A Bayesian Parametric Approach to Capture–Recapture with Misidentification

Assessment of system availability usually uses either an analytical (e.g., Markov/semi-Markov) or a simulation approach (e.g., Monte Carlo simulation-based). However, the former cannot handle complicated state changes and the latter is computationally expensive. Traditional Bayesian approaches may solve these problems; however, because of their computational difficulties, they are not widely applied. The recent proliferation of Markov Chain Monte Carlo (MCMC) approaches have led to the use of the Bayesian inference in a wide variety of fields. This study proposes a new approach to system availability assessment: a parametric Bayesian approach using MCMC, an approach that takes advantages of the analytical and simulation methods. By using this approach, mean time to failure (MTTF) and mean time to repair (MTTR) are treated as distributions instead of being “averaged”, which better reflects reality and compensates for the limitations of simulation data sample size. To demonstrate the approach, the paper considers a case study of a balling drum system in a mining company. In this system, MTTF and MTTR are determined in a Bayesian Weibull model and a Bayesian lognormal model respectively. The results show that the proposed approach can integrate the analytical and simulation methods to assess system availability and could be applied to other technical problems in asset management (e.g., other industries, other systems).

. This study introduces optimal designs for the unit exponential (UE) non linear model using local, Bayesian, and non parametric Bayesian approaches. In the local approach, optimal designs were derived by substituting initial estimates for the unknown parameters. However, recognizing the inefficiency of these designs when initial estimates are distant from their true values, we adopted a Bayesian approach, employing the D-optimal criterion with uniform and truncated normal prior distributions for unknown parameters. In situations lacking informative or historical knowledge of parameters, a non parametric Bayesian approach was employed, incorporating the Dirichlet Process (DP) prior to the space of distribution functions. Finally, the efficiency of various optimal designs was analyzed for comparison.

<abstract> <p>This study aimed to investigate the risk-return relationship, provided volatility feedback was taken into account, in the South African market. Volatility feedback, a stronger measure of volatility, was treated as an important source of asymmetry in the investigation of the risk-return relationship. This study analyzed the JSE ALSI excess returns and realized variance for the sample period from 15 October 2009 to 15 October 2019. This study modelled the novel and robust Bayesian approach in a parametric and nonparametric framework. A parametric model has modelling assumptions, such as normality, and a finite sample space. A nonparametric approach relaxes modelling assumptions and allows for an infinite sample space; thus, taking into account every possible asymmetric risk-return relationship. Given that South Africa is an emerging market, which is subject to higher levels of volatility, the presence of volatility feedback was expected to be more pronounced. However, contrary to expectations, the test results from both the parametric and nonparametric Bayesian model showed that volatility feedback had an insignificant effect in the South African market. The risk-return relationship was then investigated free from empirical distortions that resulted from volatility feedback. The parametric Bayesian model found a positive risk-return relationship, in line with traditional theoretical expectations. However, the nonparametric Bayesian model found no relationship between risk and return, in line with early South African studies. Since the nonparametric Bayesian approach is more robust than the parametric Bayesian approach, this study concluded that there is no risk-return relationship. Therefore, investors can include South Africa in their investment portfolio with higher risk countries in order to spread their risk and derive diversification benefits. In addition, risk averse investors can find a safe environment within the South African market and earn a return in accordance to their risk tolerance.</p> </abstract>

An MCMC approach to classical estimation

In a setting of many‐to‐one two‐sided matching with nontransferable utilities, for example, college admissions, we study conditions under which preferences of both sides are identified with data on one single market. Regardless of whether the market is centralized or decentralized, assuming that the observed matching is stable, we show nonparametric identification of preferences of both sides under certain exclusion restrictions. To take our results to the data, we use Monte Carlo simulations to evaluate different estimators, including the ones that are directly constructed from the identification. We find that a parametric Bayesian approach with a Gibbs sampler works well in realistically sized problems. Finally, we illustrate our methodology in decentralized admissions to public and private schools in Chile and conduct a counterfactual analysis of an affirmative action policy.

Effective utilisation of limited resources is a challenge for health care providers. Accurate and relevant information extracted from the length of stay distributions is useful for management purposes. Patient care episodes can be reconstructed from the comprehensive health registers, and in this paper we develop a Bayesian approach to analyse the length of care episode after a fractured hip. We model the large scale data with a flexible nonparametric multilayer perceptron network and with a parametric Weibull mixture model. To assess the performances of the models, we estimate expected utilities using predictive density as a utility measure. Since the model parameters cannot be directly compared, we focus on observables, and estimate the relevances of patient explanatory variables in predicting the length of stay. To demonstrate how the use of the nonparametric flexible model is advantageous for this complex health care data, we also study joint effects of variables in predictions, and visualise nonlinearities and interactions found in the data.

Constructing the Bayesian optimal design depends on the choice of a prior distribution for the unknown parameter. Lacking informative or historical knowledge of the parameter, a parametric Bayesian approach cannot be expected in complex statistical problems. In this regard, a nonparametric Bayesian approach can be used, in which random prior distribution is considered. The Dirichlet process is employed as a prior on the space of distribution functions. In this paper, a non-parametric Bayesian approach is incorporated into an optimal design criterion. This method is illustrated by an example.

We are comparing two approaches for stochastic volatility and jumps estimation in the EUR/USD time series - the non-parametric power-variation approach using high-frequency returns, and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We find that both of the methods do identify continuous stochastic volatility similarly, but they do not identify similarly the jump component. Firstly - the jumps estimated using the non-parametric high-frequency estimators are much more numerous than in the case of the Bayesian method using daily data. More importantly - we find that the probabilities of jump occurrences assigned to every day by both of the methods are virtually no rank-correlated (Spearman rank correlation is 0.0148) meaning that the two methods do not identify jumps at the same days. Actually the jump probabilities inferred using the non-parametric approach are not much correlated even with the daily realized variance and the daily squared returns, indicating that the discontinuous price changes (jumps) observed on high-frequencies may not be distinguishable (from the continuous volatility) on the daily frequency. As an additional result we find strong evidence for jump size dependence and jump clustering (based on the self-exciting Hawkes process) of the jumps identified using the non-parametric method (the shrinkage estimator).

This paper studies computationally and theoretically attractive estimators referred here as to the Laplace type estimators (LTE). The LTE include means and quantiles of Quasi-posterior distributions defined as transformations of general (non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear IV, GMM, and value-at-risk, models. The LTE's are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases.

The paper deals with the estimation of reliability parameters by combination of data from various data sources. The problem is discussed in a Bayesian framework and with reference to the estimation of failure rates. First the combination of expert opinions is considered. The well known Wash-1400 and IEEE-Std 500 approaches are recalled briefly. Then the additive error model and the multiplicative error model are discussed in some detail. The Bayesian parametric approach is illustrated as the reference method to combine expert opinions and experimental data. Finally the combination of computed parameters is discussed in both cases: homogeneous data and non-homobeneous data. As a conclusion, some comments on the various methods are given.KeywordsDecision MakerFailure RatePosterior DistributionFailure ProbabilityReliability ParameterThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We investigate production risk, technical efficiency and risk attitudes amongst contract and independent farmers. We use a Bayesian parametric approach and stochastic dominance quantile regression methods to compare technical efficiency and risk attitude of smallholders in Nepal. Using farm‐level data, we find that contract farmers appear to show lower inefficiency and lower production risk. Additionally, contract and independent farmers can increase output by reducing the scale of operation. Regardless of the commodity produced and farming arrangement (contract or independent production), we find that labour, land and other inputs are risk‐augmenting, while the role of capital is mixed. We find a second order stochastic dominance (SSD) for lentils, and first order stochastic dominance (FSD) for tomatoes, ginger and HYV paddy seed commodities. Finally, contract farmers are more risk averse than independent farmers, regardless of the commodity produced.

ObjectivesThis study compares methods for handling missing data to conduct cost-effectiveness analysis in the context of a clinical study.MethodsPatients in the Early Endovenous Ablation in Venous Ulceration (EVRA) trial had between 1 year and 5.5 years (median 3 years) of follow-up under early or deferred endovenous ablation. This study compares complete-case-analysis (CCA), multiple imputation using linear regression (MILR) and using predictive mean matching (MIPMM), Bayesian parametric approach using the R package missingHE (BPA), repeated measures fixed effect (RMFE) and repeated measures mixed model (RMM). The outcomes were total mean costs and total mean quality-adjusted life years (QALYs) at different time horizons (1 year, 3 years and 5 years).ResultsAll methods found no statistically significant difference in cost at the 5% level in all time horizons, and all methods found statistically significantly greater mean QALY at year 1. By year 3, only BPA showed a statistically significant difference in QALY between treatments. Standard errors differed substantially between the methods employed.ConclusionCCA can be biased if data are MAR and is wasteful of the data. Hence the results for CCA are likely to be inaccurate. Other methods coincide in suggesting that early intervention is cost-effective at a threshold of £30,000 per QALY 1, 3 and 5 years. However, the variation in the results across the methods does generate some additional methodological uncertainty, underlining the importance of conducting sensitivity analyses using alternative approaches.

Mean stop-signal reaction time (SSRT) is frequently employed as a measure of response inhibition in cognitive neuroscience research on ADHD. However, this measurement model is limited by two factors which may bias SSRT estimation in this population: 1) excessive skew in "go" RT distributions, and 2) trigger failures, or instances in which individuals fail to trigger an inhibition process in response to the "stop" signal. We use a Bayesian parametric approach, which allows unbiased estimation of the shape of entire SSRT distributions and the probability of trigger failures, to clarify mechanisms of stop-signal task deficits in ADHD. Children with ADHD displayed greater positive skew than their peers in both "go" RT and SSRT distributions. However, they also displayed more frequent trigger failures, which appeared to drive ADHD-related stopping difficulties. Results suggest that stop-signal task performance in ADHD reflects impairments in early attentional processes, rather than inefficiency in the stop process.

The interaction between temporal preparation and response inhibition is poorly understood in primates. Across two experiments, we investigated this relationship in four rhesus monkeys (Macaca mulatta) using a variable foreperiod (FP) stop-signal task, respectively focusing on effects of FP and its repetition/alteration across trials on response inhibition. We estimated ex-Gaussian distribution of reaction time in go trials (Go-RT) and stop-signal reaction time (SSRT) along with a probability of trigger failure (PTF). In the first experiment, increasing temporal preparation reduced the mean and variability of both the Gaussian and exponential components of Go-RT distribution, indicating generally faster and more consistent responding. In contrast, temporal preparation produced divergent effects on SSRT distribution: it numerically increased the Gaussian mean but decreased the exponential tail and overall variability. At the same time, PTF increased from short to long FP, suggesting that temporal preparation hinders the trigger of inhibition while enhancing its efficacy once triggered. In the second experiment, we found that FP effects on Go-RT distribution were largely independent of FP sequence. By contrast, response inhibition in the Gaussian component and entire distribution was modulated by FP switching: alternation between FPs prolonged inhibition latency. Also, FP switching reduced trigger failure, indicating a sequential adjustment that improved cue detection and reliability of stopping. Together, these findings demonstrate that temporal preparation shapes response execution primarily independent of state of preparation in the preceding trial, whereas its influence on response inhibition reflects short-term influences from the preceding trial.

The Los Angeles rainfall data are found to fit well to the two‐parameter generalized exponential (GE) distribution. A Bayesian parametric approach is described and used to predict the behavior of further rainfall records. Importance sampling is used to estimate the model parameters, and the Gibbs and Metropolis samplers are used to implement the prediction procedure. Copyright © 2007 John Wiley & Sons, Ltd.