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The Black-Litterman model combines investors’ personal views with historical data and gives optimal portfolio weights. In this paper we will introduce the original Black-Litterman model (Section 1), we will modify the model such that it fits in a Bayesian framework by considering the investors’ personal views to be a direct prior on the means of the returns and by including a typical Inverse Wishart prior on the covariance matrix of the returns (Section 2). We will also consider an idea of Leonard & Hsu [1992] for a prior on the logarithm of the covariance matrix (Section 3). Sensitivity analysis for the level of confidence that investors have in their own personal views was performed and performance of the models was assessed on a test data set consisting of returns over the month of January 2018.

Bayesian analysis for a covariance structure has been in use for decades. The commonly adopted Bayesian setup involves the conjugate inverse Wishart prior specification for the covariance matrix. Here we depart from this approach and adopt a novel prior specification by considering a multivariate normal prior for the elements of the matrix logarithm of the covariance structure. This specification allows for a richer class of prior distributions for the covariance structure with respect to strength of beliefs in prior location hyperparameters and the added ability to model potential correlation amongst the covariance structure. We provide three computational methods for calculating the posterior moment of the covariance matrix. The moments of interest are calculated based upon computational results via Importance sampling, Laplacian approximation and Markov Chain Monte Carlo/Metropolis–Hastings techniques. As a particular application of the proposed technique we investigate educational test score data from the project talent data set.

Two interesting morphology transformations of Au crystals are observed through reacting a mixture of N-alkylimidazole (denoted as C(n)-im, where C(n) = C(n)H(2n+1), and n = 18 and 1), AgNO(3), and HAuCl(4) at 200 degrees C. The long chain C(18)-im with increasing AgNO(3) concentration leads to a progressive truncation of octahedrons at {100} vertices to produce cubes. On the other hand, increasing the concentrations of C(1)-im and AgNO(3), results in a progressive truncation of octahedrons at {110} edges to give rhombic dodecahedrons, which further transform to the unprecedented tetrahexahedrons. The phenomenon could be understood by considering that while both C(18)-im and C(1)-im function as a capping agent with preferential adsorption on Au {111} facets, Ag(+) adsorbs and is subsequently reduced to Ag on Au {110} facets for the sterically demanding C(18)-im, but on the Au {100} facets for C(1)-im. The competition between the growth of the facets protected by imidazole and Ag controls the morphology transformation via truncation of octahedrons at vertices or edges.

Examples of polynuclear metallomesogens are few. Herein,1,2,4-triazole ligands were used to prepare mono- and polynuclear silver(I) triazole metallomesogens. Besides showing an SmA phase in the mesophase, two interesting properties were observed. First, higher ion conductivity is always found for the polynuclear complexes than for the mononuclear complexes with the same anion, an observation contrary to the knowledge that migration of a monomeric cation should be faster than that of a polymeric cation. Second, thermolysis of the polynuclear silver(I) triazole complexes in the assembled mesophase yielded Ag nanowires, in an excellent demonstration of the assembled nature of the polynuclear silver(I) ions in the thermolysis process.

Summary This paper deals with the Bayesian analysis of the additive mixed model experiments. Consider b randomly chosen subjects who respond once to each of t treatments. The subjects are treated as random effects and the treatment effects are fixed. Suppose that some prior information is available, thus motivating a Bayesian analysis. The Bayesian computation, however, can be difficult in this situation, especially when a large number of treatments is involved. Three computational methods are suggested to perform the analysis. The exact posterior density of any parameter of interest can be simulated based on random realizations taken from a restricted multivariate t distribution. The density can also be simulated using Markov chain Monte Carlo methods. The simulated density is accurate when a large number of random realizations is taken. However, it may take substantial amount of computer time when many treatments are involved. An alternative Laplacian approximation is discussed. The Laplacian method produces smooth and very accurate approximates to posterior densities, and takes only seconds of computer time. An example of a pipeline cracks experiment is used to illustrate the Bayesian approaches and the computational methods.

We investigated n-GaN etched by an inductively coupled plasma (ICP) etcher using Cl 2 /Ar and Cl 2 /He as the etching gases. A detailed study on the samples etched in different ICP power, RF power, process pressure and Cl 2 /Ar(He) mixing ratio was performed. It was found that n-GaN could be successfully etched by both Cl 2 /Ar and Cl 2 /He. The maximum etching rate could reach 8000 A min −1 for n-GaN etched in Cl 2 /Ar and 8400 A min −1 for n-GaN etched in Cl 2 /He. Furthermore, it was found that the specific contact resistance is 4.2×10 −4 and 1.37×10 −6 Ω-cm 2 for n-GaN etched by Cl 2 /Ar and Cl 2 /He, respectively. The smaller contact resistance is probably due to the lighter He which induce smaller plasma damages during ICP etching.

Consider the logistic linear model, with some explanatory variables overlooked. Those explanatory variables may be quantitative or qualitative. In either case, the resulting true response variable is not a binomial or a beta-binomial but a sum of binomials. Hence, standard computer packages for logistic regression can be inappropriate even if an overdispersion factor is incorporated. Therefore, a discrete exponential family assumption is considered to broaden the class of sampling models. Likelihood and Bayesian analyses are discussed. Bayesian computation techniques such as Laplacian approximations and Markov chain simulations are used to compute posterior densities and moments. Approximate conditional distributions are derived and are shown to be accurate. The Markov chain simulations are performed effectively to calculate posterior moments by using the approximate conditional distributions. The methodology is applied to Keeler's hardness of winter wheat data for checking binomial assumptions and to Mat...

Two applications are described of a probability model that can express uncertainty regarding a pre-specified monotonicity hypothesis for binomial proportions. The model also yields a random effects overdispersion formulation where the population proportions definitely satisfy a monotonicity specification. One application concerns an insurance data set recording mortalities of clients from ages 35 to 64. Two new actuarial graduation procedures are developed. The other application derives from a Veterans' administration hospital quality monitor and concerns the failure to return rates for psychiatric patients attending substance abuse clinics. While smoothed performance indicators are proposed, measures of their extra-binomial variation highlight problems experienced by evidence-based approaches when the data are uncontrolled.

This article presents a simple measuring apparatus that is capable of measuring column density and absolute photoabsorption cross sections. The apparatus includes a simple high-temperature heatpipe furnace, an MKS Instruments Baratron, a hydrogen discharge lamp, and an optical detecting system. The heatpipe furnace provides an absorbing medium with a steady total pressure in a closed system so that the column density can be obtained using the ideal gas relation. The apparatus is designed for a working temperature range below 1000 K and a pressure range up to 10 Torr. Encountered experimental difficulties and their found solutions will be discussed in detail. In this work, the absolute photoabsorption cross section of Mg is measured near the 3s threshold using this apparatus. The absolute photoabsorption cross section result at the 3s threshold, which is 2.1±0.3 Mb, is in good agreement with hook method data (2.36 Mb).

We explore Bayesian inference of a multivariate linear regression model with use of a flexible prior for the covariance structure. The commonly adopted Bayesian setup involves the conjugate prior, multivariate normal distribution for the regression coefficients and inverse Wishart specification for the covariance matrix. Here we depart from this approach and propose a novel Bayesian estimator for the covariance. A multivariate normal prior for the unique elements of the matrix logarithm of the covariance matrix is considered. Such structure allows for a richer class of prior distributions for the covariance, with respect to strength of beliefs in prior location hyperparameters, as well as the added ability, to model potential correlation amongst the covariance structure. The posterior moments of all relevant parameters of interest are calculated based upon numerical results via a Markov chain Monte Carlo procedure. The Metropolis-Hastings-within-Gibbs algorithm is invoked to account for the construction of a proposal density that closely matches the shape of the target posterior distribution. As an application of the proposed technique, we investigate a multiple regression based upon the 1980 High School and Beyond Survey.

SUMMARY A simple procedure is proposed for exact computation to smooth Bayesian estimates for logistic regression functions, when these are not constrained to lie on a fitted regression surface. Exact finite sample inferences and predictions are available, together with an exact residual analysis. The prior distribution relates to O'Hagan's assumptions for a normal regression function. A global shrinkage parameter and local smoothness parameter can be evaluated from the current data by hierarchical Bayesian procedures. Consideration of the shrinkage parameter permits an overall check regarding a hypothesised regression model. No optimisation technique is needed, since Monte Carlo simulations from independent logistic distributions can be directly employed. The complexity of the computations does not substantively increase with the dimensionality of the design space.

Linear mixed effects models arise quite naturally in a number of settings. Two of the more prominent uses are in experimental designs and multilevel models. Furthermore, Bayesian analysis has also been utilized with respect to such models. Here we will consider such an approach with emphasis placed on estimation of the covariance matrix for the random effects. With respect to the covariance structure, however, we depart from the traditional Bayesian prior usage of the Inverse Wishart distribution. The rationale for such a departure is that this distribution is somewhat constraining. Instead, we employ a multivariate Normal approximation procedure for the likelihood of the matrix logarithm of the random effects covariance matrix. Such an approximation allows us to use a multivariate Normal prior for the logarithm of the random effects covariance matrix and still maintain the tractability of conjugacy, at least in an approximate sense. All posterior moments are calculated via Markov Chain Monte Carlo (MCMC) techniques. The Metropolis--Hastings accept reject algorithm is utilized to appropriately account for the approximation procedures. As a particular application we consider a multilevel model where student grade point average relate to a number of standardized test scores.

An exact Bayesian analysis can be performed for normal theory variance components models, using importance sampling. But remarkably accurate approximations are available using the Laplacian T-approximation introduced by Leonard, Hsu, and Ritter. Instead of maximizing the joint posterior density, conditional upon the parameter of interest, a device described by O'Hagan is used first. The Bayesian estimators are compared to the Lindley—Stein shrinkage estimators and the Lindley—Smith joint modal estimators. It is confirmed that joint modes can overcollapse toward prior hypotheses, when compared with more sensible Bayesian procedures. This is referred to as a “collapsing phenomenon.” A numerical example from the one-way random-effects model is considered, and the risks of the different estimators are simulated under a variety of loss functions. It is concluded that although the Lindley—Stein estimator performs well, a full hierarchical Bayesian analysis performs at least equally well, while permitti...

Empirical evidence abounds that asset returns exhibit characteristics such as volatility clustering, asymmetry, and heavy-tailedness. Volatility clustering describes the tendency of returns to alternate between periods of high volatility and low volatility. In addition, volatility responds asymmetrically to positive and negative return shocks—it tends to be higher when the market falls than when it rises. The nonconstancy of volatility has been suggested as an underlying reason for returns’ fat tails. Volatility models attempt to systematically explain these stylized facts about asset returns. The Bayesian methodology offers distinct advantages over the classical framework in estimating volatility models. Parameter restrictions, such as stationarity restriction, are notoriously difficult to handle within the frequentist setting and straightforward to implement in the Bayesian one. The MCMC numerical simulation methods facilitate greatly the estimation of complex volatility models, such as Markov-switching volatility models. Keywords: generalized autoregressive conditional heteroskedastic; volatility; Bayesian; Markov-switching

Linear regression is the “workhorse” of financial modeling. Cornerstone applications, such as asset pricing models, as well as time series models, are built around linear regression's methods and tools. Casting the linear regression methodology in a Bayesian setting helps account for estimation uncertainty, allows for integration of prior information, and makes accessible the Bayesian numerical simulation framework. Keywords: Bayesian linear regression; diffuse; prior; informative; prior; Gibbs sampler

One of the basic mechanisms of learning is assimilating the information arriving from the external environment and then updating the existing knowledge base with that information. This mechanism lies at the heart of the Bayesian framework. A Bayesian decision maker learns by revising beliefs in light of the new data that become available. From the Bayesian point of view, probabilities are interpreted as degrees of belief. Therefore, the Bayesian learning process consists of revising probabilities. Contrast this with the way probability is interpreted in the classical (frequentist) statistical theory—as the relative frequency of occurrence of an event in the limit, as the number of observations goes to infinity. Bayes’ theorem provides the formal means of putting that mechanism into action; it is a simple expression combining the knowledge about the distribution of the model parameters and the information about the parameters contained in the data. Keywords: frequentist; Les Prix Nobel; prior probability; posterior probability; frequentist; Bayesian framework; likelihood function; method of maximum likelihood; Bayes' theorem; prior probability; posterior probability; continuous version of Bayes' theorem; posterior mean

Equally weighted mixture models are recommended for situations where it is required to draw precise finite sample inferences requiring population parameters, but where the population distribution is not constrained to belong to a simple parametric family. They lead to an alternative procedure to the Laird-DerSimonian maximum likelihood algorithm for unequally weighted mixture models. Their primary purpose lies in the facilitation of exact Bayesian computations via importance sampling. Under very general sampling and prior specifications, exact Bayesian computations can be based upon an application of importance sampling, referred to as Permutable Bayesian Marginalization (PBM). An importance function based upon a truncated multivariatet-distribution is proposed, which refers to a generalization of the maximum likelihood procedure. The estimation of discrete distributions, by binomial mixtures, and inference for survivor distributions, via mixtures of exponential or Weibull distributions, are considered. Equally weighted mixture models are also shown to lead to an alternative Gibbs sampling methodology to the Lavine-West approach.

The optical and electrical properties of Ni(5 nm)-Au(5 nm) and Ni(3.5 nm)-indium tin oxide (ITO) (60 nm) films were studied. It was found that the normalized transmittance of Ni/ITO film could reach 87% at 470 nm, which was much larger than that of the Ni-Au film. It was also found that the specific contact resistance was 5 /spl times/ 10/sup -4/ /spl Omega/ /spl middot/ cm/sup 2/ and 1 /spl times/ 10/sup -3/ /spl Omega/ /spl middot/ cm/sup 2/, respectively, for Ni-Au and Ni/ITO on p-GaN. Furthermore, it was found that the 20 mA output power of light-emitting diode (LED) with Ni-Au p-contact layer was 5.26 mW. In contrast, the output power could reach 6.59 mW for the LED with Ni/ITO p-contact layer.

There are several tasks in the investment management process. These include setting the investment objectives, establishing an investment policy, selecting a portfolio strategy, asset allocation, and measuring and evaluating performance. Bayesian methods have been either used or proposed as a tool for improving the implementation of several of these tasks. There are principal reasons for using Bayesian methods in the investment management process. First, they allow the investor to account for the uncertainty about the parameters of the return-generating process and the distributions of returns for asset classes and to incorporate prior beliefs in the decision- making process. Second, they address a deficiency of the standard statistical measures in conveying the economic significance of the information contained in the observed sample of data. Finally, they provide an analytically and computationally manageable framework in models where a large number of variables and parameters makes classical formulations a formidable challenge.

Three series of Au(I)-imidazole complexes with stoichiometries of [Au(Cn-bim)Cl], [Au(Cn-im)Cl], and [Au(Cn-im)2][NO3] x 2H2O (Cn-bim = N-CnH2n+1 -substituted benzimidazole and Cn-im = N-CnH2n+1-substituted imidazole) together with the compound of [Au(C18-bim)2][NO3] are synthesiszed. Typical structures of each series are determined by single crystal X-ray diffraction. The last series of compounds, are liquid crystals, and exhibit a wider mesophase range than their Ag(I) analogues. These Au(I) complexes form Au nanostructures both through chemical reduction or thermolysis. For the first time, N-long chain imidazole is utilized to stabilize colloidal Au in solution. Also for the first time, unique examples of simple thermolysis to produce large Au plates of nanothickness are demonstrated. Formation of a plate-like morphology through fusion of sphere-like nanoparticles at an early stage is evidenced by TEM images.

We set up a high-Tc SQUID system for magnetocardiography (MCG) in a moderately magnetically shielded room. The electronically balanced gradiometer consists of superconducting quantum interference device (SQUID) magnetometer. One reference SQUID was mounted above the sensing SQUID while the sensing SQUID is seated at the bottom of the cryostat. The baseline of the gradiometer is varied from 5 cm to 7 cm. The output of the MCG signal was filtered with the band pass filter (0.5 - 40 Hz) and the power-line filter. The MCG system was used to detect the magnetic signal of the human heart. Equivalent current sources were used to study the inverse problem.

A high-Tc 1st-order electronic superconducting quantum interference device (SQUID) gradiometer system is constructed to study the magnetocardiogram (MCG) of rabbits in a moderately magnetically shielded environment with active compensation. In the noisy hospital environment, the noise cannot be completely reduced with the 1st-order gradiometer, therefore, a reference SQUID with active compensation was used to further reduce the noise level leaking into the room. The MCG system was equipped with a x-y translation bed. We used a low-pass filter with the cut off frequency at 44 Hz, a high-pass filter with the cut off frequency at 0.1 Hz and the 60 Hz notch filter to reduce the power line interference. The noise level of the 1st order gradiometer MCG system in this moderately magnetically shielded room was about 1 pT/square root of Hz1/2 at 1 Hz. The MCG of a normal rabbits was measured with this system and a MCG contour map and a current density distribution was constructed.

A concept hierarchy is a kind of concise and general form of knowledge representations. Concept description is vague for human knowledge generally. Crisp description for a concept usually cannot represent human knowledge completely and practically. In this paper, we would study fuzzy characteristics of concept description and propose an agglomerative clustering scheme based on fuzzy theory to generate hierarchical fuzzy concepts from a large database automatically. The proposed method first transforms quantitative data into linguistic terms using fuzzy membership functions. The fuzzy entropy is then designed for evaluating the significant order of attributes and a clustering algorithm is developed to find meaningful fuzzy concept hierarchies effectively.

In recent years, machine learning and knowledge discovery techniques have attracted a great deal of attention in the information area. Classification is one of the important research topics on these research areas. Most of the researches on classification concern that a complete data set is given as a training set and the test data know all values of attributes clearly. Unfortunately, incomplete data are commonly seen in real-world applications. In this paper, we propose a new strategy to deal with the incomplete quantitative data and introduce a supervised learning method based on genetic programming to handle the classification problem with incomplete data in the attributes. Two experiments are designed to evaluate the effectiveness of the proposed approaches.

Carbonic anhydrase II (CAII) deficiency in humans is associated with a syndrome of renal tubular acidosis, osteopetrosis, and cerebral calcification. A strain of mice of CAII deficiency due to a point mutation also manifests renal tubular acidosis. We report here that retrograde injection of cationic liposome complexed with a CAII chimeric gene, using a cytomegalovirus (CMV) promoter/enhancer as an expression cassette to drive human CAII cDNA, into the renal pelvis of CAII-deficient mice results in expression of CAII in the kidney. The levels of both the CAII gene and its corresponding mRNA were highest by day 3 after treatment, diminishing thereafter, but remaining detectable by 1 mo. After gene therapy, CAII-deficient mice restored the ability to acidify urine after oral administration of ammonium chloride. The ability to acidify urine was maintained at 3 wk after gene therapy, and was eventually lost by 6 wk. Immunohistochemistry studies using anti-CAII antibodies showed that CAII was expressed in tubular cells of the outer medulla and corticomedullary junction. The gene therapy was not associated with nephrotoxicity as assessed by blood urea nitrogen levels and renal histology. To our knowledge, this is the first successful gene therapy of a genetic renal disease. Our results demonstrate the potential of gene therapy as a novel treatment for hereditary renal tubular defects.

It is important in many econometric and biological applications to evaluate the effective dose (ED) points in the tails of quantal response curves and the curves according to a sensible criterion. Following Geisser (1971), it seems most sensible to evaluate the posterior mean value function of the response curve, since this also gives predictive probabilities of positive responses across the design region. While plausible, it can be insufficient for small samples to base the calculations upon standard multivariate normal likelihood approximations. Exact determinations, for example, via importance sampling (see Zellner and Rossi, 1984) are needed. Extending Leonard (1982a) it is now also possible to compute the exact posterior distribution of the ED points. These are proposed as “design measures”, since they can be used to sequentially generate further design points. Related procedures (see Leonard, 1982b) yield excellent frequency properties. For example, a total of 40 observations (10 fixed in advance and 30 chosen sequentially) can assess a response curve to 6% accuracy for all design points between the ED60 and ED90 points, with an average of over 90% of the sequentially generated design points falling between the ED60 and ED90 points.

Amphiphilic ionic liquids and ionic liquid crystals, comprising a cationic imidazolium head group (represents as Im), a hydrophobic N-alkyl chain (CnH2n+1, denoted as Cn, n = 10, 12, 14, 16 and 18), and an amphiphilic N-2-(2-(2-ethoxy)ethoxy)ethanol (3OEG) functional group were synthesized (denoted as [Cn-Im-3OEG][Cl]). While the lipophilicity of [Cn-Im-3OEG][Cl] increases along with the alkyl carbon chain length, the water solubility of these compounds is enhanced with the 3OEG functionality. Compounds with lengths of n = 10, 12 and 14 are room temperature ionic liquids, whereas n = 16 and 18 show thermotropic SmA liquid crystal properties. Meanwhile, compounds of n = 14, 16 and 18 also exhibit lyotropic liquid crystal properties. The ionic and lyotropic liquid crystalline natures of these compounds lead to their superior antimicrobial activity against infectious pathogens. This is especially true for compounds with longer alkyl chains. Rupture of the bioenvelop appears to be operative in the process of antimicrobial activity.

A flexible class of prior distributions is proposed, for the covariance matrix of a multivariate normal distribution, yielding much more general hierarchical and empirical Bayes smoothing and inference, when compared with a conjugate analysis involving an inverted Wishart distribution. A likelihood approximation is obtained for the matrix logarithm of the covariance matrix, via Bellman's iterative solution to a Volterra integral equation. Exact and approximate Bayesian, empirical and hierarchical Bayesian estimation and finite sample inference techniques are developed. Some risk and asymptotic frequency properties are investigated. A subset of the Project Talent American High School data is analyzed. Applications and extensions to multivariate analysis, including a generalized linear model for covariance matrices, are indicated.

The injury-related mortality rate for Native American children between the ages of 1 and 4 years is nearly three times that of the same age group in the general population. To assess injury prevention awareness in urban Native American families, we administered 39 age-appropriate questions from the Framingham Safety Survey to 50 Native American families and 100 other families and developed an answer scoring system to analyze and compare survey responses. Survey responses revealed that Native American families are less likely to keep small objects, household products, and medicines out of the reach of their children and to possess and understand the use of ipecac. Although urban Native-American families appear to be less aware of ingestion prevention practices than other urban families, these and other deficiencies in injury prevention awareness are more likely the result of factors related to their low-income status than to culturally based practices.

1. Introductory statistical concepts 2. The discrete version of Bayes' theorem 3. Models with a single unknown parameter 4. The expected utility hypothesis and its alternatives 5. Models with several unknown parameters 6. Prior structures, posterior smoothing, and Bayes-Stein estimation Guide to worked examples Guide to self-study exercises.

A method is proposed for approximating the marginal posterior density of a continuous function of several unknown parameters, thus permitting inferences about any parameter of interest for nonlinear models when the sample size is finite. Possibly tedious numerical integrations are replaced by conditional maximizations, which are shown to be quite accurate in a number of special cases. There are similarities with the profile likelihood ideas originated by Kalbfleisch and Sprott (1970), and the method is contrasted with a Laplacian approximation recommended by Kass, Tierney, and Kadane (1988, in press), referred to here as the “KTK procedure.” The methods are used to approximate the marginal posterior densities of the log-linear interaction effects and an overall measure of association in a two-way contingency table. Snee's (1974) hair/eye color data are reanalyzed, and adjustments are proposed to Goodman's (1964) analysis for the full-rank interaction model. Another application concerns marginaliz...

There are around 40,000 births in Taipei City each year. Of them about 40% are of the 1st parity. Of all deliveries, about 80% are born to mothers under 30 years old. There are about 20,000 marriages each year. Of all brides and grooms surveyed in the present study, 39.4% and 39.1% consider the ideal time to conceive being either as early as possible or within 1 year after the wedding. In actuality, 28.08% of the respondents were already pregnant before the wedding. Excluding the inteviewees who were married for over 1 year, 34.1% are currently pregnant, 6.98% have already given birth, and 0.15% have become pregnant again after a birth. This result is similar to the findings of the KAP conducted by the Center in 1980, which showed that 41.3% of the interviewees gave birth to their 1st child within 1 year after the wedding. The same survey of 1980 also finds that the interval between the 1st and the 2nd child is 1.94 years, though women in general consider the ideal interval to be 2.6 years. How to encourage those who are to be married and the newlyweds to prolong the intervals between the wedding and the 1st child and between the 1st and the 2nd child is an important task of the health educators. The present study interviews 1013 couples who registered their marriages in October 1983. Needs, targets, and contents of education programs are identified. Better ways to communicate with the newlyweds are also indicated. The purpose of the study, based on the findings, is to propose a model most suitable for the education in family planning of those who are to be married and who are just married, in order to provide them with better services and to further reduce the fertility of young people.