Fixed-Width Output Analysis for Markov Chain Monte Carlo

Markov chain Monte Carlo is a method of producing a correlated sample in order to estimate features of a complicated target distribution via simple ergodic averages. A fundamental question in MCMC applications is when should the sampling stop? That is, when are the ergodic averages good estimates of the desired quantities? We consider a method that stops the MCMC sampling the first time the width of a confidence interval based on the ergodic averages is less than a user-specified value. Hence calculating Monte Carlo standard errors is a critical step in assessing the output of the simulation. In particular, we consider the regenerative simulation and batch means methods of estimating the variance of the asymptotic normal distribution. We describe sufficient conditions for the strong consistency and asymptotic normality of both methods and investigate their finite sample properties in a variety of examples.

Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval

In this note, we consider the scheduling problem of minimizing the sum of the weighted completion times on a single machine with one non-availability interval on the machine under the non-resumable scenario. Together with a recent 2-approximation algorithm designed by Kacem [I. Kacem, Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers & Industrial Engineering 54 (2008) 401–410], this paper is the first successful attempt to develop a constant ratio approximation algorithm for this problem. We present two approaches to designing such an algorithm. Our best algorithm guarantees a worst-case performance ratio of 2+ε. © 2008 Elsevier B.V. All rights reserved.

Point-wise confidence interval estimation by neural networks: A comparative study based on automotive engine calibration.

In developing neural network techniques for real world applications it is still very rare to see estimates of confidence placed on the neural network predictions. This is a major deficiency, especially in safety-critical systems. In this paper we explore three distinct methods of producing point-wise confidence intervals using neural networks. We compare and contrast Bayesian, Gaussian Process and Predictive error bars evaluated on real data. The problem domain is concerned with the calibration of a real automotive engine management system for both air-fuel ratio determination and on-line ignition timing. This problem requires real-time control and is a good candidate for exploring the use of confidence predictions due to its safety-critical nature.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Determinants and two-year change in anterior chamber angle width in a Chinese population

Objective: To study the population distribution and longitudinal changes in anterior chamber angle width and its determinants among Chinese adults. Design: Prospective cohort, population-based study. Participants: Persons aged 35 years or more residing in Guangzhou, China, who had not previously undergone incisional or laser eye surgery. Methods: In December 2008 and December 2010, all subjects underwent automated keratometry, and a random 50% sample had anterior segment optical coherence tomography with measurement of angle-opening distance at 500 μm (AOD500), angle recess area (ARA), iris thickness at 750 μm (IT750), iris curvature, pupil diameter, corneal thickness, anterior chamber width (ACW), lens vault (LV), and lens thickness (LT) and measurement of axial length (AL) and anterior chamber depth (ACD) by partial coherence laser interferometry. Main Outcome Measures: Baseline and 2-year change in AOD500 and ARA in the right eye. Results: A total of 745 subjects were present for full biometric testing in both 2008 and 2010 (mean age at baseline, 52.2 years; standard deviation [SD], 11.5 years; 53.7% were female). Test completion rates in 2010 varied from 77.3% (AOD500: 576/745) to 100% (AL). Mean AOD500 decreased from 0.25 mm (SD, 0.13 mm) in 2008 to 0.21 mm (SD, 13 mm) in 2010 (difference, -0.04; 95% confidence interval [CI], -0.05 to -0.03). The ARA decreased from 21.5±3.73 10^-2 mm² to 21.0±3.64 10 ^-2 mm² (difference, -0.46; 95% CI, -0.52 to -0.41). The decrease in both was most pronounced among younger subjects and those with baseline AOD500 in the widest quartile at baseline. The following baseline variables were significantly associated with a greater 2-year decrease in both AOD500 and ARA: deeper ACD, steeper iris curvature, smaller LV, greater ARA, and greater AOD500. By using simple regression models, we could explain 52% to 58% and 93% of variation in baseline AOD500 and ARA, respectively, but only 27% and 16% of variation in 2-year change in AOD500 and ARA, respectively. Conclusions: Younger persons and those with the least crowded anterior chambers at baseline have the largest 2-year decreases in AOD500 and ARA. The ability to predict change in angle width based on demographic and biometric factors is relatively poor, which may have implications for screening. Financial Disclosure(s): The author(s) have no proprietary or commercial interest in any materials discussed in this article. © 2012 American Academy of Ophthalmology.

A systematic review of the performance of ceramic and metal implant abutments supporting fixed implant reconstructions

OBJECTIVES: The objective of this systematic review was to assess the 5-year survival rates and incidences of complications associated with ceramic abutments and to compare them with those of metal abutments. METHODS: An electronic Medline search complemented by manual searching was conducted to identify randomized-controlled clinical trials, and prospective and retrospective studies providing information on ceramic and metal abutments with a mean follow-up time of at least 3 years. Patients had to have been examined clinically at the follow-up visit. Assessment of the identified studies and data abstraction was performed independently by three reviewers. Failure rates were analyzed using standard and random-effects Poisson regression models to obtain summary estimates of 5-year survival proportions. RESULTS: Twenty-nine clinical and 22 laboratory studies were selected from an initial yield of 7136 titles and data were extracted. The estimated 5-year survival rate of ceramic abutments was 99.1% [95% confidence interval (CI): 93.8-99.9%] and 97.4% (95% CI: 96-98.3%) for metal abutments. The estimated cumulative incidence of technical complications after 5 years was 6.9% (95% CI: 3.5-13.4%) for ceramic abutments and 15.9% (95% CI: 11.6-21.5%) for metal abutments. Abutment screw loosening was the most frequent technical problem, occurring at an estimated cumulative incidence after 5 years of 5.1% (95% CI: 3.3-7.7%). All-ceramic crowns supported by ceramic abutments exhibited similar annual fracture rates as metal-ceramic crowns supported by metal abutments. The cumulative incidence of biological complications after 5 years was estimated at 5.2% (95% CI: 0.4-52%) for ceramic and 7.7% (95% CI: 4.7-12.5%) for metal abutments. Esthetic complications tended to be more frequent at metal abutments. A meta-analysis of the laboratory data was impossible due to the non-standardized test methods of the studies included. CONCLUSION: The 5-year survival rates estimated from annual failure rates appeared to be similar for ceramic and metal abutments. The information included in this review did not provide evidence for differences of the technical and biological outcomes of ceramic and metal abutments. However, the information for ceramic abutments was limited in the number of studies and abutments analyzed as well as the accrued follow-up time. Standardized methods for the analysis of abutment strength are needed.

A systematic review of the survival and complication rates of implant supported fixed dental prostheses with cantilever extensions after an observation period of at least 5 years

OBJECTIVE: The aim of this systematic review was to assess the survival rates of short-span implant-supported cantilever fixed dental prostheses (ICFDPs) and the incidence of technical and biological complications after an observation period of at least 5 years. MATERIAL AND METHODS: An electronic MEDLINE search supplemented by manual searching was conducted to identify prospective or retrospective cohort studies reporting data of at least 5 years on ICFDPs. Five- and 10-year estimates for failure and complication rates were calculated using standard or random-effect Poisson regression analysis. RESULTS: The five studies eligible for the meta-analysis yielded an estimated 5- and 10-year ICFDP cumulative survival rate of 94.3% [95 percent confidence interval (95% CI): 84.1-98%] and 88.9% (95% CI: 70.8-96.1%), respectively. Five-year estimates for peri-implantitis were 5.4% (95% CI: 2-14.2%) and 9.4% (95% CI: 3.3-25.4%) at implant and prosthesis levels, respectively. Veneer fracture (5-year estimate: 10.3%; 95% CI: 3.9-26.6%) and screw loosening (5-year estimate: 8.2%; 95% CI: 3.9-17%) represented the most common complications, followed by loss of retention (5-year estimate: 5.7%; 95% CI: 1.9-16.5%) and abutment/screw fracture (5-year estimate: 2.1%; 95% CI: 0.9-5.1%). Implant fracture was rare (5-year estimate: 1.3%; 95% CI: 0.2-8.3%); no framework fracture was reported. Radiographic bone level changes did not yield statistically significant differences either at the prosthesis or at the implant levels when comparing ICFDPs with short-span implant-supported end-abutment fixed dental prostheses. CONCLUSIONS: ICFDPs represent a valid treatment modality; no detrimental effects can be expected on bone levels due to the presence of a cantilever extension per se.

Fixed low-dose ultrasound-assisted catheter-directed thrombolysis for intermediate- and high-risk pulmonary embolism

AIMS No standardized local thrombolysis regimen exists for the treatment of pulmonary embolism (PE). We retrospectively investigated efficacy and safety of fixed low-dose ultrasound-assisted catheter-directed thrombolysis (USAT) for intermediate- and high-risk PE. METHODS AND RESULTS Fifty-two patients (65 ± 14 years) of whom 14 had high-risk PE (troponin positive in all) and 38 intermediate-risk PE (troponin positive in 91%) were treated with intravenous unfractionated heparin and USAT using 10 mg of recombinant tissue plasminogen activator per device over the course of 15 h. Bilateral USAT was performed in 83% of patients. During 3-month follow-up, two [3.8%; 95% confidence interval (CI) 0.5-13%] patients died (one from cardiogenic shock and one from recurrent PE). Major non-fatal bleeding occurred in two (3.8%; 95% CI, 0.5-13%) patients: one intrathoracic bleeding after cardiopulmonary resuscitation requiring transfusion, one intrapulmonary bleeding requiring lobectomy. Mean pulmonary artery pressure decreased from 37 ± 9 mmHg at baseline to 25 ± 8 mmHg at 15 h (P < 0.001) and cardiac index increased from 2.0 ± 0.7 to 2.7 ± 0.9 L/min/m(2) (P < 0.001). Echocardiographic right-to-left ventricular end-diastolic dimension ratio decreased from 1.42 ± 0.21 at baseline to 1.06 ± 0.23 at 24 h (n = 21; P < 0.001). The greatest haemodynamic benefit from USAT was found in patients with high-risk PE and in those with symptom duration < 14 days. CONCLUSION A standardized catheter intervention approach using fixed low-dose USAT for the treatment of intermediate- and high-risk PE was associated with rapid improvement in haemodynamic parameters and low rates of bleeding complications and mortality.

Systematic review of the survival rate and incidence of biologic, technical, and esthetic complications of single implant abutments supporting fixed prostheses

Purpose: To assess the 5-year survival rate and number of technical, biologic, and esthetic complications involving implant abutments. Materials and Methods: Electronic (Medline) and hand searches were performed to assess studies on metal and ceramic implant abutments. Relevant data from a previous review were included. Two reviewers independently extracted the data. Failure and complication rates were analyzed, and estimates of 5-year survival proportions were calculated from the relationship between event rate and survival function. Multivariable robust Poisson regression was used to compare abutment characteristics. Results: The search yielded 1,558 titles and 274 abstracts. Twenty-four studies were selected for data analysis. The survival rate for ceramic abutments was 97.5% (95% confidence interval [CI]): 89.6% to 99.4%) and 97.6% (95% CI: 96.2% to 98.5%) for metal abutments. The overall 5-year rate for technical complications was 11.8% (95% CI: 8.5% to 16.3%), 8.9% (95% CI: 4.3% to 17.7%) for ceramic and 12.0% (95% CI: 8.5% to 16.8%) for metal abutments. Biologic complications occurred with an overall rate of 6.4% (95% CI: 3.3% to 12.0%), 10.4% (95% CI: 1.9% to 46.7%) for ceramic, and 6.1% (95% CI: 3.1% to 12.0%) for metal abutments. Conclusions: The present meta-analysis on single-implant prostheses presents high survival rates of single implants, abutments, and prostheses after 5 years of function. No differences were found for the survival and failure rates of ceramic and metal abutments. No significant differences were found for technical, biologic, and esthetic complications of internally and externally connected abutments.

Clinical Performance of Screw- Versus Cement-Retained Fixed Implant-Supported Reconstructions- A Systematic Review.

PURPOSE To assess the survival outcomes and reported complications of screw- and cement-retained fixed reconstructions supported on dental implants. MATERIALS AND METHODS A Medline (PubMed), Embase, and Cochrane electronic database search from 2000 to September 2012 using MeSH and free-text terms was conducted. Selected inclusion and exclusion criteria guided the search. All studies were first reviewed by abstract and subsequently by full-text reading by two examiners independently. Data were extracted by two examiners and statistically analyzed using a random effects Poisson regression. RESULTS From 4,324 abstracts, 321 full-text articles were reviewed. Seventy-three articles were found to qualify for inclusion. Five-year survival rates of 96.03% (95% confidence interval [CI]: 93.85% to 97.43%) and 95.55% (95% CI: 92.96% to 97.19%) were calculated for cemented and screw-retained reconstructions, respectively (P = .69). Comparison of cement and screw retention showed no difference when grouped as single crowns (I-SC) (P = .10) or fixed partial dentures (I-FDP) (P = .49). The 5-year survival rate for screw-retained full-arch reconstructions was 96.71% (95% CI: 93.66% to 98.31). All-ceramic reconstruction material exhibited a significantly higher failure rate than porcelain-fused-to-metal (PFM) in cemented reconstructions (P = .01) but not when comparing screw-retained reconstructions (P = .66). Technical and biologic complications demonstrating a statistically significant difference included loss of retention (P ≤ .01), abutment loosening (P ≤ .01), porcelain fracture and/or chipping (P = .02), presence of fistula/suppuration (P ≤ .001), total technical events (P = .03), and total biologic events (P = .02). CONCLUSIONS Although no statistical difference was found between cement- and screw-retained reconstructions for survival or failure rates, screw-retained reconstructions exhibited fewer technical and biologic complications overall. There were no statistically significant differences between the failure rates of the different reconstruction types (I-SCs, I-FDPs, full-arch I-FDPs) or abutment materials (titanium, gold, ceramic). The failure rate of cemented reconstructions was not influenced by the choice of a specific cement, though cement type did influence loss of retention.

Small sample confidence intervals for the mean of a positively skewed distribution

This thesis proposes some confidence intervals for the mean of a positively skewed distribution. The following confidence intervals are considered: Student-t, Johnson-t, median-t, mad-t, bootstrap-t, BCA, T1 , T3 and six new confidence intervals, the median bootstrap-t, mad bootstrap-t, median T1, mad T1 , median T3 and the mad T3. A simulation study has been conducted and average widths, coefficient of variation of widths, and coverage probabilities were recorded and compared across confidence intervals. To compare confidence intervals, the width and coverage probabilities were compared so that smaller widths indicated a better confidence interval when coverage probabilities were the same. Results showed that the median T1 and median T3 outperformed other confidence intervals in terms of coverage probability and the mad bootstrap-t, mad-t, and mad T3 outperformed others in terms of width. Some real life data are considered to illustrate the findings of the thesis.

Minimising speaker verification utterance length through confidence based early verification decisions

This paper presents a novel approach of estimating the confidence interval of speaker verification scores. This approach is utilised to minimise the utterance lengths required in order to produce a confident verification decision. The confidence estimation method is also extended to address both the problem of high correlation in consecutive frame scores, and robustness with very limited training samples. The proposed technique achieves a drastic reduction in the typical data requirements for producing confident decisions in an automatic speaker verification system. When evaluated on the NIST 2005 SRE, the early verification decision method demonstrates that an average of 5–10 seconds of speech is sufficient to produce verification rates approaching those achieved previously using an average in excess of 100 seconds of speech.

Confidence to cook vegetables and the buying habits of Australian households

Cooking skills are emphasized in nutrition promotion but their distribution among population subgroups and relationship to dietary behavior is researched by few population-based studies. This study examined the relationships between confidence to cook, sociodemographic characteristics, and household vegetable purchasing. This cross-sectional study of 426 randomly selected households in Brisbane, Australia, used a validated questionnaire to assess household vegetable purchasing habits and the confidence to cook of the person who most often prepares food for these households. The mutually adjusted odds ratios (ORs) of lacking confidence to cook were assessed across a range of demographic subgroups using multiple logistic regression models. Similarly, mutually adjusted mean vegetable purchasing scores were calculated using multiple linear regression for different population groups and for respondents with varying confidence levels. Lacking confidence to cook using a variety of techniques was more common among respondents with less education (OR 3.30; 95% confidence interval [CI] 1.01 to 10.75) and was less common among respondents who lived with minors (OR 0.22; 95% CI 0.09 to 0.53) and other adults (OR 0.43; 95% CI 0.24 to 0.78). Lack of confidence to prepare vegetables was associated with being male (OR 2.25; 95% CI 1.24 to 4.08), low education (OR 6.60; 95% CI 2.08 to 20.91), lower household income (OR 2.98; 95% CI 1.02 to 8.72) and living with other adults (OR 0.53; 95% CI 0.29 to 0.98). Households bought a greater variety of vegetables on a regular basis when the main chef was confident to prepare them (difference: 18.60; 95% CI 14.66 to 22.54), older (difference: 8.69; 95% CI 4.92 to 12.47), lived with at least one other adult (difference: 5.47; 95% CI 2.82 to 8.12) or at least one minor (difference: 2.86; 95% CI 0.17 to 5.55). Cooking skills may contribute to socioeconomic dietary differences, and may be a useful strategy for promoting fruit and vegetable consumption, particularly among socioeconomically disadvantaged groups.

Asset life prediction and maintenance decision-making using a non-linear non-Gaussian state space model

Estimating and predicting degradation processes of engineering assets is crucial for reducing the cost and insuring the productivity of enterprises. Assisted by modern condition monitoring (CM) technologies, most asset degradation processes can be revealed by various degradation indicators extracted from CM data. Maintenance strategies developed using these degradation indicators (i.e. condition-based maintenance) are more cost-effective, because unnecessary maintenance activities are avoided when an asset is still in a decent health state. A practical difficulty in condition-based maintenance (CBM) is that degradation indicators extracted from CM data can only partially reveal asset health states in most situations. Underestimating this uncertainty in relationships between degradation indicators and health states can cause excessive false alarms or failures without pre-alarms. The state space model provides an efficient approach to describe a degradation process using these indicators that can only partially reveal health states. However, existing state space models that describe asset degradation processes largely depend on assumptions such as, discrete time, discrete state, linearity, and Gaussianity. The discrete time assumption requires that failures and inspections only happen at fixed intervals. The discrete state assumption entails discretising continuous degradation indicators, which requires expert knowledge and often introduces additional errors. The linear and Gaussian assumptions are not consistent with nonlinear and irreversible degradation processes in most engineering assets. This research proposes a Gamma-based state space model that does not have discrete time, discrete state, linear and Gaussian assumptions to model partially observable degradation processes. Monte Carlo-based algorithms are developed to estimate model parameters and asset remaining useful lives. In addition, this research also develops a continuous state partially observable semi-Markov decision process (POSMDP) to model a degradation process that follows the Gamma-based state space model and is under various maintenance strategies. Optimal maintenance strategies are obtained by solving the POSMDP. Simulation studies through the MATLAB are performed; case studies using the data from an accelerated life test of a gearbox and a liquefied natural gas industry are also conducted. The results show that the proposed Monte Carlo-based EM algorithm can estimate model parameters accurately. The results also show that the proposed Gamma-based state space model have better fitness result than linear and Gaussian state space models when used to process monotonically increasing degradation data in the accelerated life test of a gear box. Furthermore, both simulation studies and case studies show that the prediction algorithm based on the Gamma-based state space model can identify the mean value and confidence interval of asset remaining useful lives accurately. In addition, the simulation study shows that the proposed maintenance strategy optimisation method based on the POSMDP is more flexible than that assumes a predetermined strategy structure and uses the renewal theory. Moreover, the simulation study also shows that the proposed maintenance optimisation method can obtain more cost-effective strategies than a recently published maintenance strategy optimisation method by optimising the next maintenance activity and the waiting time till the next maintenance activity simultaneously.