Bounds on survival probability given mean probability of failure per demand; And the paradoxical advantages of uncertainty

When deciding whether to accept into service a new safety-critical system, or choosing between alternative systems, uncertainty about the parameters that affect future failure probability may be a major problem. This uncertainty can be extreme if there is the possibility of unknown design errors (e.g. in software), or wide variation between nominally equivalent components. We study the effect of parameter uncertainty on future reliability (survival probability), for systems required to have low risk of even only one failure or accident over the long term (e.g. their whole operational lifetime) and characterised by a single reliability parameter (e.g. probability of failure per demand - pfd). A complete mathematical treatment requires stating a probability distribution for any parameter with uncertain value. This is hard, so calculations are often performed using point estimates, like the expected value. We investigate conditions under which such simplified descriptions yield reliability values that are sure to be pessimistic (or optimistic) bounds for a prediction based on the true distribution. Two important observations are: (i) using the expected value of the reliability parameter as its true value guarantees a pessimistic estimate of reliability, a useful property in most safety-related decisions; (ii) with a given expected pfd, broader distributions (in a formally defined meaning of "broader"), that is, systems that are a priori "less predictable", lower the risk of failures or accidents. Result (i) justifies the simplification of using a mean in reliability modelling; we discuss within which scope this justification applies, and explore related scenarios, e.g. how things improve if we can test the system before operation. Result (ii) offers more flexible ways of bounding reliability predictions, but also has important, often counter-intuitive implications for decision making in various areas, like selection of components, project management, and product acceptance or licensing. For instance, in regulatory decision making dilemmas may arise in which the goal of minimising risk runs counter to other commonly held priorities, like predictability of risk; in safety assessment using expert opinion, the commonly recognised risk of experts being "overconfident" may be less dangerous than their being underconfident

Loss-size and Reliability Trade-offs Amongst Diverse Redundant Binary Classifiers

Many applications involve the use of binary classifiers, including applications where safety and security are critical. The quantitative assessment of such classifiers typically involves receiver operator characteristic (ROC) methods and the estimation of sensitivity/specificity. But such techniques have their limitations. For safety/security critical applications, more relevant measures of reliability and risk should be estimated. Moreover, ROC techniques do not explicitly account for: 1) inherent uncertainties one faces during assessments, 2) reliability evidence other than the observed failure behaviour of the classifier, and 3) how this observed failure behaviour alters one's uncertainty about classifier reliability. We address these limitations using conservative Bayesian inference (CBI) methods, producing statistically principled, conservative values for risk/reliability measures of interest. Our analyses reveals trade-offs amongst all binary classifiers with the same expected loss { the most reliable classifiers are those most likely to experience high impact failures. This trade-off is harnessed by using diverse redundant binary classifiers

Interval reliability inference for multi-component systems

This thesis is a collection of investigations on applications of imprecise probability theory to system reliability engineering with emphasis on using survival signatures for modelling complex systems. Survival signatures provide efficient representation of system structure and facilitate several reliability assessments by separating the computationally expensive combinatorial part from the subsequent evaluations submitted to only polynomial complexity. This proves useful for situations which also account for the statistical inference on system component lifetime distributions where Bayesian methods require repeated numerical propagation for the samples from the posterior distribution. Similarly, statistical methods involving imprecise probabilistic models composed of sets of precise probability distributions also benefit from the simplification by the signature representation. We will argue the pragmatic benefits of using statistical models based on imprecise probability models in reliability engineering from the perspective of inferential validity and provision of objective guarantees for the statistical procedures. Imprecise probability methods generally require solving an optimization problem to obtain bounds on the assessments of interest, but monotone system structures simplify them without much additional complexity. This simplification extends to survival signature models, therefore many reliability assessments with imprecise (interval) component lifetime models tend to be tractable as will be demonstrated on several examples

Hospital performance including quality: creating economic incentives consistent with evidence-based medicine

This thesis addresses questions of how to incorporate quality of care, represented by disutility-bearing effects such as mortality, morbidity and re-admission, in measuring relative performance of public hospitals. Currently, case-mix funding and performance, measured with costs per case-mix adjusted separation, hold hospitals accountable for costs, but not effects, of care, creating economic incentives for quality of care minimising cost per admission. To allow an appropriate trade-off between the value and cost of quality of care a correspondence is demonstrated between maximising net benefit and minimising costs plus decision makers’ value of disutility events, where effects of care can be represented by disutility events and hospitals face a common comparator. Applying this correspondence to performance measurement, frontier methods specifying disutility events as inputs are illustrated to have distinct advantages over output specifications, allowing estimation of: 1. economic efficiency conditional on the value of avoiding disutility events. 2. technical, scale and congestion sources of net benefit efficiency; 3. best practice peers over potential decision makers’ value of quality; and 4. industry shadow price of avoiding disutility events. The accountability this performance measurement framework provides for effects and cost of quality of care are also illustrated as the basis for moving from case-mix funding towards a funding mechanism based on maximising net benefit. Links to evidence-based medicine in health technology assessment are emphasised in illustrating application of the correspondence to comparison of multiple strategies in the cost-disutility plane, where radial properties as shown to provide distinct advantages over comparison in the cost-effectiveness plane. The identified performance measurement and funding framework allows policy makers to create economic incentives consistent with evidence-based medicine in practice, while avoiding incentives for cream-skimming and cost-shifting. The linear nature of the net benefit correspondence theorem allows simple inclusion of multiple effects of quality, whether expressed as not meeting a standard, functional limitation or disutility directly. In applying the net benefit correspondence theorem to hospitals a clinical activity level is suggested, to allow correspondence conditions to be robustly satisfied in identification of effects with decision analytic methods, adjustment for within DRG risk factors and data linkage to effects beyond separation

Social Welfare

"Social Welfare" offers, for the first time, a wide-ranging, internationally-focused selection of cutting-edge work from leading academics. Its interdisciplinary approach and comparative perspective promote examination of the most pressing social welfare issues of the day. The book aims to clarify some of the ambiguity around the term, discuss the pros and cons of privatization, present a range of social welfare paradoxes and innovations, and establish a clear set of economic frameworks with which to understand the conditions under which the change in social welfare can be obtained

Entrepreneurial Action and Entrepreneurial Rents

This dissertation is comprised of three independently standing research papers (chapters 2, 3 and 4) that come together in the common theme of investigating the relationship between entrepreneurial action and performance. The introduction chapter argues that this theme is the main agenda of an entrepreneurial approach to strategy, and provides some background and context for the core chapters. The entrepreneurial approach to strategy falls in line with an array of action-based theories of strategy that trace their economic foundations to the Austrian school of economics. Chapters 2 and 3 take a game theoretical modeling and computer simulation approach and represent one of the first attempts at formal analysis of the Austrian economic foundations of action-based strategy theory. These chapters attempt to demonstrate ways in which formal analysis can begin to approach compatibility with the central tenets of Austrian economics (i.e., subjectivism, dynamism, and methodological individualism). The simulation results shed light on our understanding of the relationship between opportunity creation and discovery, and economic rents in the process of moving towards and away from equilibrium. Chapter 4 operationalizes creation and discovery as exploration and exploitation in an empirical study using data from the Kauffman Firm Survey and highlights the trade-offs faced by start-ups in linking action to different dimensions of performance (i.e., survival, profitability, and getting acquired). Using multinomial logistic regression for competing risks analysis and random effects panel data regression, we find that high technology start-ups face a trade-off between acquisition likelihood and profitability-given-survival while low and medium technology start-ups face a trade-off between survival and profitability-given-survival. Chapter 5 concludes the dissertation by highlighting some of the overall contributions and suggesting avenues for future research

관측할 수 없는 변량 효과에 관한 통계적 추론

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 통계학과, 2023. 8. 임요한.This thesis is composed of six topics related to statistical inference on unobserved random effects, each centered around the concept of extended likelihood that incorporates information about the random unknowns. The first two topics focus on the theoretical properties of confidence distribution, whose density can be interpreted as an extended likelihood. The latter four topics reformulate the hierarchical likelihood, as an extended likelihood at specific scale, and investigate its theoretical properties, as well as its applications to deep learning. In the first topic, an epistemic confidence of the observed confidence intervals is introduced. Furthermore, the relevant subset problem associated is explained by incorporating the existence of betting markets into the Ramsey-De Finetti's Dutch book argument. It is demonstrated that the epistemic confidence is free from such issues. In the second topic, it is revealed that the existence of a point mass in confidence distribution plays an important role in maintaining the essential properties of the confidence distribution. The point mass has been considered paradoxical in Stein's paradox and satellite collision problems, but in fact, it gives an advantage to the confidence distribution. The proposed confidence distribution is free from the false confidence for the parameter of interest, and it maintains the confidence feature in both Stein's problem and the satellite conjunction problem. The third topic introduces the reformulation of hierarchical likelihood (h-likelihood) and establishes the theoretical properties for h-likelihood inference. This novel hierarchical likelihood can provide maximum likelihood estimators for fixed parameters and asymptotically the best unbiased estimators for random parameters, resolving the ambiguity of Lee and Nelder's (1996) original hierarchical likelihood. The last three topics deal with applications of the h-likelihood approach to deep learning models. While the most deep learning models implicitly assume the independence of data, real-world large scale data is often clustered with temporal-spatial correlations. In such cases, prediction performance of deep learning models can be improved by introducing random effects via h-likelihood. The fourth topic deals with deep learning models for continuous data with temporal-spatial correlations, and the fifth topic focuses on deep learning models for count data with non-Gaussian random effects. The sixth topic proposes h-likelihood approach to semi-parametric deep neural networks with gamma frailty for analyzing clustered censored data. In all three topics, the proposed methods improve prediction performance by introducing random effects into the existing deep learning models.이 논문은 관측할 수 없는 변량 효과에 대한 통계적 추론에 관련된 여섯 개의 주제로 구성되어 있으며, 각각의 주제는 관측할 수 없는 변량에 관한 정보를 갖고 있는 확장된 가능도(extended likelihood)를 중심으로 연결되어 있다. 전반부의 두 주제는 신뢰도(confidence) 이론에 관한 내용으로, 신뢰분포의 밀도함수(confidence density)를 확장된 가능도로 해석하여, 신뢰도에 관한 이론적 성질을 규명하였다. 후반부의 네 주제는 특수한 스케일에서의 확장된 가능도로 정의되는 계층적 가능도(hierarchical likelihood)에 관한 이론적 성질과 딥러닝으로의 확장 및 응용에 관한 내용을 다룬다. 첫번째 주제에서는 관측된 신뢰구간에 대해 인식론적 신뢰도(epistemic confidence)를 정의하고 이를 계산하기 위한 방법을 제시하였다. 또한, 빈도주의적 관점에서 정의되는 신뢰도가 갖는 relevant subset 문제를 Ramsey-De Finetti의 Dutch book 논의에 betting market의 존재를 도입함으로써 설명하고, 인식론적 신뢰도가 이러한 문제로부터 자유로울 수 있음을 보였다. 두번째 주제에서는 Stein의 역설과 인공위성 충돌 문제를 통해 신뢰분포가 특정 지점에서 point mass를 갖는 문제를 새로운 관점에서 해석하여, 역설적으로 여겨지던 point mass의 존재가 신뢰분포의 핵심적인 성질을 유지하도록 만들어주는 데 중요한 역할을 한다는 것을 밝혔다. 이와 더불어, 제안한 형태의 신뢰 분포가 확률 형태의 추론이 갖는 근본적인 한계점으로 지적된 거짓 신뢰(false confidence) 문제에서 (적어도 목표 가설에 한해) 자유롭다는 것을 밝히고, 기존의 다른 방법론들과 달리 Stein 문제 및 인공위성 충돌 문제에서 적정 신뢰도를 유지할 수 있음을 보였다. 세번째 주제에서는 계층 가능도를 새롭게 정의하고 이론적 성질을 규명하였다. 새로운 계층 가능도는 고정 효과의 최대 가능도 추정량과 변량 효과의 점근적 최소분산 불편추정량을 제공할 수 있으며, 기존의 계층 가능도가 갖고 있던 이론적 모호성을 해소할 수 있다. 마지막 세 주제는 새롭게 정의한 계층 가능도를 기반으로 한 딥러닝 모형을 다루고 있다. 대부분의 딥러닝 모형들이 데이터의 독립성을 암묵적으로 가정하고 있지만, 실제 데이터는 시공간적 상관관계를 갖는 경우가 많다. 딥러닝 모형에 변량 효과를 도입함으로써 이러한 문제를 해결할 수 있으며, 계층 가능도 기반 접근법은 기존의 방법론에 비해 여러가지 장점을 갖는다. 네번째 주제에서는 시공간 상관관계를 갖는 연속형 데이터를 다루기 위한 딥러닝 모형을 다루었고, 다섯번째 주제에서는 비정규 변량 효과를 갖는 가산형 데이터를 다루기 위한 딥러닝 모형을 다루었다. 여섯번째 주제에서는 군집화된 절단자료를 분석하기 위한 계층 가능도 기반 준모수적(semi-parameteric) 접근법에 대해 다루었다. 세 주제 모두, 제안한 방법을 통해 딥러닝 모형에 변량 효과를 도입함으로써 기존 방법론의 예측 성능을 향상시킬 수 있었다.Abstract i List of Figures viii List of Tables xii 1 Introduction 1 2 Epistemic confidence in the observed confidence interval 6 2.1 Introduction 6 2.2 Main theory 10 2.2.1 Relevant subsets 10 2.2.2 Confidence distribution 12 2.2.3 Main theorem 15 2.2.4 Ancillary statistics 20 2.2.5 Computation of epistemic confidence 23 2.3 Examples 24 2.3.1 Simple model 24 2.3.2 Location family model 25 2.3.3 Exponential family model 26 2.4 Discussion 35 2.5 Appendix 37 2.5.1 Curved exponential model: N(θ, θ2) 37 2.5.2 Discrete case 41 2.5.3 When maximal ancillaries are not unique 44 3 Point mass in confidence distributions 47 3.1 Introduction 47 3.2 Ambiguity in confidence of an observed CI 50 3.3 GFD and probability dilution 54 3.4 CD and related methods 57 3.4.1 CD and confidence level of an observed CI 59 3.4.2 CD versus GFD 62 3.4.3 CD versus RP 64 3.5 On false confidence. 66 3.5.1 False confidence and probability dilution 69 3.6 Hypothesis testing 71 3.7 Concluding remarks 74 3.8 Appendix 75 3.8.1 Proof of Theorem 3 175 4 Foundations of h-likelihood inference for random unknowns 77 4.1 Introduction 77 4.2 Hierarchical likelihood 79 4.2.1 Reformulation of H-Likelihood 82 4.2.2 Bartlizable scale of random effects 86 4.3 Main Results 91 4.4 H-likelihood theory for irregular cases 95 4.4.1 Missing data problem when v − v = Op(1) 96 4.4.2 Exponential-exponential HGLM when θ − θ = Op(1) 102 4.5 When the h-likelihood is not explicit. 107 4.6 Appendix 108 5 DNN with temporal-spatial random effects via h-likelihood 119 5.1 Introduction 119 5.2 Integrated likelihood approach for LMMs 121 5.3 H-likelihood approach for LMMs 124 5.4 Learning algorithm with the h-likelihood 128 5.4.1 REML procedure 132 5.4.2 Adjustments for random effects 133 5.5 Comparison with existing methods 134 5.6 Numerical studies 136 5.7 Real data analysis. 139 5.8 Concluding remarks 141 5.9 Appendix 143 5.9.1 The computation of h-likelihood when q1 is large 143 5.9.2 Methods-of-moments estimators 144 5.9.3 Technical details 144 6 DNN for clustered count data via h-likelihood 150 6.1 Introduction 150 6.2 Model Descriptions 152 6.2.1 Poisson DNN 152 6.2.2 Poisson-gamma DNN 153 6.3 Construction of h-likelihood 155 6.4 Learning algorithm with the h-likelihood 158 6.4.1 Loss function for online learning 158 6.4.2 The local minima problem 159 6.4.3 Pretraining variance components 160 6.5 Experimental Studies 161 6.6 Real Data Analysis 166 6.7 Concluding Remarks 168 6.8 Appendix 168 6.8.1 Convergence of the method-of-moments estimator 168 6.8.2 Technical details 170 7 DNN for semi-parametric frailty models via h-likelihood 173 7.1 Introduction 173 7.2 A review of DNN-Cox model 174 7.2.1 DNN-Cox model 174 7.2.2 Prediction measures 176 7.3 Proposed DNN for frailty model 178 7.3.1 DNN-FM 179 7.3.2 Construction of h-likelihood 179 7.4 Learning algorithm using the profiled h-likelihood 182 7.4.1 Local minima problem 184 7.4.2 ML learning algorithm 184 7.5 Experimental studies 186 7.5.1 Experimental design 186 7.5.2 Experimental results 188 7.6 Multi-center bladder cancer data 194 7.7 Concluding remarks 197 7.8 Appendix 198 7.8.1 Derivation for the predictive likelihood 198 7.8.2 Evaluation measures for DNN-FM 199 7.8.3 Online learning for the DNN-FM 201 7.8.4 Proofs 203 Bibliography 208 Abstract in Korean 224박

Futures Studies in the Interactive Society

This book consists of papers which were prepared within the framework of the research project (No. T 048539) entitled Futures Studies in the Interactive Society (project leader: Éva Hideg) and funded by the Hungarian Scientific Research Fund (OTKA) between 2005 and 2009. Some discuss the theoretical and methodological questions of futures studies and foresight; others present new approaches to or procedures of certain questions which are very important and topical from the perspective of forecast and foresight practice. Each study was conducted in pursuit of improvement in futures fields