Page 682 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 682
STATISTICS AND FINANCIAL MATHEMATICS
Theorem 1. If the functions f and rj are differentiable w.r.t. their inputs, then we have
∂f (x) = ∇jf (x)T Jjc (xj , u) or ∂f (x) = ∇jf (x)T Jjc xj, rj−1(x∼j) ; (1)
∂xj ∂xj (2)
∂f (x) = ∇jf (x)T Jwc k xj, rj−1(x∼j) ∀ k ∈ {1, . . . d − 1} .
∂xwk
References
[1] M. Lamboni. Practical dependency models for sensitivity analysis with dependent vari-
ables, submitted to MCS.
[2] G. L. O’Brien, The comparison method for stochastic processes, The Annals of Probability
3 (1) (1975) 80-88
[3] E. Arjas, T. Lehtonen, Approximating many server queues by means of single server
queues, Mathematics of Operations Research 3 (1978) 205-223.
[4] L. Rüschendorf, Stochastically ordered distributions and monotonicity of the oc-function
of sequential probability ratio tests, Series Statistics 12 (3) (1981) 327-338.
[5] A. V. Skorohod, On a representation of random variables, Theory Probab. Appl. 21 (3)
(1976) 645-648.
[6] L. Rüschendorf, V. de Valk, On regression representations of stochastic processes,
Stochastic Processes and their Applications 46 (2) (1993) 183-198.
[7] M. Lamboni and S. Kucherenko, Multivariate sensitivity analysis and derivative-based
global sensitivity measures with dependent variables, Reliability Engineering and System
Safety, Volume 212, (2021) 107519.
Initial data analysis for longitudinal data – a general framework
Lara Lusa, lara.lusa@famnit.upr.si
University of Primorska, Slovenia
Coauthor: Marianne Huebner
Systematic initial data analysis (IDA) and clear reporting of the findings is an important step
towards reproducible research. A general framework of IDA for observational studies was
proposed to include data cleaning, data screening, and possible refinements of the preplanned
analyses (Huebner 2018). Longitudinal studies, where participants are observed repeatedly over
time, have special features that should be taken into account in the IDA steps before addressing
the research question. Our aim was to propose a framework for IDA in longitudinal studies.
Based on the IDA framework from Huebner et al. (2018) we refined it for use in longitudinal
studies and provided guidance on how to prepare an IDA plan for longitudinal studies. The
framework includes several steps that are specific to longitudinal data, or bear greater impor-
tance when data are longitudinal. Appropriate numerical and graphical tools for longitudinal
data allow the researchers to conduct IDA in a reproducible manner to avoid non-transparent
impact on the interpretation of model results. For example, in the framework we propose how
680
Theorem 1. If the functions f and rj are differentiable w.r.t. their inputs, then we have
∂f (x) = ∇jf (x)T Jjc (xj , u) or ∂f (x) = ∇jf (x)T Jjc xj, rj−1(x∼j) ; (1)
∂xj ∂xj (2)
∂f (x) = ∇jf (x)T Jwc k xj, rj−1(x∼j) ∀ k ∈ {1, . . . d − 1} .
∂xwk
References
[1] M. Lamboni. Practical dependency models for sensitivity analysis with dependent vari-
ables, submitted to MCS.
[2] G. L. O’Brien, The comparison method for stochastic processes, The Annals of Probability
3 (1) (1975) 80-88
[3] E. Arjas, T. Lehtonen, Approximating many server queues by means of single server
queues, Mathematics of Operations Research 3 (1978) 205-223.
[4] L. Rüschendorf, Stochastically ordered distributions and monotonicity of the oc-function
of sequential probability ratio tests, Series Statistics 12 (3) (1981) 327-338.
[5] A. V. Skorohod, On a representation of random variables, Theory Probab. Appl. 21 (3)
(1976) 645-648.
[6] L. Rüschendorf, V. de Valk, On regression representations of stochastic processes,
Stochastic Processes and their Applications 46 (2) (1993) 183-198.
[7] M. Lamboni and S. Kucherenko, Multivariate sensitivity analysis and derivative-based
global sensitivity measures with dependent variables, Reliability Engineering and System
Safety, Volume 212, (2021) 107519.
Initial data analysis for longitudinal data – a general framework
Lara Lusa, lara.lusa@famnit.upr.si
University of Primorska, Slovenia
Coauthor: Marianne Huebner
Systematic initial data analysis (IDA) and clear reporting of the findings is an important step
towards reproducible research. A general framework of IDA for observational studies was
proposed to include data cleaning, data screening, and possible refinements of the preplanned
analyses (Huebner 2018). Longitudinal studies, where participants are observed repeatedly over
time, have special features that should be taken into account in the IDA steps before addressing
the research question. Our aim was to propose a framework for IDA in longitudinal studies.
Based on the IDA framework from Huebner et al. (2018) we refined it for use in longitudinal
studies and provided guidance on how to prepare an IDA plan for longitudinal studies. The
framework includes several steps that are specific to longitudinal data, or bear greater impor-
tance when data are longitudinal. Appropriate numerical and graphical tools for longitudinal
data allow the researchers to conduct IDA in a reproducible manner to avoid non-transparent
impact on the interpretation of model results. For example, in the framework we propose how
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