A Comparison of Bayesian and Frequentist Approaches for the Case

of Accident and Safety Analysis, as a Precept for All AI Expert

Models

Moldir Zholdasbayeva and Vasilios Zarikas

Department of Mechanical and Aerospace Engineering, Nazarbayev University, Nur-Sultan, Kazakhstan

Keywords: Artificial Intelligence with Uncertainty, Bayesian Networks, Supervised Learning, Regression Method,

Frequentist Statistics, Causal Analysis, Elevator Accidents, Safety Rules.

Abstract: Statistical modelling techniques are widely used in accident studies. It is a well-known fact that frequentist

statistical approach includes hypothesis testing, correlations, and probabilistic inferences. Bayesian networks,

which belong to the set of advanced AI techniques, perform advanced calculations related to diagnostics,

prediction and causal inference. The aim of the current work is to present a comparison of Bayesian and

Regression approaches for safety analysis. For this, both advantages and disadvantages of two modelling

approaches were studied. The results indicated that the precision of Bayesian network was higher than that of

the ordinal regression model. However, regression analysis can also provide understanding of the information

hidden in data. The two approaches may suggest different significant explanatory factors/causes, and this

always should be taken into consideration. The obtained outcomes from this analysis will contribute to the

existing literature on safety science and accident analysis.

1 INTRODUCTION

The choice of a modelling approach remains one of

the main issues in accident studies (Alkheder,

Alrukaibi, & Aiash, 2020; Mujalli, Calvo, & O, 2011;

Zong, Xu, & Zhang, 2013; Gregoriades and

Christodoulides, 2017). For these studies, the severity

of accident or injury is often chosen as a key

dependent/target variable (Eboli et al., 2020; Fountas,

Ch, & Mannering, 2018; Michalaki & Quddus, 2015).

By expert judgement, several factors, which affect the

severity of accident or injury, can be found. In recent

years, researchers elaborate on studying the causes of

the occurrence of various accidents by running a

concrete diagnostics and making predictions using

modern statistical and Artificial Intelligent (AI)

methods.

A frequentist statistical approach allows an expert

to infer associations between factors (i.e. the

characteristics of injured people: age and gender, the

description of accidents, etc.). It evaluates the

likelihood of previous and current events, therefore

making it possible to prevent fatal accidents from its

occurrence. Studying the causation of events (i.e. a

causal approach) may be a dynamical case. Hence, it

can be beneficial to find the causes of this event and

predict the effect based on a dynamic change of

evidences. It can be implemented efficiently with

Bayesian Networks (BNs) that have learning

capabilities. However, modern implementations of

regression algorithms can also be updated as far as the

conditions of the experiment remain the same. BNs

are more robust regarding a more general type of

updating with the cost of the decision/prediction

dependency on the values of priors.

In accident studies, accident involvement is a

dependent/target variable, whereas accident causes

affect the frequency occurrence of accident

results/outcomes. As this type of the analysis is

statistical, the explanatory variables/causes and other

characteristics of this accident may be correlated.

This particular analysis regarding accidents is helpful

to have “a first look” on data (Cummings, Mcknight,

& Weiss, 2003; Zarikas et al., 2013).

One of the well-known statistical approaches is

regression models. The regression model has been

widely used in various fields, particularly in research

studies on medical issues or traffic accident severity

(Mujalli et al., 2011; Zong et al., 2016). Logistic and

ordered probit statistical methods are used in traffic

1054

Zholdasbayeva, M. and Zarikas, V.

A Comparison of Bayesian and Frequentist Approaches for the Case of Accident and Safety Analysis, as a Precept for All AI Expert Models.

DOI: 10.5220/0010315810541065

In Proceedings of the 13th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2021) - Volume 2, pages 1054-1065

ISBN: 978-989-758-484-8

studies (Fountas et al., 2018). The utilization of

regression models comes with model assumptions

and the underlying relationships (e.g. the linear

relationships between dependent and independent

variables). If any violation takes place, then

likelihood of the severity of accident or injury may

not be estimated (Zong et al., 2016). In medical

sciences, the sample size and missing values may

cause problems with inconsistencies while updating

(Ducher et al., 2013).

From the point of using conventional frequentist

statistics, before executing the regression model it

may be of some importance to study the frequency,

correlation and variance analysis of explanatory

variables (e.g. accident type, severity of accident,

month&day&time of accident and province). It can

provide information about the nature of fatalities

(Shao, Hu, Liu, Chen, & He, 2019). In the work of

Shao, the frequency analysis was executed to find

inconsistencies in data. The correlation analysis was

held to get causal relationships between factors. The

collected data can be distributed uniformly (Chen,

Chou, & Lu, 2013). Thus, the probabilities are

calculated.

Expert judgment can provide an initial

identification of explanatory variables/causes of

accident and target variables. Next, the correlation

analysis can be executed. The chi-square test can be

completed to test the strength of relationships (i.e. or

how statistically significant the observed data vs the

expected one). The goodness-of-fit test can be used to

test how well data fits for the used distribution type

(Ugurlu et al., 2020).

On the other hand, Bayesian networks are an

alternative AI technique, which are used for

investigating causal relationships between variables

and, therefore, predicting outcomes or effects

depending on the number of observations (Conrady,

Jouffe, & Elwert, 2014). In addition, Bayesian

networks have been applied in in environmental,

agricultural, risk management, safety and reliability

(Amrin, Zarikas, & Spitas, 2018; Zarikas et al., 2015;

Zarikas, 2007; Gerstenberger, Christophersen,

Buxton, & Nicol, 2015; Kabir & Papadopoulos, 2019;

Marcos, Wijesiri, Vergotti, & Glória, 2018; Martos,

Pacheco-torres, Ordóñez, & Jadraque-gago, 2016;

Mukashema, Veldkamp, & Vrieling, 2014; Ropero,

Renooij, & Gaag, 2018; Tang, Yi, Yang, & Sun,

2016). It can be used for prognostics and conducting

diagnostics (Amrin et al., 2018; Bapin & Zarikas,

2014; Conrady et al., 2014). Therefore, BNs can be

applied under uncertainty. This distinctive feature

differs Bayesian networks from other statistical

methods (Iqbal, Yin, Hao, Ilyas, & Ali, 2015;

Nannapaneni, Mahadevan, & Rachuri, 2016).

Bayesian networks are utilized for calculating the

posterior probabilities of events A or B. It is based on

building direct acyclic graphs, which in turn allow

studying causal relationships rather than just finding

the associations between variables.

However, “Any complication that creates

problems for one method of inference creates

problems for all alternative methods of generating

inference, just in different ways" – Don Rubin

(interview, April 15, 2014). There are the usual

problems of hidden variables, common factors/causes

influencing explanatory variables and target variables

or weakly identifiable parameters, sensitivity to priors

and the outcome etc.

Nevertheless, the advances of BNs include (i)

inference of individual causal effects, (ii) integration

with decision theory, (iii) suitability for post-

treatment variables, sequential treatments and spatial

and temporal data, (iv) modern BNs include learning

and Conditional Probability Tables (CPTs) are filled

automatically from data.

For building the Bayesian network from data, the

nodes and edges are created, whereas nodes represent

variables and edges show the relationships between

these nodes. Let P(A) be the prior probability

distribution of a random variable A and assume that

P(B) is the prior probability distribution of a set of

random variables or a dataset B. Based on the

Bayesian theorem, the posterior probability is

calculated by this formula:





 PB|A ∙ PA/PB (1)

If the value of P





is maximized by the model

structure, then the relative Bayesian structure is

chosen. Bayesian networks allow choosing the

structure from two learning techniques (i.e.

unsupervised and supervised). The unsupervised

learning method has no target variable, whereas with

the supervised learning method it is important to

choose a target variable. For this, a target variable is

a parent node, whereas child nodes are connected

with “causal” relationships. Further, the supervised

learning procedure can be used by creating naïve

model (Figure 1(a)). Another model is called

augmented naïve model (Figure 1(b)), which can be

applied to a small set of data. The higher precision

and accuracy are added by creating new causal

relationships (Montgomery & Runger, 2014).

A Comparison of Bayesian and Frequentist Approaches for the Case of Accident and Safety Analysis, as a Precept for All AI Expert Models

1055

Figure 1: A simplistic naïve and augmented naïve models

(Y – target node; N1, N2, N3 – child nodes): a) naïve

model; b) augmented naïve model.

Bayesian networks provide pre-assumptions

(Ducher et al., 2013; Zong et al., 2016). It means that

the prediction is based on preliminarily provided

evidence. Another issue with missing data can be

solved by an automatic imputation in the network.

For a missing value, implemented modern BNs use an

estimated probability of having this missing datum

according to other factors, which depend on it. The

data is updated, which in turn means that the

calculated coefficients in the network are not frozen

(Ducher et al., 2013). It could be also be stated that

new probabilities of the event depending on

evidences are also calculated. As an example for

traffic accident severity, Bayesian networks can be

used to identify factors associated with the severity of

injury (i.e. killed or seriously injured) by inference

(Mujalli et al., 2011).

1.1 Accidents Example

Vertical transportation devices are widely used both

for personal and professional purposes. Accidents

may happen by violating safety rules. Accidents

regarding cranes (Im & Park, 2020; Mccann, 2003;

Raviv, Fishbain, & Shapira, 2017; Shin, 2015;

Swuste, 2013; Swuste et al., 2020) or escalators

(Almeida, Hirzel, Patrão, Fong, & Dütschke, 2012;

Chi, Chang, & Tsou, 2006; Neil, Steele, Huisingh, &

Smith, 2008; Xing, Dissanayake, Lu, Long, & Lou,

2019) are vastly discussed. However, there is a

limited number of research works regarding elevator

accidents. Elevator accidents take place during the

installation or operation stages (Göksenli & Eryürek,

2009; Zarikas et al., 2013). For that, the EU has

published EN 81-80 issuing 74 dangerous occasions

and prevention proactive measures with elevator

fatalities (Zarikas et al., 2013). Nevertheless, these

safety rules may be ignored. It is vital, therefore, to

investigate the causality and reasons behind elevator

accidents. More than 160 thousand people died from

accidents around the world in 2016, from which

France took an all high of 4.6 percent. One example

of these heavy accidents that occurred was in Paris:

 An elevator accident happened in 2011 during

the maintenance job in an apartment block. An

elevator fell down to workers. Three people were

injured and another worker was dead (Warren,

2011).

In current studies, elevator accidents in France,

Zarikas, 2020, (“Elevator accidents France”,

Mendeley Data, V1, doi: 10.17632/sstxdjj32h.1) will

be studied and investigated to find causal

relationships between factors (i.e. explanatory factors

such as the characteristics of an injured person or the

date and place of an accident). The violation of safety

rules based on EN 80-81 will be also studied by the

execution of two modelling techniques: the ordinal

regression and supervised learning methods.

In further sections, data collection method and

data arrangement will be represented. Two statistical

models will be shortly presented. The use of the

ordinal regression model will be discussed shortly for

reasons behind its application. The prediction model

based on Bayesian networks will also discussed

regarding the use of supervised learning. In sections

3 and 4, results and discussion of results will be

presented and discussed. In section 5, conclusions and

recommendations will be given at the end based on

the analysis of using both statistical methods to

prevent elevator accidents.

2 METHODOLOGY

At an initial stage, a considerable amount of time was

spent to collect data regarding elevator accidents from

hospitals, health and safety organizations. The

provided data from these organizations was not fully

representative for elevator accidents. Due to this fact,

most data provided by governmental data sources, for

several reasons, was insufficient for current data

analysis:

 Reporting system was only valuable to provide

information on all accident types for categories

such as “falls”, “slips” and etc.;

 Data regarding elevator accidents was lack of

information such as the characteristics of injured

people or accident type;

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 Information on accidents for each year was

insufficient due to the gap in data collection (i.e.

only officially registered cases were in the

system).

Consequently, data concerning elevator

accidents was extracted from EU Open Data Portal. It

has been proven that it was a reliable source for

several research works (Ugurlu et al., 2020;

Gutierrez-osorio & Pedraza, 2019; Juana-espinosa &

Luj, 2020). For France, data was collected for the

period of 18

February, 2003 to 17

December, 2009.

As a case, only accidents related for the last 6 years

were studied in the current analysis due to fact that:

 most data regarding the earlier years was found

to be unreliable and incomplete;

 most data regarding recent years was not

collected due to the lack of resources for the

reasons stated previously.

Regardless of the limited resources in current

data collection, more than 200 cases were collected in

Excel sheet including the information on date and

places of an accident, the characteristics of an

elevator accident (accident type, the type of fault),

details about injured people (the severity of an injury,

gender and age), the description of violated rules for

each accident. It should be noted that an individual

information on each accident type and of an injured

person was collected with an overall number of

violated safety rules separately. The sample size was

considered to be sufficient for the purpose of the

current research (Haghighattalab, Chen, Fan, &

Mohammadi, 2019; Zarikas et al., 2013).

2.1 Data Arrangement

Table 1 shows the representation of data regarding

elevator accident in France for 2003-2009. The

resulting table has provided information on

characteristics of an injured person including the ones

with the unknown gender and age of certain injured

group of people:

 Date (year and month);

 Place;

 Sum of injured;

 Gender and age of an injured person (i.e.

including unknown people);

 Accident type;

 Fault type;

 Severity of injury;

 Safety rules/regulations violated (i.e. an overall

summary and a separate file with rules).

Table 1: Parameters and their possible states.

Paramete

Possible states

Date Year and month of elevator

accidents:

2003 - 2009

Place i.e. 28 cities:

Angres, Avignon, Bordeaux, Brest,

Dijon, Dunkirk, Grinoble, Le

Havre, Lille, Limoges, Lyon,

Marseille, Metz, Mulhouse, Nancy,

Nanterre, Nantes, Nice, Paris,

Reims, Rennes, Roubaix, Saint-

Dennis, Saint-Pierre, Strasbourge,

Toulon, Toulouse, Versailles

Sum of injured The overall number of injured

Gender The gender of an injured person:

Female: F

Male: M

Unknown: U (i.e. for a group of

)

Age The gender of an injured person:

Young aged (1-12): C12

Teenagers (13-18): Ad18

Middle aged (19-59): A59

Seniors (aged) (60-85): SA60

Unknown a

ed: UNV

Accident type Professional: PRO

Private: PRI

Fault type Types of elevator faulties:

doors, electrocution, falls, fire,

floor, general, landing, machinery,

power, repair, speeding, sudden

sto

s, vandalis

Severity of

injury

Light: 1 or A

Heavy: 2 or B

Fatal: 3 or C

Light/Heavy:4 or AB

Light/Fatal: 5 or AC

Heavy/Fatal: 6 or BC

Safety rules Rules related to installing,

repairing, modernizing and

maintaining lifts: IRMM

Rules related to risks and hazardous

situations: RHS

Rules related to safety tips for

assen

ers: STP

2.2 A Statistical Approach

The main objective of the current work is to

investigate the possible links between factors

presented in Table 1 using two statistical approaches

and, as a case, identify those variables, which

contribute most to the violation of safety rules. For

this, two models were constructed for carrying out the

statistical analysis in IBM SPSS Statistics 23 and

BayesiaLab 2020. For model A, an ordinal regression

A Comparison of Bayesian and Frequentist Approaches for the Case of Accident and Safety Analysis, as a Precept for All AI Expert Models

1057

model was used. Model B was constructed by

following the rules of supervised learning.

The descriptive statistics was executed to obtain

the first summary on the data set checking the

distributions (Perez & Exposito, 2009). Frequency

and correlation tables were built for variables in Table

1 to have a preliminary look on data and draw

conclusions based on this information. Some of those

results will be presented on the next section.

Model A was constructed to identify associations

between one dependent and several independent

variables. The first step was to choose a certain

variable, which should be ordinal in nature. In fact,

the severity of injury was labelled as a dependent

variable to investigate on the effect of other variables

contributing to it. Next, several predictors, which

contributed to the location of the model, were

selected. It is worth noting that for this type of the

analysis it is uncertain what predictors should be

considered first. For the start, all possible contributors

were added into the model and, if not useful, then they

were excluded and the model was estimated again.

For this, all independent variables or, differently,

predictors, were included such as gender, age,

accident type, rules violated, fault type. An initial

analysis was implemented without covariates to see if

the location-only model was sufficient to draw

conclusions. For many cases, the location-only model

is adequate. However, scale variables (e.g. year and

month of an accident) could also be included, if

summary data is inadequate from the location-only

model. It was decided to add a scale variable (i.e.

individually) such as year and month or sum of

injured to investigate possible associations. The basic

approach was to include all of those variables and

subtract from the analysis, if no correlation was found

related to dependent variables. The next step was to

choose the link function between complementary log-

log or Cauchit or even logit based on graphical

representation of the dependent variable. For this,

complementary log-log and logit functions are mostly

similar. The choice of the link function for elevator

accidents in France will be explained in further

sections.

The next step was to evaluate the model itself and,

furthermore, to describe the statistics. Model fitting

information was constructed, whereas the log-

likelihoods could be interpreted as chi-square

statistics. Finally, it gives information if the presented

model gives a significant improvement over the

intercept model. The significance level should be less

than 0.05. Therefore, chi-square-based statistics

shows how strong these relationships could be

between factors (Wood, 2005). It is very useful type

of statistics for the analysis of very few categorical

variables. Next, pseudo R-squared statistics was

implemented by measures such of Cox&Snell,

Nagelkerke and McFadden, which represented how

good the model fits based on the proportion of the

variance. Based on this, if R-squared is high, then the

appropriate measure should be chosen. In the final

step, parameter estimates were obtained for the

dependent variable versus predictors. Results and

conclusions on ordinal regression model for each

country will be presented in sections 3 and 4.

For model B a prediction model was built using

supervised learning. Causal relationships or possible

associations between a target variable and

independent variables was found by building

Bayesian networks using supervised learning. A

supervised learning technique was used in order to

find relationships between the severity of injury as a

target variable and the rest of predictors. For this

purpose, a target variable was chosen as discrete. In

order to define the learning set, no test set has been

considered because the presented data was sufficient

for the preliminary analysis. All variables have been

defined as discrete except the sum of injured which

was stated as continuous. Next, the discretization

method was chosen to be “Tree” for a continuous

variable. After, mutual information of arcs was

analyzed between a target variable and each predictor

in order to find which nodes added most information

to the presented model. The main objective of such an

analysis was to decide on a final network structure, so

that Naïve and Augmented Naïve models were

constructed. Network performance based on a target

analysis was investigated to calculate the precision

and reliability of each model. The next step was to run

the structural coefficient analysis and, if it was

necessary, to adjust the structural coefficient and

rerun the model. The last step was to identify causal

relationships by finding the inference between a

target variable and predictors. For that, an adaptive

questionnaire was also included into the model. The

chosen model and results related to this from

supervised learning will be presented in next sections.

3 RESULTS

In this section, models A and B were built separately

due to the difference in associations between

explanatory factors. Only the selected results from

the number of derived ones will be presented in order

to concentrate on important outcomes.

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3.1 Model A Outcomes

Firstly, a quick statistical analysis has been executed

related to elevator accidents consisting of 205 cases

in France. Therefore, Tables 2 – 10 represent

preliminary obtained results from descriptive

statistics based on frequencies regarding data with

categories on the overall number of injured people

and relevant safety rules, which have been violated.

Based on this statistical analysis, several outcomes

are as follows:

 Related to Table 2, the highest number of

elevator accidents took place in 2007, 2008 and

2006 (with 36, 35 and 30 cases respectively).

 In Table 3, from the distribution it can be said

that accidents happened frequently in January

with 23 cases. The most frequent accidents

occurred in June with 25 cases. Also, 20 cases

took place in February and September.

 As for Table 4, it can be seen that mostly elevator

accidents have occurred in Dunkirk with 12

cases, Angres, Marseille and Toulouse with 11

cases and, lastly, Versailles with 10 cases.

 More females (i.e. appx. 42 percent) have been

injured than males (i.e. almost 35 percent) based

on Table 5.

 Regarding the accident distribution over age

categories in Table 6, mostly adults from 19 to

59 or A59 have been injured (i.e. 42 percent),

whereas the least percentage was noticed in the

case of young adults from 12 to 18 and the

undefined age group.

 In Table 7, injuries from the private use were

prevalent (53.7 percent) than the ones used for

professional purposes (46.3 percent).

 As for the severity of injury in Table 8, fatal

injuries defined as “C” were likely to happen

(with 41.5 percent) compared to light or heavy

injuries. However, it is worth noting that heavy

injuries have taken 35.1 percent.

 Related to fault types as shown in Table 9,

unexpected accidents related to elevators

occurred with floor leveling problems (i.e. 13.2

percent) or with doors openings (i.e. 11.2

percent) and lift speeding (10.7 percent) based on

Table 9.

 As for the violated rules in Table 10, safety

measures have been violated regarding the cases

of IRMM and IRMM/RHS with 30.2 percent

each.

Table 2: The distribution over year of the accident.

Year Frequency Percent Cumulative

ercent

2003 28 13.7 13.7

2004 21 10.2 23.9

2005 27 13.2 37.1

2006 30 14.6 51.7

2007 36 17.6 69.3

2008 35 17.1 86.3

2009 28 13.7 100.0

Total 205 100.0

Table 3: The distribution over month of the accident.

Month Frequency Percent Cumulative

ercent

Januar

23 11.2 11.2

Februar

20 9.8 21.0

March 19 9.3 30.2

April 15 7.3 37.6

May 16 7.8 45.4

June 25 12.2 57.6

Jul

13 6.3 63.9

ust 12 5.9 69.8

tembe

20 9.8 79.5

Octobe

15 7.3 86.8

Novembe

12 5.9 92.7

Decembe

15 7.3 100.0

Total 205 100.0

Table 4: The distribution over place of the accident.

Place Frequency Percent Cumulative

ercent

res 11 5.4 5.4

Avi

non 7 3.4 8.8

Bordeaux 9 4.4 13.2

Brest 7 3.4 16.6

on 4 2.0 18.5

Dunkir

12 5.9 24.4

Grenoble 6 2.9 27.3

Le Havre 8 3.9 31.2

Lille 4 2.0 33.2

Limoges 6 2.9 36.1

on 7 3.4 39.5

Marseille 11 5.4 44.9

Metz 6 2.9 47.8

Mulhouse 7 3.4 51.2

Nanc

8 3.9 55.1

Nanterre 8 3.9 59.0

Nantes 6 2.9 62.0

Nice 3 1.5 63.4

Paris 8 3.9 67.3

Reims 5 2.4 69.8

Rennes 8 3.9 73.7

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Table 4: The distribution over place of the accident (cont.).

Place Frequency Percent Cumulative

ercent

Roubaix 7 3.4 77.1

Saint-Denis 9 4.4 81.5

Saint-Pierre 4 2.0 83.4

Strasbour

e 7 3.4 86.8

Toulon 6 2.9 89.8

Toulouse 11 5.4 95.1

Versailles 10 4.9 100.0

Total 205 100.0

Table 5: The distribution over gender of an injured person.

Gender Frequency Percent Cumulative

ercent

F 87 42.4 42.4

M 71 34.6 77.1

U 47 22.9 100.0

Total 205 100.0

Table 6: The distribution over age of the accident.

Age Frequency Percent Cumulative

ercent

A59 86 42.0 42.0

Ad18 11 5.4 47.3

C12 12 5.9 53.2

SA60 45 22.0 75.1

UNV 51 24.9 100.0

Total 205 100.0

Table 7: The distribution over the type of the accident.

Accident

Frequency Percent Cumulative

ercent

PRI 110 53.7 53.7

PRO 95 46.3 100.0

Total 205 100.0

Table 8: The distribution over the severity of an injury.

Severity of

injury

Frequency Percent Cumulative

ercent

AB 22 10.7 10.7

ABC 2 1.0 11.7

AC 24 11.7 23.4

B 72 35.1 58.5

C 85 41.5 100.0

Total 205 100.0

Next, Tables 11 - 13 represent the outcomes from

the execution of an ordinal regression model.

Regarding model A, the best model has been found to

be with “severity of injury” as a dependent variable,

“sum of injured people” as a scale covariate and

predictor variables such as “gender” and “age”.

Table 9: The distribution over the type of fault.

Fault type Frequency Percent Cumulative

ercent

Doors 23 11.2 11.2

Electro-

cution

10 4.9 16.1

Falls 16 7.8 23.9

Fire 14 6.8 30.7

Floo

27 13.2 43.9

General 18 8.8 52.7

Landin

10 4.9 57.6

Machiner

14 6.8 64.4

Powe

13 6.3 70.7

Repai

19 9.3 80.0

eedin

22 10.7 90.7

Ste

s 7 3.4 94.1

Sudden

stops

6 2.9 97.1

Vandalis

6 2.9 100.0

Total 205 100.0

Table 10: The distribution over safety rules.

Safety rules Frequency Percent Cumulative

ercent

IRMM 62 30.2 30.2

IRMM/RHS 62 30.2 60.5

IRMM/STP 31 15.1 75.6

RHS 28 13.7 89.3

RHS/STP 9 4.4 93.7

STP 13 6.3 100.0

Total 205 100.0

Accident type has no effect on the dependent

variable, assuming that only two categories exist. No

missing data has been detected. The choice of a link

function - logit (i.e. it is similar to log-log function).

Firstly, from the Goodness-of-Fit model it is

concluded that the presented data is consistent. As in

Table 11, it is shown from the model fitting

information that the final model outperforms the

intercept-only model (i.e. a significance level is less

than 0.05). The next step was to verify if the chosen

link functions was reliable. In Table 12, three pseudo

R-squared values have been represented, whereas

Nagelkerke’s is the best with the value of 0.643. The

test of parallel lines shows that our model rejects the

null hypothesis (i.e. a significance level is higher than

0.05).

Returning to parameter estimates in Table 13, it is

seen that a significance level is high for [SOI = 2]

with the negative estimate and [SOI = 6] with the

positive estimate in relation with the severity of

injury. A significance level for [SOI=4] is equal to

0.023, which states that it is lower than 0.05

contributing to the model. [SOI=3] has no effect on

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the model, which exceeds 0.05. As for the location,

[Gender.category = F] is in the higher position of

severity of injury with respect to the reference

category [Gender.category = U]. The category

[Gender.category = M] is in the lower position of

severity of injury with respect to the reference

category [Gender.category = U].

As for age categories, [Age.category = A59] has

a negative associations with the severity of injury

with the highest significance level. As for

[Age.category = SA60], it is located in the lower

position compared to [Age.category = C12], however

showing the highest association with the dependent

variable with respect to the reference category

[Age.category = UNV]. [Age.category = A18] has the

lowest level of association regarding the severity of

injury with respect to the reference category

[Age.category = UNV]. Sum of injured is a covariate.

Table 11: Model A fitting information.

Model

-2 Log

Likelihoo

Chi-

Square df Sig.

Intercept

Only

275.942

Final 92.237 183.705 7 .000

Link function: Logit.

Table 12: Model A pseudo R-squared.

Cox and Snell .592

Nagelkerke .643

McFadden .353

Link function: Logit.

Table 13: Model A parameter estimates.

Estimate Sig.

Threshold

[SOI.cat = 2] -4.640 .000

[SOI.cat = 3] -.358 .705

[SOI.cat = 4] 2.097 .023

[SOI.cat = 6] 5.596 .000

ocation

SumofIn

ure

.892 .012

[Gender.cate

=F] -2.245 .010

Estimate Sig.

[Gender.category=M] -2.110 .013

[Gender.cate

=U] 0

e.cate

=A59] -3.286 .001

e.cate

=Ad18] -2.355 .028

[Age.category=C12] -3.040 .006

[Age.category=SA60] -3.286 .001

[Age.category=UNV] 0

Link function: Lo

it.

a. This

arameter is set to zero because it is redundant.

3.2 Model B Outcomes

For model B, the Bayesian network was constructed.

To investigate causal relationships between the

severity of injury and other predictors, a simple

statistical model was built using the supervised

learning method. As it has been noted down before,

supervised learning methods need a target variable.

For the current analysis, it is important to find factors

which affect most to the severity of injury and which

rules are mostly violated depending on those factors.

Before the start of the initial analysis a dataset

with variables (i.e. a .csv file) was imported to the

Bayesian network. All variables were considered to

be continuous. The variable “Month” in Table 2 has

not been used due to the insufficient input to the

overall model. The violation of rules IRMM, RHS

and STP has been included from the separate file.

The first step was to identify causal relationships

between variables. Figure 2(a,b) illustrates naïve and

augmented naïve models in case of elevator accidents

in France. It can be noted that the violated rules were

presented separately and derived from the overall rule

types of IRMM, RHS and STP. From Figure 2(b), it

is seen that new causal relationships have occurred

between categories:

 “1,4,2i” and “Gender.category”;

 “1,1,3” and “Age.category”;

 “Fault.category” and “Accident.category”;

 “Accident.category” and several violated rules

of “1,1,2”, “1,3,1h”, “1,4,1a”, “1,4,1c”, “1,4,2d”,

“1,4,2h”, “1,5,3”, “2,4,4” and “3,5,1”.

The next step was to choose the model type. The

final model choice was augmented naïve model

explained by higher precision and accuracy (Table

14). Through running the structural coefficient

analysis, the value of 0.1 was chosen to increase the

precision of the presented model. The most reliable

network was augmented naïve model with structural

coefficient with the value of 0.1. From Table 14, it is

clear that the precision has increased from

approximately 87 percent using naïve model to

almost 95 percent using augmented naïve model.

Overall log –loss value is equal to 0.1282 with R of

0.9652, which indicates a higher accuracy regarding

the future validation of the model.

After choosing the right network, inferential

analysis has been implemented. In Figure 3, mutual

information with the severity of injury as a target

node is presented. From the initial investigation, it is

clear that the sum of injured has the strongest effect

on the severity of injury with the amount of mutual

information of 0.7552. Certain variables have the

A Comparison of Bayesian and Frequentist Approaches for the Case of Accident and Safety Analysis, as a Precept for All AI Expert Models

1061

amount of mutual information higher than 0.5 such as

“Age.category” and “Gender.category”, which have

higher contribution to the model. Next, the mutual

information shared with a target node between the

values of 0.2 to 0.5 is identified by categorical

variables such as “Fault.category” with the value of

0.1550 and “Place.category” with the value of 0.4092.

The contribution to the model with the value of 0.02

to 0.10 is added by the main predictor “Year” and

violated rules such as “1,3,2”, “1,1,1c” and “1,4,2g”

as shown in Figure 4.

Table 14: Precision of the model.

Model: Naïve (SC=1) Augmented

Naïve (SC=0.1)

Overall

Precision

86.8293% 95.1220%

Mean Precision 93.0098% 97.4771%

Overall

Reliability

86.7843% 95.1296%

Mean

Reliability

92.4860% 96.7967%

Overall Relative

Gini Index

91.1203% 98.9249%

Mean Relative

Gini Index

95.2681% 99.3890%

Overall Relative

Lift Index

96.1551% 99.5718%

Mean Relative

Lift Index

97.9070% 99.7768%

Overall ROC

Index

95.5679% 99.4702%

Mean ROC

Index

97.6655% 99.7259%

Overall

Calibration

Index

83.3532% 78.7967%

Mean

Calibration

Index

77.7412% 84.9008%

Overall Log-

Loss

0.3357 0.1282

Mean Binary

Log-Loss

0.1343 0.0513

R 0.9426 0.9652

R2 0.8886 0.9315

(a)

(b)

Figure 2: Naïve and augmented naïve models for elevator

accidents in France: a) SC = 1 and b) SC = 0.1.

Figure 3: Mutual information with the target node for

elevator accidents in France.

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Figure 4: Prior probabilities based on target correlations

with an adaptive questionnaire.

4 DISCUSSIONS

Based on the implementation of both statistical and

graphical approaches, the current study has

concentrated on finding the causal relationships

between variables. These outcomes are based on a

limited set of data. It is explained by the fact that

reports for occupational injuries are rarely submitted.

Preliminarily, the severity of injury was chosen as a

target variable. Descriptive statistics has given initial

insight on the frequency of data, which was found to

be important to study the inconsistencies. An ordinal

regression model was used to study the likelihood of

the event.

From those results, elevators accidents in France

may have an upward trend. Nevertheless, the

limitation of this trend is that provided data concerns

only a limited number of reports. As the case, those

injured people from elevator accidents, presumably,

tend to ignore providing reports for light or heavy

injuries. Further, elevator accidents took place in

summer and winter periods in France. The safety

rules were violated due to low technical support and

maintenance measures. Elevator accidents occurred

in well-known cities such as Marseille, Toulouse and

Versailles. As for the characteristics of an injured

person, more female users were injured than male

users. It can be explained by the fact that most injuries

were due to: problems with floor leveling or elevator

doors. Further, mostly adults were injured in elevator

accidents. By building Bayesian network model

based on a supervised learning, it has been found that

mostly safety rules in Figure 3 have been broken

related to

 providing lift workers with necessary safety

information;

 the working process with the machinery;

 providing technicians with safety rules in the

machine room.

The outcomes from model A using an ordinal

regression model have shown a high precision based

on the test of parallel lines and goodness-of-fit in

Table 11. Strong correlations have been found

between gender and age of an injured person. The

only limitation of an ordinal regression model was

that the range (i.e. size) of data and the missing values

in data could affect the outcomes of the accident

analysis (Eboli et al., 2020; Ropero et al., 2018; Wu,

Hou, Wen, Liu, & Wu, 2019). It is also explained by

the fact that more independent variables related to the

type of accident should have been included to the

model in order to find the relationships between the

severity of injury and the number of violated safety

rules.

Model B has outperformed the regression model

for several reasons: pre-assumptions are not

necessary, an automatic missing data imputation is

available and new evidences can be included during

execution. Bayesian network model is valuable to

study both quantitative and qualitative data (Ugurlu

et al., 2020; Juned & Bouwer, 2014; Zhou, Diew,

Shan, & Fai, 2018). It can also be noted that the

missing values can be handled by the missing value

imputation during the analysis (Ducher et al., 2013).

By building Bayesian network model, it is possible to

study data with adding new cases and calculating

further probabilities. It is done by providing new

evidences to data and the dependency on the severity

of injury will be shown regarding the strength of

mutual information shared between variables. These

characteristics differ Bayesian network from other

statistical models (Zong et al., 2016). However, the

limitation is that a sufficient amount of data should be

added in order to spot the inconsistencies in data and

study the reasons for unforeseen accidents behind its

occurrence.

5 CONCLUSIONS

In this study, two modelling approaches have been

used. The above-presented outcomes have brought

important insights on elevator accidents. The chosen

explanatory factors that affect the severity of injury

have been studied. The Bayesian network model has

A Comparison of Bayesian and Frequentist Approaches for the Case of Accident and Safety Analysis, as a Precept for All AI Expert Models

1063

been found to be useful for studying accident data for

making predictions. The precision of utilizing

Bayesian network is higher than that of the ordinal

regression model. The conventional statistics is a

valuable tool to observe the correlations between

factors. Further, these results could be useful at the

beginning of building the efficient strategy to prevent

accidents. The limitation of current studies is the lack

of explanatory variables. Further studies are

suggested to them into the model to study the effect

of these factors on injury severity.

In summary, this work epitomizes a good practise

of use for safety analysis. It is not correct to rely on a

single tool for causal analysis (Pearl, 2019). Anyway,

causal analysis still needs further theoretical

development and integration of a combination of

experimental as well observational data together with

a stronger mathematical framework, which is still

under investigation. A framework, that as Judea Pearl

says, should mathematically encapsulate the fact that

symptoms are not causes of diseases. If data via

different methods can derive similar “causal” effects

from different sets of assumptions, then this is very

encouraging and supportive. However, if results from

different methodologies contradict each other, this is

useful also to know. The usage of background expert

knowledge is necessary in this case to disentangle the

discrepancies. This is a precept for everyone wants to

design a meaningful AI expert model.

As a future work we need to improve these

preliminarily results taking into account a larger

dataset and utilizing Rubin’s causal model called the

Potential Outcomes Framework, (Rubin, 2005) to

verify inferences.

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