Fisher information and statistical inference for phase-type distributions

Bladt, Mogens; Esparza, Luz Judith R.; Nielsen, Bo Friis

doi:10.1017/s0021900200099289

Cited by 5 publications

(8 citation statements)

References 4 publications

(1 reference statement)

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“…In Section 4, we showcase the applicability of the proposed algorithm to t real-world operating room service time data as well as a set of benchmark traces generated from conventional distributions. We compare the accuracy of our results with two other algorithms designed by Th ummler et al [4] and Bladt et al [11]. In Section 5, we provide the conclusions and show directions for future research.…”

Section: Introductionmentioning

confidence: 87%

“…In Eq. (6) (11) In this section, we demonstrated the PH representation of MSNB distribution and its properties such as approximating any distribution on N, wide range of CoV, and fat-tailed property.…”

Section: Mixed Shifted Negative Binomial Distribution and Its Propertiesmentioning

confidence: 99%

“…The three datasets are collected from orthopedic operating theatre in the Scottish NHS hospital from 1998 to 1999, and are used in other studies [22]. We compare the tting quality of the proposed EM algorithm (EM-MSNBD) with the quality of an EM algorithm designed for general DPH distributions (EM-DPH) presented by Bladt et al [11] and the EM algorithm for the continuous HErD (EM-HErD) developed by Th ummler et al [4]. This algorithm is one of the best-performing algorithms in tting CPH [23].…”

Section: Fitting Msnb Distributions To Real Operating Room Datamentioning

confidence: 99%

“…Their algorithm was an adapted version of the EM algorithm proposed by Asmussen et al [10], which applied to continuous PH distributions. Three di erent methods, namely an EM algorithm, a Gibbs sampler algorithm, and a Quasi-Newton method, were applied for maximum likelihood estimation of general DPH distributions by Bladt et al [11].…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Parameters of Mixed Shifted Negative Binomial Distributions via an EM Algorithm

et al. 2018

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Abstract. Discrete Phase-Type (DPH) distributions have one property that is not shared by Continuous Phase-Type (CPH) distributions, i.e., representing a deterministic value as a DPH random variable. This property distinguishes the application of DPH in stochastic modeling of real-life problems, such as stochastic scheduling, in which service time random variables should be compared with a deadline that is usually a constant value. In this paper, we consider a restricted class of DPH distributions, called Mixed Shifted Negative Binomial (MSNB), and show its exibility in producing a wide range of variances as well as its adequacy in tting fat-tailed distributions. These properties render MSNB applicable to represent data on certain types of service time. Therefore, we adapt an ExpectationMaximization (EM) algorithm to estimate the parameters of MSNB distributions that accurately t trace data. To present the applicability of the proposed algorithm, we use it to t real operating room times and a set of benchmark traces generated from continuous distributions as case studies. Finally, we illustrate the e ciency of the proposed algorithm by comparing its results with those of two existing algorithms in the literature. We conclude that our proposed algorithm outperforms other DPH algorithms in tting trace data and distributions.

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Section: Introductionmentioning

confidence: 87%

Section: Mixed Shifted Negative Binomial Distribution and Its Propertiesmentioning

confidence: 99%

Section: Fitting Msnb Distributions To Real Operating Room Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating the Parameters of Mixed Shifted Negative Binomial Distributions via an EM Algorithm

et al. 2018

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“…These methods assume ƒ has no repeated eigenvalues and rely on eigendecomposition. When ƒ has repeated eigenvalues, we compute the integrals by using the uniformization approach [26,27].…”

Section: Inner Expectations: Conditional Moments Of Occupancy Duratiomentioning

confidence: 99%

Fitting and interpreting continuous‐time latent Markov models for panel data

Lange

Minin

2013

Statistics in Medicine

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Multistate models are used to characterize disease processes within an individual. Clinical studies often observe the disease status of individuals at discrete time points, making exact times of transitions between disease states unknown. Such panel data pose considerable modeling challenges. Assuming the disease process progresses according a standard continuous-time Markov chain (CTMC) yields tractable likelihoods, but the assumption of exponential sojourn time distributions is typically unrealistic. More flexible semi-Markov models permit generic sojourn distributions yet yield intractable likelihoods for panel data in the presence of reversible transitions. One attractive alternative is to assume that the disease process is characterized by an underlying latent CTMC, with multiple latent states mapping to each disease state. These models retain analytic tractability due to the CTMC framework but allow for flexible, duration-dependent disease state sojourn distributions. We have developed a robust and efficient expectation-maximization (EM) algorithm in this context. Our complete data state space consists of the observed data and the underlying latent trajectory, yielding computationally efficient expectation and maximization steps. Our algorithm outperforms alternative methods measured in terms of time to convergence and robustness. We also examine the frequentist performance of latent CTMC point and interval estimates of disease process functionals based on simulated data. The performance of estimates depends on time, functional, and data-generating scenario. Finally, we illustrate the interpretive power of latent CTMC models for describing disease processes on a data-set of lung transplant patients. We hope our work will encourage wider use of these models in the biomedical setting.

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A stochastic Expectation–Maximisation (EM) algorithm for construction of mortality tables

Esparza

Baltazar-Larios

2017

Ann. actuar. sci.

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In this paper, we present an extension of the model proposed by Lin & Liu that uses the concept of physiological age to model the ageing process by using phase-type distributions to calculate the probability of death. We propose a finite-state Markov jump process to model the hypothetical ageing process in which it is possible the transition rates between non-consecutive physiological ages. Since the Markov process has only a single absorbing state, the death time follows a phase-type distribution. Thus, to build a mortality table the challenge is to estimate this matrix based on the records of the ageing process. Considering the nature of the data, we consider two cases: having continuous time information of the ageing process, and the more interesting and realistic case, having reports of the process just in determined times. If the ageing process is only observed at discrete time points we have a missing data problem, thus, we use a stochastic Expectation–Maximisation (SEM) algorithm to find the maximum likelihood estimator of the intensity matrix. And in order to do that, we build Markov bridges which are sampled using the Bisection method. The theory is illustrated by a simulation study and used to fit real data.

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Fisher information and statistical inference for phase-type distributions

Cited by 5 publications

References 4 publications

Estimating the Parameters of Mixed Shifted Negative Binomial Distributions via an EM Algorithm

Estimating the Parameters of Mixed Shifted Negative Binomial Distributions via an EM Algorithm

Fitting and interpreting continuous‐time latent Markov models for panel data

A stochastic Expectation–Maximisation (EM) algorithm for construction of mortality tables

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