Stochastic monotonicity and conditional Monte Carlo for likelihood ratios

Likelihood ratios are used in computer simulation to estimate expectations with respect to one law from simulation of another. This importance sampling technique can be implemented with either the likelihood ratio at the end of the simulated time horizon or with a sequence of likelihood ratios at intermediate times. Since a likelihood ratio process is a martingale, the intermediate values are conditional expectations of the final value and their use introduces no bias.We provide conditions under which using conditional expectations in this way brings guaranteed variance reduction. We use stochastic orderings to get positive dependence between a process and its likelihood ratio, from which variance reduction follows. Our analysis supports the following rough statement: for increasing functionals of associated processes with monotone likelihood ratio, conditioning helps. Examples are drawn from recursively defined processes, Markov chains in discrete and continuous time, and processes with Poisson input.

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Stochastic monotonicity and conditional Monte Carlo for likelihood ratios

Advances in Applied Probability ◽

10.1017/s0001867800025192 ◽

1993 ◽

Vol 25 (01) ◽

pp. 103-115 ◽

Cited By ~ 1

Author(s):

Paul Glasserman

Keyword(s):

Likelihood Ratio ◽

Variance Reduction ◽

Stochastic Monotonicity ◽

Likelihood Ratios ◽

Monotone Likelihood Ratio ◽

Positive Dependence ◽

Poisson Input ◽

Conditional Expectations ◽

Conditional Monte Carlo ◽

Simulated Time

Likelihood ratios are used in computer simulation to estimate expectations with respect to one law from simulation of another. This importance sampling technique can be implemented with either the likelihood ratio at the end of the simulated time horizon or with a sequence of likelihood ratios at intermediate times. Since a likelihood ratio process is a martingale, the intermediate values are conditional expectations of the final value and their use introduces no bias. We provide conditions under which using conditional expectations in this way brings guaranteed variance reduction. We use stochastic orderings to get positive dependence between a process and its likelihood ratio, from which variance reduction follows. Our analysis supports the following rough statement: for increasing functionals of associated processes with monotone likelihood ratio, conditioning helps. Examples are drawn from recursively defined processes, Markov chains in discrete and continuous time, and processes with Poisson input.

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Dependence ordering for Markov processes on partially ordered spaces

Journal of Applied Probability ◽

10.1239/jap/1158784947 ◽

2006 ◽

Vol 43 (3) ◽

pp. 793-814 ◽

Cited By ~ 5

Author(s):

Hans Daduna ◽

Ryszard Szekli

Keyword(s):

Markov Processes ◽

Variance Reduction ◽

Transition Probabilities ◽

Asymptotic Variance ◽

Sufficient Conditions ◽

Stochastic Monotonicity ◽

Positive Dependence ◽

Partially Ordered ◽

Monotonicity Assumption ◽

Concordance Order

We compare dependence in stochastically monotone Markov processes with partially ordered Polish state spaces using the concordance and supermodular orders. We show necessary and sufficient conditions for the concordance order to hold both in terms of the one-step transition probabilities for discrete-time processes and in terms of the corresponding infinitesimal generators for continuous-time processes. We give examples showing that a stochastic monotonicity assumption is not necessary for such orderings. We indicate relations between dependence orderings and, variously, the asymptotic variance-reduction effect in Monte Carlo Markov chains, Cheeger constants, and positive dependence for Markov processes.

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Dependence ordering for Markov processes on partially ordered spaces

Journal of Applied Probability ◽

10.1017/s0021900200002114 ◽

2006 ◽

Vol 43 (03) ◽

pp. 793-814 ◽

Cited By ~ 2

Author(s):

Hans Daduna ◽

Ryszard Szekli

Keyword(s):

Markov Processes ◽

Variance Reduction ◽

Transition Probabilities ◽

Asymptotic Variance ◽

Sufficient Conditions ◽

Stochastic Monotonicity ◽

Positive Dependence ◽

Partially Ordered ◽

Monotonicity Assumption ◽

Concordance Order

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Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches

Universe ◽

10.3390/universe7060174 ◽

2021 ◽

Vol 7 (6) ◽

pp. 174

Author(s):

Karl Wette

Keyword(s):

Gravitational Wave ◽

Likelihood Ratio ◽

Signal To Noise Ratio ◽

Geometric Approach ◽

The Other ◽

Efficient Computation ◽

Likelihood Ratios ◽

Signal To Noise ◽

Noise Ratio ◽

Optimal Signal

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or F-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the F-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios had identical detection power to the F-statistic. This approach demonstrates a route to viewing the F-statistic in a Bayesian context, while retaining the advantages of its efficient computation.

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Restrictive spirometric pattern and true pulmonary restriction in a general population sample aged 50 - 64 years

BMC Pulmonary Medicine ◽

10.1186/s12890-020-1096-z ◽

2020 ◽

Vol 20 (1) ◽

Cited By ~ 3

Author(s):

Kjell Torén ◽

Linus Schiöler ◽

Jonas Brisman ◽

Andrei Malinovschi ◽

Anna-Carin Olin ◽

...

Keyword(s):

General Population ◽

Likelihood Ratio ◽

Population Sample ◽

Positive Likelihood Ratio ◽

Negative Likelihood Ratio ◽

Population Based ◽

Forced Expiratory Volume ◽

Likelihood Ratios ◽

Volume Determination ◽

Total Lung Volume

Abstract Background There is low diagnostic accuracy of the proxy restrictive spirometric pattern (RSP) to identify true pulmonary restriction. This knowledge is based on patients referred for spirometry and total lung volume determination by plethysmograpy, single breath nitrogen washout technique or gas dilution and selected controls. There is, however, a lack of data from general populations analyzing whether RSP is a valid proxy for true pulmonary restriction. We have validated RSP in relation to true pulmonary restriction in a general population where we have access to measurements of total lung capacity (TLC) and spirometry. Methods The data was from the Swedish CArdioPulmonary bioImage Study (SCAPIS Pilot), a general population-based study, comprising 983 adults aged 50–64. All subjects answered a respiratory questionnaire. Forced expiratory volume in 1 s (FEV1) and forced vital capacity (FVC) were obtained before and after bronchodilation. TLC and residual volume (RV) was recorded using a body plethysmograph. All lung function values are generally expressed as percent predicted (% predicted) or in relation to lower limits of normal (LLN). True pulmonary restriction was defined as TLC < LLN5 defined as a Z score < − 1.645, i e the fifth percentile. RSP was defined as FEV1/FVC ≥ LLN and FVC < LLN after bronchodilation. Specificity, sensitivity, positive and negative likelihood ratios were calculated, and 95% confidence intervals (CIs) were calculated. Results The prevalence of true pulmonary restriction was 5.4%, and the prevalence of RSP was 3.4%. The sensitivity of RSP to identify true pulmonary restriction was 0.34 (0.20–0.46), the corresponding specificity was 0.98 (0.97–0.99), and the positive likelihood ratio was 21.1 (11.3–39.4) and the negative likelihood ratio was 0.67 (0.55–0.81). Conclusions RSP has low accuracy for identifying true pulmonary restriction. The results support previous observations that RSP is useful for ruling out true pulmonary restriction.

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Alanina aminotransferasa como marcador en el diagnóstico de síndrome metabólico y riesgo cardiovascular en niños con obesidad

ACTA MEDICA PERUANA ◽

10.35663/amp.2019.364.897 ◽

2019 ◽

Vol 36 (4) ◽

pp. 253-8

Author(s):

Ysel Cabrera ◽

Melissa Martínez ◽

Almendra Cabello ◽

Samuel Pereyra ◽

...

Keyword(s):

Likelihood Ratio ◽

Likelihood Ratios ◽

Síndrome Metabólico

Objetivo: Evaluar la alanina aminotransferasa (ALT) como marcador en el diagnóstico de síndrome metabólico (SM) y riesgo cardiovascular (RCV) en niños con obesidad exógena.Materiales y métodos: Estudio transversal. Se incluyeron niños con obesidad exógena de 2 a 14 años, atendidos en la Unidad de Endocrinología Pediátrica del Hospital NacionalCayetano Heredia, entre el 2014 al 2018. Se definió enfermedad hepática no alcohólica (EHNA) considerando dos puntos de corte de ALT; en mujeres: >22,1U/L y >44U/L, en varones: >25,8U/L y >50U/L. Se definió SM según la Academia Americana de Pediatría y RCV con TG/HDL-C ≥3,5. Aplicamos Chi cuadrado, considerándose significativo p<0,05. Estimamos sensibilidad(S), especificidad (E) y likelihood ratios (LR). Resultados: Se incluyeron 347 niños obesos (54,7% varones). La frecuencia de EHNA fue de 23,1%. La sensibilidad y especificidad para el diagnóstico de SM con ALT >22,1U/L y >25,8U/L fue 79,4% y 37,6% respectivamente y, con ALT>44U/L y >50U/L fue 28,6% y 83,3%. La ALT con punto de corte mayor en conjunto con TG/HDL-C≥3,5 mostró una especificidad del 96,9% y un likelihood ratio + (LR+) de 6,7. Conclusión: La ALT con un punto de corte >44U/L en mujeres y >50U/L en varones, es un marcador bioquímico útil en la identificación de SM y riesgo cardiovascular en niños con obesidad exógena desde los primeros años de vida.

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Probabilistic Evaluation of SMS Messages as Forensic Evidence

Emerging Digital Forensics Applications for Crime Detection, Prevention, and Security ◽

10.4018/978-1-4666-4006-1.ch010 ◽

2013 ◽

pp. 138-149

Author(s):

Shunichi Ishihara

Keyword(s):

Likelihood Ratio ◽

Low Cost ◽

Scientific Evidence ◽

Short Message ◽

Likelihood Ratios ◽

Forensic Evidence ◽

Probabilistic Evaluation ◽

Popular Medium ◽

Log Likelihood ◽

Message Service

This study is one of the first likelihood ratio-based forensic text comparison studies in forensic authorship analysis. The likelihood-ratio-based evaluation of scientific evidence has started being adopted in many disciplines of forensic evidence comparison sciences, such as DNA, handwriting, fingerprints, footwear, voice recording, etc., and it is largely accepted that this is the way to ensure the maximum accountability and transparency of the process. Due to its convenience and low cost, short message service (SMS) has been a very popular medium of communication for quite some time. Unfortunately, however, SMS messages are sometimes used for reprehensible purposes, e.g., communication between drug dealers and buyers, or in illicit acts such as extortion, fraud, scams, hoaxes, and false reports of terrorist threats. In this study, the author performs a likelihood-ratio-based forensic text comparison of SMS messages focusing on lexical features. The likelihood ratios (LRs) are calculated in Aitken and Lucy’s (2004) multivariate kernel density procedure, and are calibrated. The validity of the system is assessed based on the magnitude of the LRs using the log-likelihood-ratio cost (Cllr). The strength of the derived LRs is graphically presented in Tippett plots. The results of the current study are compared with those of previous studies.

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Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

Sustainability ◽

10.3390/su11030815 ◽

2019 ◽

Vol 11 (3) ◽

pp. 815 ◽

Cited By ~ 1

Author(s):

Yijuan Liang ◽

Xiuchuan Xu

Keyword(s):

Monte Carlo ◽

Variance Reduction ◽

Convergence Rates ◽

Option Price ◽

Correlation Coefficients ◽

Control Variate ◽

Stochastic Volatilities ◽

Conditional Monte Carlo ◽

Mc Simulation ◽

Martingale Representation Theorem

Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

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