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Title:

Learning from multinomial data: a nonparametric predictive alternative to the Imprecise Dirichlet Model

Description:

A new model for learning from multinomial data has recently been developed, giving predictive inferences in the form of lower and upper probabilities for a future observation. Apart from the past observations, no information on the sample space is assumed, so explicitly no assumptions are made on the number of possible categories. In this paper,...

A new model for learning from multinomial data has recently been developed, giving predictive inferences in the form of lower and upper probabilities for a future observation. Apart from the past observations, no information on the sample space is assumed, so explicitly no assumptions are made on the number of possible categories. In this paper, we briefly present the general lower and upper probabilities corresponding to this model, and illustrate their properties via two examples taken from Walley’s paper [16], which introduced the imprecise Dirichlet model (IDM). As our approach is nonparametric, its applicability is more restricted. However, our inferences do not suffer from some disadvantages of the IDM. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://maths.dur.ac.uk/stats/people/fc/npi/Coolen-Augustin.pdf

http://maths.dur.ac.uk/stats/people/fc/npi/Coolen-Augustin.pdf Minimize

Document Type:

text

Language:

en

Subjects:

data

data Minimize

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Title:

On nonparametric predictive inference and objective Bayesianism

Description:

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate N...

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://www.kent.ac.uk/secl/philosophy/jw/2005/progic/papers/Coolen.pdf

http://www.kent.ac.uk/secl/philosophy/jw/2005/progic/papers/Coolen.pdf Minimize

Document Type:

text

Language:

en

Subjects:

A (n ; circular data ; exchangeability ; grouped data ; imprecise probabilities

A (n ; circular data ; exchangeability ; grouped data ; imprecise probabilities Minimize

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Title:

Jury size and composition -- a predictive approach

Description:

We consider two basic aspects of juries that must decide on guilt verdicts, namely the size of juries and their composition in situations where society consists of sub-populations. We refer to the actual jury that needs to provide a verdict as the ‘first jury’, and as their judgement should reflect that of society, we consider an imaginary ‘seco...

We consider two basic aspects of juries that must decide on guilt verdicts, namely the size of juries and their composition in situations where society consists of sub-populations. We refer to the actual jury that needs to provide a verdict as the ‘first jury’, and as their judgement should reflect that of society, we consider an imaginary ‘second jury’ to represent society. The focus is mostly on a lower probability of a guilty verdict by the second jury, conditional on a guilty verdict by the first jury, under suitable exchangeability assumptions between this second jury and the first jury. Using a lower probability of a guilty verdict naturally provides a ‘benefit of doubt to the defendant’ robustness of the inference. By use of a predictive approach, no assumptions on the guilt of a defendant are required, which distinguishes this approach from those presented before. The statistical inferences used in this paper are relatively straightforward, as only cases are considered where the lower probabilities according to Coolen’s Nonparametric Predictive Inference for Bernoulli random quantities [5] and Walley’s Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-10-13

Source:

http://www.dur.ac.uk/brett.houlding/resources/isipta07-juries.pdf

http://www.dur.ac.uk/brett.houlding/resources/isipta07-juries.pdf Minimize

Document Type:

text

Language:

en

Subjects:

lower probability ; Nonparametric Predictive Inference ; representation of sub-populations

lower probability ; Nonparametric Predictive Inference ; representation of sub-populations Minimize

DDC:

160 Logic *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

On Nonparametric Predictive Inference and Objective Bayesianism

Description:

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A(n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A(n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI...

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A(n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A(n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A(n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-06-27

Source:

http://maths.dur.ac.uk/stats/people/fc/npi/coolen-jlli.pdf

http://maths.dur.ac.uk/stats/people/fc/npi/coolen-jlli.pdf Minimize

Document Type:

text

Language:

en

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Title:

Parametric probability distributions in reliability ∗

Description:

In this paper, we present an overview of basic parametric probability distributions which are frequently used in reliability. We present some main characteristics of these distributions, and briefly discuss underlying assumptions related to their suitability as models for specific reliability scenarios.

In this paper, we present an overview of basic parametric probability distributions which are frequently used in reliability. We present some main characteristics of these distributions, and briefly discuss underlying assumptions related to their suitability as models for specific reliability scenarios. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-06

Source:

http://maths.dur.ac.uk/stats/people/fc/pmdist.pdf

http://maths.dur.ac.uk/stats/people/fc/pmdist.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Binomial distribution ; Exponential distribution ; Gamma distribution ; Normal distribution ; Poisson distribution ; Weibull distribution

Binomial distribution ; Exponential distribution ; Gamma distribution ; Normal distribution ; Poisson distribution ; Weibull distribution Minimize

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Title:

On optimality criteria for age replacement

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Description:

Age replacement is a well-known topic in the literature of Operational Research and Reliability. Traditionally, the probability distribution of a unit’s failure time is assumed to be known, and the cost criterion is derived via the renewal reward theorem, which implicitly assumes that the same preventive replacement strategy will be used over a ...

Age replacement is a well-known topic in the literature of Operational Research and Reliability. Traditionally, the probability distribution of a unit’s failure time is assumed to be known, and the cost criterion is derived via the renewal reward theorem, which implicitly assumes that the same preventive replacement strategy will be used over a very long period of time. As an alternative, one can use a one-cycle criterion, aiming at minimisation of costs per unit of time only over the period that one unit is in place. We discuss these two criteria, and we also consider possible alternatives. Recently, we have presented a nonparametric predictive approach to age replacement, which is based on rather minimal assumptions for the failure time distributions, and provides full flexibility to the information from the process. We summarize the main conclusions from this research, where we also considered both the renewal criterion and the one-cycle criterion. We discuss further aspects related to age replacement, highlighting several interesting topics for future research. Key words: Age replacement, nonparametric predictive inference, optimality criteria 1. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-06

Source:

http://maths.dur.ac.uk/stats/people/ps/jrr1.pdf

http://maths.dur.ac.uk/stats/people/ps/jrr1.pdf Minimize

Document Type:

text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Nonparametric adaptive age replacement with a one-cycle criterion

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Description:

Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplifies the mathematics involved but requires the a...

Age replacement of technical units has received much attention in the reliability literature over the last four decades. Mostly, the failure time distribution for the units is assumed to be known, and minimal costs per unit of time is used as optimality criterion, where renewal reward theory simplifies the mathematics involved but requires the assumption that the same process and replacement strategy continues over a very large (‘infinite’) period of time. Recently, there has been increasing attention to adaptive strategies for age replacement, taking into account the information from the process. Although renewal reward theory can still be used to provide an intuitively and mathematically attractive optimality criterion, it is more logical to use minimal costs per unit of time over a single cycle as optimality criterion for adaptive age replacement. In this paper, we first show that in the classical age replacement setting, with known failure time distribution with increasing hazard rate, the one-cycle criterion leads to earlier replacement than the renewal reward criterion. Thereafter, we present adaptive age replacement with a one-cycle criterion within the nonparametric predictive inferential framework. We study the performance of this approach via simulations, which are also used for comparisons with the use of the renewal reward criterion within the same statistical framework. Key words: Age replacement; nonparametric predictive inference; one-cycle optimality criterion; renewal reward theorem. 1 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-06

Source:

http://maths.dur.ac.uk/stats/people/ps/ress1cyc.pdf

http://maths.dur.ac.uk/stats/people/ps/ress1cyc.pdf Minimize

Document Type:

text

Language:

en

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Nonparametric predictive inference for voting systems

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Description:

We present upper and lower probabilities for reliability of voting systems, also known as k-outof-m systems, which include series- and parallel-systems. We restrict attention to systems with identical components. These interval probabilities are based on the nonparametric predictive inferential (NPI) approach for Bernoulli data presented by Cool...

We present upper and lower probabilities for reliability of voting systems, also known as k-outof-m systems, which include series- and parallel-systems. We restrict attention to systems with identical components. These interval probabilities are based on the nonparametric predictive inferential (NPI) approach for Bernoulli data presented by Coolen (1998). In this approach, it is assumed that test data are available on the components, and that the future components to be used in the system are exchangeable with these. This approach fits into the general framework of Imprecise Reliability, which has received increasing attention in recent years (Utkin and Coolen 2007). An early overview of NPI in Reliability was presented by Coolen, Coolen-Schrijner and Yan (2002), in recent years NPI has been further developed and presented as an attractive statistical theory for situations where one aims at inference for future observables on the basis of available data, adding only rather limited additional assumptions (Coolen 2006a). A particularly attractive feature of NPI in Reliability, with lower and upper probabilities, is that data containing zero failures can be dealt with in an attractive manner, which will also be illustrated in this paper for reliability of voting systems. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-06

Source:

http://maths.dur.ac.uk/stats/people/fc/mmr07-voting.pdf

http://maths.dur.ac.uk/stats/people/fc/mmr07-voting.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Title:

Non-parametric predictive inference for age replacement with a renewal argument. Quality and Reliablity Engineering

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Description:

We consider an age replacement problem with cost function based on the renewal reward theorem. However, instead of assuming a known probability distribution for the lifetimes, we apply Hill’s assumption A (n) for predicting probabilities for the lifetime of a future item. Lower and upper bounds for the survival function of a future item are used...

We consider an age replacement problem with cost function based on the renewal reward theorem. However, instead of assuming a known probability distribution for the lifetimes, we apply Hill’s assumption A (n) for predicting probabilities for the lifetime of a future item. Lower and upper bounds for the survival function of a future item are used, resulting in upper and lower cost functions. Minimising these upper and lower cost functions to obtain the optimal age replacement times is simplified due to the special form of these functions. To discuss some features of our approach, we first study the consequences of using n equally spaced percentiles from a known distribution instead of n observed data. Secondly, we report on a simulation study where the lifetimes are simulated from known distributions, so that the optimal replacement times corresponding to our approach can be compared with the theoretical optimal replacement times. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-08-06

Source:

http://maths.dur.ac.uk/stats/people/ps/arts2.pdf

http://maths.dur.ac.uk/stats/people/ps/arts2.pdf Minimize

Document Type:

text

Language:

en

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Title:

Nonparametric predictive comparison of proportions

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Description:

We use the lower and upper predictive probabilities from Coolen [5] to compare future numbers of successes in Bernoulli trials for different groups. We consider both pairwise and multiple comparisons. These inferences are in terms of lower and upper probabilities that the number of successes in m future trials from one group exceeds the number o...

We use the lower and upper predictive probabilities from Coolen [5] to compare future numbers of successes in Bernoulli trials for different groups. We consider both pairwise and multiple comparisons. These inferences are in terms of lower and upper probabilities that the number of successes in m future trials from one group exceeds the number of successes in m future trials from another group, or such numbers from all other groups. We analyse these lower and upper probabilities via application to two data sets from the literature, and discuss the imprecision in relation to m. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-16

Source:

http://maths.dur.ac.uk/stats/people/fc/npi/props-rev.pdf

http://maths.dur.ac.uk/stats/people/fc/npi/props-rev.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Key Words ; Bernoulli trials ; Lower and upper probabilities ; Multiple comparisons ; Nonparametric predictive inference

Key Words ; Bernoulli trials ; Lower and upper probabilities ; Multiple comparisons ; Nonparametric predictive inference Minimize

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