In fact, both Cox PH model and Weibull parametric regression model have considered but the latter model was the most appropriate for analyses of a credit risk of microfinance loan repayment in Gambella region. The significant factors identified through the relevant model are; age, residence, occupation, business sectors, repayment period, suitability of installment period and frequency of loan collection are the risk factor that cause the defaulted of loan.
Conclusion: Hence, governmental and non-governmental stakeholders should pay attention to give training on the risk factors identified on the current paper so as to optimize individual’s knowledge and awareness so that unpaid on due minimally reduced.

Key words: Credit risk; Loan repayment; Microcredit; Cox PH model ; parametric regression model.

The reinvention of Markov chain Monte Carlo (MCMC) methods and their implementation within the Bayesian framework in the early 1990s has established the Bayesian approach as one of the standard methods within the applied quantitative sciences. Their extensive use in complex real life problems has lead to the increased demand for a friendly and easily accessible software, which implements Bayesian models by exploiting the possibilities provided by MCMC algorithms. WinBUGS is the software that covers this increased need. It is the Windows version of BUGS (Bayesian inference using Gibbs sampling) package appeared in the mid-1990s. It is a free and a relatively easy tool that estimates the posterior distribution of any parameter of interest in complicated Bayesian models. In this article, we present an overview of the basic features of WinBUGS, including information for the model and prior specification, the code and its compilation, and the analysis and the interpretation of the MCMC output. Some simple examples and the Bayesian implementation of the Lasso are illustrated in detail.

The author presents a method of hierarchical bayesian estimation to estimate the value of the different income variables on the basis of studies of household budgets and POLTAX tax register. Calculations have been made for the case where approximately known a priori evaluation of hyperparameters used to construct a conditional probability, which is used in the model. The author compares the efficiency of the estimates obtained by using other hierarchical methods of estimation for small areas, including the EBLUP estimators type. This gave congruity in precision of the estimated parameters using both techniques.

In this study we consider the Bayesian estimators for the
unknown parameters of Log-logistic distribution. The observed Fisher Information matrix, as well as the asymptotic variance-covariance matrix are derived. Bayes estimators cannot be
obtained in explicit forms. So, Bayes estimators relative to LINEX loss function are obtained using Lindley approximation technique. An extensive Monte Carlo simulation study is carried out to compare the performances of different methods.
A real data set is analyzed for illustrative purposes.
Keywords: Bayesian estimators, Observed Fisher Information matrix, Log-logistic distribution, LINEX loss function, Lindley approximation technique.

Bayesian statistical methods are becoming increasingly popular and often seen in direct opposition with the frequentist Null Hypothesis Significance Testing (NHST). During this talk, I will try to briefly address pros and cons of both approaches and then specifically focus on the circumstances in which Bayesian estimation is more useful. I will show how to use SPSS Amos to run Bayesian analysis, and all the possible applications provided by this software. I will illustrate some practical examples and show how to properly interpret and report the results obtained.

We review the Bayesian approach to the problem of the elimination of nuisance parameters from a statistical model. Many Bayesian statisticians feel that the framework of Bayesian statistics is so clear and simple that the elimination of nuisance parameters should not be considered a problem: one has simply to compute the marginal posterior distribution of the parameter of interest. However we will argue that this exercise need not be so simple from a practical perspective.

During the last years, development of open learning environments that support effectively their users has been a challenge for the research community of educational technologies. The open interactive nature of these environments results in users experiencing difficulties in coping with the plethora of available functions, especially during their initial efforts to use the system. In addition,-from the tutors' perspectivethe problem solving strategies of the students are often particularly difficult to identify. In this paper, we ...

Adult age-at-death is presented in a number of different ways by anthropologists. Ordinal categories predominate in osteoarchaeology, but do not reflect individual variation in ageing, with too many adults being classified as "middle adults". In addition, mean ages (derived from reference samples) are overly-relied upon when developing and testing methods. In both cases, "age mimicry" is not adequately accounted for. To highlight the many inherent biases created when developing, testing and applying age-estimation methods without fully considering the impact of "age mimicry" and individual variation. The paper draws on previously published research (Web of Science, Pub Med, Google Scholar) on age estimation methods and their use in anthropology. There is a lack of consistency in the methods used to estimate age and for the mode of combining them. Ordinal categories are frequently used in osteoarchaeology, whereas forensic anthropologists are more likely...

In 1912, Max Wertheimer published his paper on phi motion, widely recognized as the start of Gestalt psychology. Because of its continued relevance in modern psychology, this centennial anniversary is an excellent opportunity to take stock of what Gestalt psychology has offered and how it has changed since its inception. We first introduce the key findings and ideas in the Berlin school of Gestalt psychology, and then briefly sketch its development, rise, and fall. Next, we discuss its empirical and conceptual problems, and indicate how they are addressed in contemporary research on perceptual grouping and figure-ground organization. In particular, we review the principles of grouping, both classical (e.g., proximity, similarity, common fate, good continuation, closure, symmetry, parallelism) and new (e.g., synchrony, common region, element and uniform connectedness), and their role in contour integration and completion. We then review classic and new image-based principles of figure-ground organization, how it is influenced by past experience and attention, and how it relates to shape and depth perception. After an integrated review of the neural mechanisms involved in contour grouping, border ownership, and figure-ground perception, we conclude by evaluating what modern vision science has offered compared to traditional Gestalt psychology, whether we can speak of a Gestalt revival, and where the remaining limitations and challenges lie. A better integration of this research tradition with the rest of vision science requires further progress regarding the conceptual and theoretical foundations of the Gestalt approach, which is the focus of a second review article.

Numerous collecting expeditions of Theobroma cacao L. germplasm have been undertaken in Latin-America. However, most of this germplasm has not contributed to cacao improvement because its relationship to cultivated selections was poorly understood. Germplasm labeling errors have impeded breeding and confounded the interpretation of diversity analyses. To improve the understanding of the origin, classification, and population differentiation within the species,

My  contention  is  that  using  Bayes  without  any  prior  or  subsequent objective data  is using it in  a pseudo-statistical way. Just consider how  you could use Bayes to evaluate my bare assertion, without any objective evidence, that I’m levitating right now. All miracle claims must begin and end with objective evidence. Without it, there is nothing else to say or to but dismiss  them.  No  math  is  needed.  No  other  issue  demands  to  be  asked  or answered.