scholarly journals Fair Cake Division Under Monotone Likelihood Ratios

2021 ◽  
Author(s):  
Siddharth Barman ◽  
Nidhi Rathi
Keyword(s):  
Lipschitz Constant ◽  
Concave Function ◽  
Likelihood Ratios ◽  
Exponential Distributions ◽  
Monotone Likelihood Ratio ◽  
Cake Cutting ◽  
Bit Complexity ◽  
Arbitrary Precision ◽  
Cutting Problem ◽  
Positive Results

This work develops algorithmic results for the classic cake-cutting problem in which a divisible, heterogeneous resource (modeled as a cake) needs to be partitioned among agents with distinct preferences. We focus on a standard formulation of cake cutting wherein each agent must receive a contiguous piece of the cake. Although multiple hardness results exist in this setup for finding fair/efficient cake divisions, we show that, if the value densities of the agents satisfy the monotone likelihood ratio property (MLRP), then strong algorithmic results hold for various notions of fairness and economic efficiency. Addressing cake-cutting instances with MLRP, first we develop an algorithm that finds cake divisions (with connected pieces) that are envy free, up to an arbitrary precision. The time complexity of our algorithm is polynomial in the number of agents and the bit complexity of an underlying Lipschitz constant. We obtain similar positive results for maximizing social, egalitarian, and Nash social welfare. Many distribution families bear MLRP. In particular, this property holds if all the value densities belong to any one of the following families: Gaussian (with the same variance), linear, Poisson, and exponential distributions, linear translations of any log-concave function. Hence, through MLRP, the current work obtains novel cake-cutting algorithms for multiple distribution families.

scholarly journals Deterministic, Strategyproof, and Fair Cake Cutting

2017 ◽  
Author(s):  
Vijay Menon ◽  
Kate Larson
Keyword(s):  
Mechanism Design ◽  
Impossibility Result ◽  
Restricted Class ◽  
Piecewise Constant ◽  
Incentive Compatible ◽  
Negative Results ◽  
Cake Cutting ◽  
Design Perspective ◽  
A Minor ◽  
Cutting Problem

We study the classic cake cutting problem from a mechanism design perspective, in particular focusing on deterministic mechanisms that are strategyproof and fair. We begin by looking at mechanisms that are non-wasteful and primarily show that for even the restricted class of piecewise constant valuations there exists no direct-revelation mechanism that is strategyproof and even approximately proportional. Subsequently, we remove the non-wasteful constraint and show another impossibility result stating that there is no strategyproof and approximately proportional direct-revelation mechanism that outputs contiguous allocations, again, for even the restricted class of piecewise constant valuations. In addition to the above results, we also present some negative results when considering an approximate notion of strategyproofness, show a connection between direct-revelation mechanisms and mechanisms in the Robertson-Webb model when agents have piecewise constant valuations, and finally also present a (minor) modification to the well-known Even-Paz algorithm that has better incentive-compatible properties for the cases when there are two or three agents.

scholarly journals On the Complexity of Chore Division

2018 ◽  
Author(s):  
Alireza Farhadi ◽  
MohammadTaghi Hajiaghayi
Keyword(s):  
Lower Bound ◽  
Division Problem ◽  
Cake Cutting ◽  
Cutting Problem ◽  
Cutting Problems

We study the proportional chore division problem where a protocol wants to divide an undesirable object, called chore, among n different players. This problem is the dual variant of the cake cutting problem in which we want to allocate a desirable object. In this paper, we show that chore division and cake cutting problems are closely related to each other and provide a tight lower bound for proportional chore division.

Stochastic monotonicity and conditional Monte Carlo for likelihood ratios

1993 ◽  
Vol 25 (01) ◽  
pp. 103-115 ◽  
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.

Stochastic monotonicity and conditional Monte Carlo for likelihood ratios

1993 ◽  
Vol 25 (1) ◽  
pp. 103-115 ◽  
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.

scholarly journals Evaluation of antigen detection and antibody detection tests for Trypanosoma evansi infections of buffaloes in Indonesia

1999 ◽  
Vol 123 (1) ◽  
pp. 149-155 ◽  
Author(s):  
H. C. DAVISON ◽  
M. V. THRUSFIELD ◽  
S. MUHARSINI ◽  
A. HUSEIN ◽  
S. PARTOUTOMO ◽  
...  
Keyword(s):  
Operating Characteristic ◽  
False Negative ◽  
Trypanosoma Evansi ◽  
Antibody Detection ◽  
Test Results ◽  
Likelihood Ratios ◽  
Significant Difference ◽  
Post Test ◽  
Positive Results ◽  
Rule Out

Two Ag-ELISAs, an IgG-specific antibody detection ELISA (IgG ELISA) and a card agglutination test (CATT) for the detection of Trypanasoma evansi infections in buffaloes in Indonesia, were compared. Diagnostic sensitivity estimates were obtained by testing sera from 139 Indonesian buffaloes which had been found to be infected by parasitological tests. Diagnostic specificity was estimated by testing sera from 263 buffaloes living in Australia. Response-operating characteristic curves were constructed, and optimal ELISA cut-off values, which minimized the number of false–negative and false–positive results, were chosen. The IgG ELISA had the highest sensitivity (89%) and the CATT had the highest specificity (100%). There was a significant difference between the sensitivities (71 and 81%), but not between the specificities (75 and 78%), of the two Ag-ELISAs. The four tests were further compared by calculation of post-test probabilities of infection for positive and negative test results using a range of prevalence values, and likelihood ratios. The results suggested that the CATT was the best test to ‘rule-in’ infection (i.e. the highest probability of infection in test-positive animals) and the IgG ELISA was the best test to ‘rule-out’ infection (i.e. the lowest probability of infection in test-negative animals).

Sentence Repetition: A Clinical Marker for Developmental Language Disorder in Danish

2019 ◽  
Vol 62 (12) ◽  
pp. 4450-4463
Author(s):  
Rikke Vang Christensen
Keyword(s):  
Language Disorder ◽  
Future Research ◽  
Typically Developing ◽  
Developmental Language Disorder ◽  
Older Children ◽  
Likelihood Ratios ◽  
Clinical Marker ◽  
Sentence Repetition ◽  
Good Identification ◽  
Syntactic Properties

Purpose The aim of the study was to explore the potential of performance on a Danish sentence repetition (SR) task—including specific morphological and syntactic properties—to identify difficulties in children with developmental language disorder (DLD) relative to typically developing (TD) children. Furthermore, the potential of the task as a clinical marker for Danish DLD was explored. Method SR performance of children with DLD aged 5;10–14;1 (years;months; n = 27) and TD children aged 5;3–13;4 ( n = 87) was investigated. Results Compared to TD same-age peers, children with DLD were less likely to repeat the sentences accurately but more likely to make ungrammatical errors with respect to verb inflection and use of determiners and personal pronouns. Younger children with DLD also produced more word order errors that their TD peers. Furthermore, older children with DLD performed less accurately than younger TD peers, indicating that the SR task taps into morphosyntactic areas of particular difficulty for Danish children with DLD. The classification accuracy associated with SR performance showed high levels of sensitivity and specificity (> 90%) and likelihood ratios indicating good identification potential for clinical and future research purposes. Conclusion SR performance has a strong potential for identifying children with DLD, also in Danish, and with a carefully designed SR task, performance has potential for revealing morphosyntactic difficulties. Supplemental Material https://doi.org/10.23641/asha.10314437

Clausal Density Between Ages 4 and 9 Years for the Edmonton Narrative Norms Instrument: Reference Data and Psychometric Properties

2020 ◽  
pp. 1-15
Author(s):  
Ling-Yu Guo ◽  
Phyllis Schneider ◽  
William Harrison
Keyword(s):  
Diagnostic Accuracy ◽  
Psychometric Properties ◽  
Language Impairment ◽  
Reference Data ◽  
Reliability And Validity ◽  
Correlation Coefficients ◽  
Criterion Validity ◽  
Likelihood Ratios ◽  
Generation Task ◽  
Sensitivity Specificity

Purpose This study provided reference data and examined psychometric properties for clausal density (CD; i.e., number of clauses per utterance) in children between ages 4 and 9 years from the database of the Edmonton Narrative Norms Instrument (ENNI). Method Participants in the ENNI database included 300 children with typical language (TL) and 77 children with language impairment (LI) between the ages of 4;0 (years;months) and 9;11. Narrative samples were collected using a story generation task, in which children were asked to tell stories based on six picture sequences. CD was computed from the narrative samples. The split-half reliability, concurrent criterion validity, and diagnostic accuracy were evaluated for CD by age. Results CD scores increased significantly between ages 4 and 9 years in children with TL and those with LI. Children with TL produced higher CD scores than those with LI at each age level. In addition, the correlation coefficients for the split-half reliability and concurrent criterion validity of CD scores were all significant at each age level, with the magnitude ranging from small to large. The diagnostic accuracy of CD scores, as revealed by sensitivity, specificity, and likelihood ratios, was poor. Conclusions The finding on diagnostic accuracy did not support the use of CD for identifying children with LI between ages 4 and 9 years. However, given the attested reliability and validity for CD, reference data of CD from the ENNI database can be used for evaluating children's difficulties with complex syntax and monitoring their change over time. Supplemental Material https://doi.org/10.23641/asha.13172129

Diagnostic accuracy of magnetic resonance angiography for acute pulmonary embolism - a systematic review and meta-analysis

VASA ◽  
2016 ◽  
Vol 45 (2) ◽  
pp. 149-154 ◽  
Author(s):  
Jie Li ◽  
Lei Feng ◽  
Jiangbo Li ◽  
Jian Tang
Keyword(s):  
Pulmonary Embolism ◽  
Magnetic Resonance ◽  
Magnetic Resonance Angiography ◽  
Diagnostic Accuracy ◽  
Acute Pulmonary Embolism ◽  
Meta Analysis ◽  
Likelihood Ratios ◽  
Summary Receiver Operating Characteristic ◽  
Acute Pe ◽  
Limited Sensitivity

Abstract. Background: The aim of this meta-analysis was to evaluate the diagnostic accuracy of magnetic resonance angiography (MRA) for acute pulmonary embolism (PE). Methods: A systematic literature search was conducted that included studies from January 2000 to August 2015 using the electronic databases PubMed, Embase and Springer link. The summary receiver operating characteristic (SROC) curve, sensitivity, specificity, positive likelihood ratios (PLR), negative likelihood ratios (NLR), and diagnostic odds ratio (DOR) as well as the 95 % confidence intervals (CIs) were calculated to evaluate the diagnostic accuracy of MRA for acute PE. Meta-disc software version 1.4 was used to analyze the data. Results: Five studies were included in this meta-analysis. The pooled sensitivity (86 %, 95 % CI: 81 % to 90 %) and specificity (99 %, 95 % CI: 98 % to 100 %) demonstrated that MRA diagnosis had limited sensitivity and high specificity in the detection of acute PE. The pooled estimate of PLR (41.64, 95 % CI: 17.97 to 96.48) and NLR (0.17, 95 % CI: 0.11 to 0.27) provided evidence for the low missed diagnosis and misdiagnosis rates of MRA for acute PE. The high diagnostic accuracy of MRA for acute PE was demonstrated by the overall DOR (456.51, 95 % CI: 178.38 - 1168.31) and SROC curves (AUC = 0.9902 ± 0.0061). Conclusions: MRA can be used for the diagnosis of acute PE. However, due to limited sensitivity, MRA cannot be used as a stand-alone test to exclude acute PE.

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