Bayes approach

The naive Bayes approach has several well-known difficulties. The conditional independence of descriptors of a molecule structure is not true as a rule. The probability P A Di) estimations can be close or even equal to 0 or 1 and in such case coefficients a,- become too large or infinite. To overcome this problem, we have substituted the logarithms of probabilities ratios n[P A D j —P A Di )] for ArcSin(2P(T Z),)—1). The ArcSin(2P( Z),)—1) shape coincides with the shape of ln[P(T Z),)/(l—P( Ai))] for almost all values of P(A Z),), but ArcSin(2P( P)i)—1) values are bounded by the values ti/2. 

Interestingly, the naive Bayes approach is too simple , but as a rule it provides high accuracy of recognition. ... 

In practice, despite the conceptual simplicity of the Bayes approach, it is computationally difficult to implement. 

The optimal decision rule is found by the use of the Bayes approach. The unknown parameter, whose value we want to decide about, is random variable Y e 0,1 with probability function q(y). The decision will be made on the basis of the value of random vector X with the density function r(x). Let r(x y) be the conditional density function of X on condition Y =y, S JiF 0,1 the decision function andi/ the set of all decision functions 5 0,1. The loss... 

There are several approaches to setting the threshold. In the Bayes approach, a threshold is chosen to minimize the total probability of an error, given by Pe = Po X fa -I- Pi X Pm. In general, Pq and Pi are unknown at the start of the experiment, but may be estimated from preliminary experiments. Pe is minimized by the following detection strategy. The processor will declare Hi is true if... 

Hauer, E. 1983. An application of the likelihood/Bayes approach to the estimation of safety countermeasure effectiveness. Accident Analysis and Prevention, 4(15), 278-298. 

Our simulation study is limited to a selected set of parameter values and only a limited number of simulation runs. We need to investigate a more rich experimental space and to increase the number of simulation repetitions to more fully investigate the degree of any learning in the failure intensity predictions under an empirical Bayes approach for situations such as that motivated by Scottish Water. 

In the recent literature, one can find models of inspection frequency optimization with the use e.g. simulation processes (see e.g. (Alfares 1999, Vaghefi and Sarhangian 2009)), probability analysis (see e.g. (Baohe 2002)), Bayes or quasi-Bayes approach (see e.g. (Durango-Cohen and Madanat 2008, Jones et al. 2010)), or Markov processes (see e.g. (Kenzin and Frostig 2009)). Moreover, the analysed problems include e.g. the periodic inspection optimization for systems with failure interaction (see e.g. (Golmakani and Moakedi 2012, Zeque-ira and Berenguer 2005)), or the introduction of imperfect inspection (see e.g. (Berrade et al. 2013, Zhao et al. 2007)). 

Durango-Cohen, P.L., Madanat, S.M. (2008). Optimization of inspection and maintenance decisions for infrastructure fadlities under performance model uncertainty A quasi-Bayes approach. Transportation Research Part A 42 1074-1085. 

Bris, R. Bayes approach in RDT using accelerated and long-term life data, Reliability Engineering and System Safety, vol. 67, pp. 9-16, 2000. 

Fisher Approach Bayes Approach Population Approaches... 

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