Use Of Bayesian Analysis Research Articles

Bayesian analysis of inductively coupled plasma mass spectra in the range 46–88 Daltons derived from biological materials

This paper describes the use of Bayesian analysis for the deconvolution of ICP-MS spectra, covering the mass range from 46–88 Daltons, derived from multi-element standards and biological reference materials: TORT 1—Lobster Hepatopancreas, NIST 1547—Peach Leaves and NIST 1577b—Bovine Liver. This approach provides information on both the nature of the species that comprise the observed spectrum and the magnitude of their individual contributions. Various tests are applied to determine the goodness of fit between the actual and predicted spectrum, including the statistical evidence, the deviation at each mass and the predicted value for the isotopic abundances, the latter proving to be particularly difficult to rationalise for all elements in the data set. Bayesian deconvolution is not a calibration technique, but the data derived from it are used to produce calibrations and subsequently to carry out quantitative analyses of the reference materials. The algorithm uses the known isotopic distribution patterns in synthesising spectra, but these are corrupted by mass bias introduced by the instrument. Estimates of isotopic mass bias are used to model the instrument response function in order to remove this distortion from the data before it is subjected to processing. The effects of applying such corrections to the data are demonstrated.

Use of Bayesian analysis of growth functions to estimate crossbreeding parameters in Iberian pigs

Bayesian techniques allow to analyze performance data from growth functions taking into account all the information recorded from each animal, its relatives and the individuals whose data are located in the same systematic effects. This procedure was used to estimate crossbreeding parameters for growth performance up to 95 kg using two data sets from a complete diallel cross among four strains of Iberian pigs: (i) 14 037 weight records from 1274 pigs with restricted feeding; and (ii) 3280 records from 450 pigs hand-fed to appetite. The intercept ( a) and the slope ( b) of the linear growth function were analyzed with a bivariate animal model including as covariables the crossbreeding parameters. The means of posterior distributions of heritabilities and genetic correlation were: h 2 a =0.48 and 0.58, h 2 b =0.32 and 0.55, r G =0.81 and 0.99, for the two data sets, respectively. Expressed as percentage of parental strains, the values of the mean heterosis were 14.1 and 12.1 for the intercept and 14.6 and 10.9 for the slope.

Bayesian analysis of biexponential time-decaying signals

In this paper we demonstrate the use of Bayesian analysis methods for the extraction of information from time-domain biexponentially decaying functions. In several forms of time-domain spectroscopy the physically interesting spectrum consists of multiple exponentially decaying functions. Here we demonstrate the use of Bayesian analysis to extract information on both exponentially decaying signals from a biexponentially decaying signal in the presence of noise. Other spectral factors will be considered.

Monte Carlo evaluation of multivariate normal probabilities

This paper extends research on the simulation of multivariate normal probabilities of high-order dimension by developing a new family of simulators. Such simulators are useful for models with limited dependent variables, including multinomial probit, in panel studies, spatial analysis, and time series analysis. The simulators are derived from a Cholesky decomposition of the covariance matrix, combined with a suitable choice of an importance sampling distribution. The paper studies, among others, the impact of antithetical sampling. The insights gained in this paper are of use in Bayesian analysis as well, in the evaluation of posterior densities.

Bayesian analysis of time-domain Voigt functions

We demonstrate the use of Bayesian analysis methods for the extraction of information from time-domain Voigt functions. In several forms of time-domain spectroscopy the physically interesting spectrum consists of a single exponentially decaying function. Often, however, this spectrum is contaminated by the presence of a non-exponentially decaying “instrumental” contribution. Here we demonstrate the use of Bayesian analysis to extract the exponential term from a Voigt function in which the instrumental contribution has been modeled by a Gaussian decay. The extension to other instrumental contributions is straightforward.

Use of Bayesian Analysis in Medical Domain

Use of Bayesian Analysis in Medical Domain

The Use of Bayesian Analysis of PCR-derived Genomic DNA Sequences to Enable a Biologically Relevant Interpretation of Immunoglobulin Variable Region Gene Expression

We analyzed by means of polymerase chain reactions (PCRs) and DNA sequencing techniques the immunoglobulin heavy chain variable region genes of bone marrow B lineage cells. We first formulated an explanatory model to guide understanding of the biological mechanisms determining both the size of the total available pool of relevant genes and clonal expansion following heavy chain gene rearrangement. We then followed Box's paradigm of criticism and estimation to interpret our experimental findings.

Practical Reporting of Bayesian Analyses of Clinical Trials

Agreement on appropriate ways of presenting Bayesian analyses of clinical trials is essential if these methods are to obtain more widespread use and not fall into disrepute. Using an example based upon a trial currently in progress, two aspects of reporting are proposed. Using noninformative priors gives standardized likelihoods from which point and interval estimates, and probabilities associated with adverse effects, can be obtained with numerically similar values to classical estimates, confidence intervals, and p-values. Standardized likelihoods are therefore a useful means of introducing Bayesian analyses into trial reports and emphasizing the change in interpretation to quantifying beliefs. The second important use of Bayesian analyses is to illustrate strength of evidence coming from a trial by showing the sensitivity of the conclusions drawn to choice of prior distribution made. This can be achieved by employing other well–defined priors, notably that based on previous trial results and that refle...

Using empirical bayes methods in biopharmaceutical research

A compound sampling model, where a unit-specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter, underlies a wide variety of biopharmaceutical data. For example, in a multi-centre clinical trial the true treatment effect varies from centre to centre. Observed treatment effects deviate from these true effects through sampling variation. Knowledge of the prior distribution allows use of Bayesian analysis to compute the posterior distribution of clinic-specific treatment effects (frequently summarized by the posterior mean and variance). More commonly, with the prior not completely specified, observed data can be used to estimate the prior and use it to produce the posterior distribution: an empirical Bayes (or variance component) analysis. In the empirical Bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects. In both the Bayes and empirical Bayes approaches, estimated clinic effects are shrunken towards a common value from estimates based on single clinics. This shrinkage produces more efficient estimates. In addition, the compound model helps structure approaches to ranking and selection, provides adjustments for multiplicity, allows estimation of the histogram of clinic-specific effects, and structures incorporation of external information. This paper outlines the empirical Bayes approach. Coverage will include development and comparison of approaches based on parametric priors (for example, a Gaussian prior with unknown mean and variance) and non-parametric priors, discussion of the importance of accounting for uncertainty in the estimated prior, comparison of the output and interpretation of fixed and random effects approaches to estimating population values, estimating histograms, and identification of key considerations in the use and interpretation of empirical Bayes methods.

Validation of the use of Bayesian analysis in the optimization of gentamicin therapy from the commencement of dosing.

A computer program based on the statistical technique of Bayesian analysis has been adapted to run on several microcomputers. The clinical application of this method for gentamicin has been validated in 13 patients with varying degrees of renal function by a comparison of the accuracy of this method to a predictive algorithm method and one using standard pharmacokinetic principles. Blood samples for serum gentamicin analysis were taken after the administration of an intravenous loading dose of gentamicin. The results produced by each method were used to predict the peak and trough values measured on day 3 of therapy. Of the three methods studied, Bayesian analysis, using a serum gentamicin concentration drawn four hours after the initial dose, was the least biased and the most precise method for predicting the observed levels. The mean prediction error of the Bayesian analysis method, using the four-hour sample, was -0.03 mg/L for the peak serum concentration and -0.07 mg/L for the trough level on day 3. Using this method the corresponding root mean squared prediction error was 0.60 mg/L and 0.36 mg/L for the peak and trough levels, respectively.

A test of the accuracy of probability assessment techniques in auditing*

Abstract. Sixty‐two practising auditors participated in an account balance estimation experiment. Having been provided with written and oral training material, they used four elicitation techniques (CDF, PDF, EPS, and HFS) to quantify their subjective beliefs regarding the accounts receivable balance of an audit case study. Their responses were compared to the results of a 600 sample simulation study, using the quadratic scoring rule. Their responses were also compared to the consensus distribution of all subjects using the Kolmogorov‐Smirnov measure. The results indicated that PDF is the elicitation technique generating the most accurate prior probability distribution for use in Bayesian analysis. The other three elicitation techniques were about equal in the degree to which they were less accurate than the PDF technique.

Power Plant Availability Prediction Using Standard Bayesian Analysis of NERC/GADS Component Cause Code Failure Data

Prediction of power plant outage hours by cause can be very, effective in implementing a cost effective availability improvement program. If the predictions identify those causes for lost generation due to either full, pr partial outages most likely to happen in the next 3 years or less, attention can be focused on making improvements only in these areas and not for other causes that are not expected to be troublesome until later on in the life of the unit. With this approach, cognizance is given to the time value of money and overall less cost results because expenditures are deferred as long as possible. The necessity to differentiate between near-term causes of lost generation and long-term average expected performance, coupled with an incomplete data set, argues for the use of Bayesian analysis. A method of applying standard Bayesian analysis is demonstrated which uses as input only readily available data and produces as output, pre-dictions of forced outage hours (full or partial) for a unit during its next year of operation. The down hours are by cause and uncertainty of the predictions are indicated by plotting the results as probability densities (PD). How these PD can be used in an economic analysis to identify candidate availability improvement projects is demonstrated. Finally, a 7-year comparison between actual and predicted unit outage hours for sixth thermal units is presented as a measure of the goodness of the predictions and to serve as a base to measure future improvements to the prediction technique.

Use of bayesian analysis to design of clinical trials with one treatment

Assuming a Weibull distribution, the posterior distribution for the median survival time is derived in the presence of arbitrary right censorship. In the design of clinical triaLs, suppose k follow-up periods have been completed and it is desired to plan the follow-up period k+1. In this context, criteria are presented that can be employed in determining the number of new patients to be enrolled in the follow-up period k+1.

Planning and efficiency of diagnostic tests.

SUMMARYThe basic principles and techniques of medical decision making are outlined and illustrated. The techniques include ROC curve production, the use of the 2*2 Table, with its derivations, the use of Bayesian analysis to produce Predictive Values, and an introduction to Decision Trees and the use of Utilities. The necessity for a basic knowledge is stressed, particularly in light of current pressures on public and peer accountability.

Use of Bayesian Analysis of Semi-Markov Process Models to Study Consumer Buying Behavior

SYNOPTIC ABSTRACTAnalytical techniques are developed for a combined treatment of the interpurchase-times and brand-choices of frequently purchased consumer goods, in the framework of a semi-Markov process. The inverse Gaussian distribution is used as a model for the interpurchase times. To account for heterogeneity of the consumer population, a natural conjugate prior for the model parameters is developed and the compounding distribution is fitted to panel data of toothpaste purchases. Some important summary measures are derived, including: the market share of a brand as a function of time; the long-run behavior of the interval transition probabilities and the market share; and, the distribution of the number of purchases in a given time span.

Bayesian Analysis - A Method for Updating Risk Estimates

In the first stages of formulating decision strategies, risk estimates may have to be based on sketchy information and limited experience. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. Introduction In recent years there has been a great deal of emphasis on the use of expected-value concepts in the analysis of decisions under uncertainty. Expected values are risk-adjusted criteria that can be used by the decision maker to compare and select capital investment projects. A significant aspect of expected value criteria is that they provide a means to express the degree of risk and uncertainty in quantitative terms. These quantitative risk statements (or estimates) are the probabilities of occurrence of the various possible outcomes of a decision choice. As one might suspect, the probability numbers, or risk estimates, are critical factors in the expected value analysis of decisions involving risk and uncertainty. Frequently we must analyze decision choices in situations where there is very little information or experience upon which to base the risk estimates. Although these probabilities may be only approximate, they presumably represent the best estimates of risk at the time of presumably represent the best estimates of risk at the time of decision making and must be used to formulate initial decision strategies. It is often important to be able to revise, or improve, the original risk estimates as new information becomes available. This is where Bayesian analysis comes in. The purpose of this paper is to explain the logic and philosophy of Bayesian analysis - a formalized, statistical method philosophy of Bayesian analysis - a formalized, statistical method of updating risk analysis. First we shall consider Bayes' theorem and the mechanics of Bayesian computations. Then we shall discuss how Bayesian analysis is used in situations involving a series of new information - that is, in sequential sampling. Finally, we shall discuss the key issues of both sides of the controversy that surrounds the use of Bayesian analysis in business decisions. The Decision-Making Process - An Overview The decision-making process is actually a series of steps, or phases. Enumeration of these steps makes clearer the role of phases. Enumeration of these steps makes clearer the role of Bayesian analysis: Define the possible outcomes (states of nature) and the decision choices available to the decision maker. Associate the probabilities of occurrence and economic considerations with each of the possible outcomes. Select investment strategy, based on expected-value criteria. Note the results (outcomes) of the initial choice. Revise the risk estimates using Bayesian analysis and whatever information stems from Step 4. Modify the investment strategy, if necessary, on the basis of new expected-value analysis and revised risk estimates. The first three steps are basic to the initial quantitative analysis of any investment decision involving uncertainty. The remaining steps represent a "monitoring system" to provide the basis for managerial decisions regarding changes in investment strategies with time. JPT P. 193

Sequential Models in Probabilistic Depreciation

Abstract : Probabilistic depreciation is a method of determining the proper depreciation charge in each year of an asset's service life, when the service life is a random variable with known distribution. The paper discusses how the service life distribution is modified as more information is obtained about the actual lifetime of the asset. The problem of determining the proper amount to be charged each year to depreciation while at the same time maintaining the proper balance in the accumulated depreciation account is considered. The analysis is done both for a single asset case and for group depreciation. A final section discusses the use of Bayesian analysis for estimating the particular form of the service life distribution while the assets are in service.

Percentage Points of the Beta Distribution for Use in Bayesian Analysis of Bernoulli Processes

We tabulate percentage points of the beta distribution z II such that F β(z II|r, n) = II. The percentage points are given to four decimal places for II = .01, .05(.05).95, .99, n = 2(1)30, 40, 50 and t = 1(1)[n/2]. The tables are primarily for use in Bayesian analysis of Bernoulli processes as treated in Raiffa and Schlaifer [7]. Numerical integration of a function with respect to the beta distribution is also discussed. An example is given.