Computing Bonus–Malus Premiums under Partial Prior Information

ABSTRACTThe use of classical bonus–malus systems entails very high maluses and other problems which, during recent years, have been criticised by actuaries. To avoid these problems, new bonus–malus models have been developed. For instance, it is well known that the use of an exponential loss function reduces the differences between overcharges and undercharges, solving the problem of high maluses. In order to measure the sensitivity of the exponential bonus–malus system, and according to robust Bayesian analysis, we first model the structure function by specifying a subclass of the generalised moments class. We then examine the range of relativities for each prior. Finally, we illustrate our method with a numerical example based on real data.

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Robust Bayesian Analysis of Lifetime Data from Maxwell Distribution

Austrian Journal of Statistics ◽

10.17713/ajs.v47i4.692 ◽

2018 ◽

Vol 48 (1) ◽

pp. 38-55

Author(s):

M. S. Panwar ◽

Sanjeev K Tomer

Keyword(s):

Bayesian Analysis ◽

Real Data ◽

Type I ◽

Lifetime Data ◽

Maxwell Distribution ◽

Data Set ◽

Squared Error ◽

Robust Bayesian Analysis ◽

Linex Loss ◽

Mean Lifetime

In this paper, we consider robust Bayesian analysis of lifetime data from the Maxwell distribution assuming an $\varepsilon$-contamination class of prior distributions for the parameter. We obtain robust Bayes estimates of the parameter and mean lifetime under squared error and LINEX loss functions in presence of uncensored as well as Type-I progressively hybrid censored lifetime data. A real data set is analysed for numerical illustrations.

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Hands Stencils in El Castillo Cave (Puente Viesgo, Cantabria, Spain). An Interdisciplinary Study

Proceedings of the Prehistoric Society ◽

10.1017/ppr.2021.11 ◽

2021 ◽

pp. 1-21

Author(s):

Sergio Ripoll ◽

Vicente Bayarri ◽

Francisco J. Muñoz ◽

Ricardo Ortega ◽

Elena Castillo ◽

...

Keyword(s):

High Resolution ◽

Real Data ◽

Digital Processing ◽

The Other ◽

Major Step ◽

The People ◽

High Resolution Images ◽

Real Picture ◽

Interdisciplinary Study ◽

Very High

Our Palaeolithic ancestors did not make good representations of themselves on the rocky surfaces of caves and barring certain exceptions – such as the case of La Marche (found on small slabs of stone or plaquettes) or the Cueva de Ambrosio – the few known examples can only be referred to as anthropomorphs. As such, only hand stencils give us a real picture of the people who came before us. Hand stencils and imprints provide us with a large amount of information that allows us to approach not only their physical appearance but also to infer less tangible details, such as the preferential use of one hand over the other (i.e., handedness). Both new and/or mature technologies as well as digital processing of images, computers with the ability to process very high resolution images, and a more extensive knowledge of the Palaeolithic figures all help us to analyse thoroughly the hands in El Castillo cave. The interdisciplinary study presented here contributes many novel developments based on real data, representing a major step forward in knowledge about our predecessors.

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Digital Currency Illegal Behavior Detection Based on Mutual Information Prior Loss

Scientific Programming ◽

10.1155/2021/9954204 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Feng Yang ◽

Guixin Dong ◽

Chaoran Cui ◽

Xiaojie Li ◽

Yaxi Su ◽

...

Keyword(s):

Mutual Information ◽

Loss Function ◽

Prior Information ◽

Rapid Development ◽

Good Effect ◽

Behavior Detection ◽

Digital Currency ◽

Illegal Behavior ◽

Illegal Activities ◽

Criminal Behaviors

In recent years, with the rapid development of digital currency, digital currency brings us convenience and wealth, but also breeds some illegal and criminal behaviors. Different from traditional currencies, digital currency provides concealment to criminals while also exposing their behavior. The analysis of their behavior can be used to detect whether the current digital currency transaction is legal. There is a problem that most digital currency transactions are in compliance with laws and regulations, and only a small part of them uses digital currency to conduct illegal activities. It belongs to the problem of sample imbalance. It is quite challenging to accurately distinguish which transactions are legal and which are illegal in the massive digital currency transactions. For this reason, this study combines the mutual information and the traditional cross-entropy loss function and obtains the loss function based on the mutual information prior. The loss function based on the mutual information prior is that the bias of the category prior distribution is added after the output of the model (before the softmax), which makes the model consider category prior information to a certain extent when predicting. The experimental results show that the use of the loss function based on mutual information prior to the detection of digital currency illegal behavior has a good effect in SVM, DNN, GCN, and GAT methods.

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Robust Bayesian analysis of the binomial empirical Bayes problem

Canadian Journal of Statistics ◽

10.2307/3315663 ◽

1993 ◽

Vol 21 (1) ◽

pp. 107-119 ◽

Cited By ~ 11

Author(s):

S. Sivaganesan ◽

James Berger

Keyword(s):

Bayesian Analysis ◽

Empirical Bayes ◽

Robust Bayesian Analysis

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A Robust Localization System for Inspection Robots in Sewer Networks

Sensors ◽

10.3390/s19224946 ◽

2019 ◽

Vol 19 (22) ◽

pp. 4946 ◽

Cited By ~ 6

Author(s):

David Alejo ◽

Fernando Caballero ◽

Luis Merino

Keyword(s):

Cross Sections ◽

Prior Information ◽

Real Data ◽

Localization System ◽

Sewer Network ◽

Localization And Mapping ◽

Localization Errors ◽

Robust Localization ◽

Monte Carlo Localization ◽

Inspection Robots

Sewers represent a very important infrastructure of cities whose state should be monitored periodically. However, the length of such infrastructure prevents sensor networks from being applicable. In this paper, we present a mobile platform (SIAR) designed to inspect the sewer network. It is capable of sensing gas concentrations and detecting failures in the network such as cracks and holes in the floor and walls or zones were the water is not flowing. These alarms should be precisely geo-localized to allow the operators performing the required correcting measures. To this end, this paper presents a robust localization system for global pose estimation on sewers. It makes use of prior information of the sewer network, including its topology, the different cross sections traversed and the position of some elements such as manholes. The system is based on a Monte Carlo Localization system that fuses wheel and RGB-D odometry for the prediction stage. The update step takes into account the sewer network topology for discarding wrong hypotheses. Additionally, the localization is further refined with novel updating steps proposed in this paper which are activated whenever a discrete element in the sewer network is detected or the relative orientation of the robot over the sewer gallery could be estimated. Each part of the system has been validated with real data obtained from the sewers of Barcelona. The whole system is able to obtain median localization errors in the order of one meter in all cases. Finally, the paper also includes comparisons with state-of-the-art Simultaneous Localization and Mapping (SLAM) systems that demonstrate the convenience of the approach.

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Sample Size Determination for Robust Bayesian Analysis

Journal of the American Statistical Association ◽

10.1198/016214505000000510 ◽

2006 ◽

Vol 101 (473) ◽

pp. 278-291 ◽

Cited By ~ 32

Author(s):

Fulvio De Santis

Keyword(s):

Bayesian Analysis ◽

Sample Size ◽

Sample Size Determination ◽

Size Determination ◽

Robust Bayesian Analysis

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Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

Canadian Mathematical Bulletin ◽

10.4153/cmb-1970-076-x ◽

1970 ◽

Vol 13 (3) ◽

pp. 391-393 ◽

Cited By ~ 4

Author(s):

B. K. Kale

Keyword(s):

Maximum Likelihood ◽

Normal Distribution ◽

Maximum Likelihood Estimator ◽

Loss Function ◽

Prior Information ◽

Mean Squared Error ◽

Closed Interval ◽

Likelihood Estimator ◽

Usual Estimator ◽

Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

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