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Andrey Novikov - One of the best experts on this subject based on the ideXlab platform.
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Sequential Hypothesis tests under random horizon
Sequential Analysis, 2020Co-Authors: Andrey Novikov, Juan Luis Palacios-sotoAbstract:We consider a problem of sequential testing a Simple Hypothesis against a Simple alternative, based on observations of a discrete-time stochastic process X 1 , X 2 , … , in the presence of a random...
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Locally Most Powerful Sequential Tests of a Simple Hypothesis vs. One-Sided Alternatives for Independent Observations
Theory of Probability & Its Applications, 2012Co-Authors: Andrey Novikov, P. A. NovikovAbstract:Let a stochastic process with independent values $X_1,X_2,\dots, X_n,\dots$ be observed and let its distribution $P_\theta$ depend on an unknown parameter $\theta$. In this paper we consider the problem of testing a Simple Hypothesis $H_0:\theta=\theta_0$ vs. a composite alternative $H_1:\theta>\theta_0$, where $\theta_0\in\Theta$ is a fixed value of the parameter. In the first part of this work we present conditions for differentiability (at $\theta_0$) of the power function of any sequential test and obtain some inequalities of informational type relating the average sample number with the type-I probability error to the derivative of the power function of sequential tests. In the second part of the work we characterize the structure of locally most powerful (in the sense of Berk [Ann. Statist., 3 (1975), pp. 373--381]) sequential tests in this problem (maximizing derivative of a power function under given constraints on the type-I probability error and the average sample number).
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Locally most powerful sequential tests of a Simple Hypothesis vs. One-sided alternatives for independent observations
arXiv: Methodology, 2010Co-Authors: Andrey Novikov, P. A. NovikovAbstract:Let $X_1,X_2,..., X_n,...$ be a stochastic process with independent values whose distribution $P_\theta$ depends on an unknown parameter $\theta$, $\theta\in\Theta$, where $\Theta$ is an open subset of the real line. The problem of testing $H_0:$ $\theta=\theta_0$ vs. a composite alternative $H_1:$ $\theta>\theta_0$ is considered, where $\theta_0\in\Theta$ is a fixed value of the parameter. The main objective of this work is the characterization of the structure of the locally most powerful (in the sense of Berk) sequential tests in this problem.
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Locally Most Powerful Sequential Tests of a Simple Hypothesis vs One-Sided Alternatives
Journal of Statistical Planning and Inference, 2010Co-Authors: Andrey Novikov, Petr NovikovAbstract:Abstract Let X 1 , X 2 , … be a discrete-time stochastic process with a distribution P θ , θ ∈ Θ , where Θ is an open subset of the real line. We consider the problem of testing a Simple Hypothesis H 0 : θ = θ 0 vs. a composite alternative H 1 : θ > θ 0 , where θ 0 ∈ Θ is some fixed point. The main goal of this article is to characterize the structure of locally most powerful sequential tests in this problem. For any sequential test ( ψ , φ ) with a (randomized) stopping rule ψ and a (randomized) decision rule φ let α ( ψ , φ ) be the type I error probability, β ˙ 0 ( ψ , φ ) the derivative, at θ = θ 0 , of the power function, and N ( ψ ) an average sample number of the test ( ψ , φ ) . Then we are concerned with the problem of maximizing β ˙ 0 ( ψ , φ ) in the class of all sequential tests such that α ( ψ , φ ) ≤ α and N ( ψ ) ≤ N , where α ∈ [ 0 , 1 ] and N ≥ 1 are some restrictions. It is supposed that N ( ψ ) is calculated under some fixed (not necessarily coinciding with one of P θ ) distribution of the process X 1 , X 2 , … . The structure of optimal sequential tests is characterized.
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Optimal Sequential Testing of Two Simple Hypotheses in Presence of Control Variables
arXiv: Statistics Theory, 2008Co-Authors: Andrey NovikovAbstract:Suppose that at any stage of a statistical experiment a control variable X that affects the distribution of the observed data Y can be used. The distribution of Y depends on some unknown parameter �, and we consider the classical problem of testing a Simple Hypothesis H0 : � = �0 against a Simple alternative H1 : � = �1 allowing the data to be controlled by X, in the following sequential context. The experiment starts with assigning a value X1 to the control variable and observing Y1 as a response. After some analysis, we choose another value X2 for the control variable, and observe Y2 as a response, etc. It is supposed that the experiment eventually stops, and at that moment a final decision in favour of H0 or H1 is to be taken. In this article, our aim is to characterize the structure of optimal sequential procedures, based on this type of data, for testing a Simple Hypothesis against a Simple alternative. Mathematics Subject Classification: 62L10, 62L15, 60G40, 62C99, 93E20
Robert L Wolpert - One of the best experts on this subject based on the ideXlab platform.
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a unified conditional frequentist and bayesian test for fixed and sequential Simple Hypothesis testing
Annals of Statistics, 1994Co-Authors: James O. Berger, Lawrence D Brown, Robert L WolpertAbstract:Preexperimental frequentist error probabilities are arguably inadequate, as summaries of evidence from data, in many Hypothesis-testing settings. The conditional frequentist may respond to this by identifying certain subsets of the outcome space and reporting a conditional error probability, given the subset of the outcome space in which the observed data lie. Statistical methods consistent with the likelihood principle, including Bayesian methods, avoid the problem by a more extreme form of conditioning. In tits paper we prove that the conditional frequentist's method can be made exactly equivalent to the Bayesian's in Simple versus Simple Hypothesis testing: specifically, we find a conditioning strategy for which the conditional frequentist's reported conditional error probabilities are the same as the Bayesian's posterior probabilities of error. A conditional frequentist who uses such a strategy can exploit other features of the Bayesian approachfor example, the validity of sequential Hypothesis tests (including versions of the sequential probability ratio test, or SPRT) even if the stopping rule is incompletely specified
Pier Paolo Piccaluga - One of the best experts on this subject based on the ideXlab platform.
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Cross-Immunization Against Respiratory Coronaviruses May Protect Children From SARS-CoV2: More Than a Simple Hypothesis?
Frontiers in Pediatrics, 2021Co-Authors: Pier Paolo Piccaluga, Giovanni Malerba, Mohsen Navari, Erica Diani, Ercole Concia, Davide GibelliniAbstract:In January 2020, a new coronavirus was identified as responsible for a pandemic acute respiratory syndrome. The virus demonstrated a high infectious capability and not-neglectable mortality in humans. However, similarly to previous SARS and MERS, the new disease COVID-19 caused by SARS-CoV-2 seemed to relatively spare children and younger adults. Some hypotheses have been proposed to explain the phenomenon, including lower ACE2 expression in children, cross-immunization from measles/rubella/mumps and BCG-vaccination, as well as the integrity of respiratory mucosa. Herein, we hypothesize that an additional mechanism might contribute to children's relative protection from SARS-CoV-2, the cross-immunization conferred by previous exposures to other common respiratory coronaviruses. To support our Hypothesis, we show a statistically significant similarity in genomic and protein sequences, including epitopes for B- and T-cell immunity, of SARS-CoV-2 and the other beta coronaviruses. Since these coronaviruses are highly diffused across pediatric populations, cross-reactive immunity might reasonably induce an at least partial protection from SARS-CoV-2 in children.
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cross immunization against respiratory coronaviruses may protect children from sars cov2 more than a Simple Hypothesis
Frontiers in Pediatrics, 2021Co-Authors: Pier Paolo Piccaluga, Giovanni Malerba, Mohsen Navari, Erica Diani, Ercole Concia, Davide GibelliniAbstract:In January 2020, a new coronavirus was identified as responsible for a pandemic acute respiratory syndrome. The virus demonstrated a high infectious capability and not neglectable mortality in humans. However, similarly to previous SARS and MERS, the new disease Covid-19 caused by SARS-CoV2 seemed to relatively spare children and younger adults. Some hypotheses have been proposed to explain the phenomenon, including lower ACE2 expression in children, cross-immunization from measles/rubella/mumps and BCG-vaccination, as well as the integrity of respiratory mucosa. Herein, we hypothesize that an additional mechanism might contribute to the children relative protection from SARS-CoV2, the cross immunization conferred by previous exposures to other common respiratory coronaviruses. To support our Hypothesis, we show a statistically significant similarity in genomic and protein sequences, including epitopes for B- and T-cell immunity, of SARS-CoV2 and the other beta coronaviruses. Since these coronaviruses are highly diffused across pediatric populations, cross-reactive immunity might reasonably induce an at least partial protection from SARS-CoV2 in children.
Davide Gibellini - One of the best experts on this subject based on the ideXlab platform.
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Cross-Immunization Against Respiratory Coronaviruses May Protect Children From SARS-CoV2: More Than a Simple Hypothesis?
Frontiers in Pediatrics, 2021Co-Authors: Pier Paolo Piccaluga, Giovanni Malerba, Mohsen Navari, Erica Diani, Ercole Concia, Davide GibelliniAbstract:In January 2020, a new coronavirus was identified as responsible for a pandemic acute respiratory syndrome. The virus demonstrated a high infectious capability and not-neglectable mortality in humans. However, similarly to previous SARS and MERS, the new disease COVID-19 caused by SARS-CoV-2 seemed to relatively spare children and younger adults. Some hypotheses have been proposed to explain the phenomenon, including lower ACE2 expression in children, cross-immunization from measles/rubella/mumps and BCG-vaccination, as well as the integrity of respiratory mucosa. Herein, we hypothesize that an additional mechanism might contribute to children's relative protection from SARS-CoV-2, the cross-immunization conferred by previous exposures to other common respiratory coronaviruses. To support our Hypothesis, we show a statistically significant similarity in genomic and protein sequences, including epitopes for B- and T-cell immunity, of SARS-CoV-2 and the other beta coronaviruses. Since these coronaviruses are highly diffused across pediatric populations, cross-reactive immunity might reasonably induce an at least partial protection from SARS-CoV-2 in children.
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cross immunization against respiratory coronaviruses may protect children from sars cov2 more than a Simple Hypothesis
Frontiers in Pediatrics, 2021Co-Authors: Pier Paolo Piccaluga, Giovanni Malerba, Mohsen Navari, Erica Diani, Ercole Concia, Davide GibelliniAbstract:In January 2020, a new coronavirus was identified as responsible for a pandemic acute respiratory syndrome. The virus demonstrated a high infectious capability and not neglectable mortality in humans. However, similarly to previous SARS and MERS, the new disease Covid-19 caused by SARS-CoV2 seemed to relatively spare children and younger adults. Some hypotheses have been proposed to explain the phenomenon, including lower ACE2 expression in children, cross-immunization from measles/rubella/mumps and BCG-vaccination, as well as the integrity of respiratory mucosa. Herein, we hypothesize that an additional mechanism might contribute to the children relative protection from SARS-CoV2, the cross immunization conferred by previous exposures to other common respiratory coronaviruses. To support our Hypothesis, we show a statistically significant similarity in genomic and protein sequences, including epitopes for B- and T-cell immunity, of SARS-CoV2 and the other beta coronaviruses. Since these coronaviruses are highly diffused across pediatric populations, cross-reactive immunity might reasonably induce an at least partial protection from SARS-CoV2 in children.
James O. Berger - One of the best experts on this subject based on the ideXlab platform.
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a unified conditional frequentist and bayesian test for fixed and sequential Simple Hypothesis testing
Annals of Statistics, 1994Co-Authors: James O. Berger, Lawrence D Brown, Robert L WolpertAbstract:Preexperimental frequentist error probabilities are arguably inadequate, as summaries of evidence from data, in many Hypothesis-testing settings. The conditional frequentist may respond to this by identifying certain subsets of the outcome space and reporting a conditional error probability, given the subset of the outcome space in which the observed data lie. Statistical methods consistent with the likelihood principle, including Bayesian methods, avoid the problem by a more extreme form of conditioning. In tits paper we prove that the conditional frequentist's method can be made exactly equivalent to the Bayesian's in Simple versus Simple Hypothesis testing: specifically, we find a conditioning strategy for which the conditional frequentist's reported conditional error probabilities are the same as the Bayesian's posterior probabilities of error. A conditional frequentist who uses such a strategy can exploit other features of the Bayesian approachfor example, the validity of sequential Hypothesis tests (including versions of the sequential probability ratio test, or SPRT) even if the stopping rule is incompletely specified
