_{1}

The number of piracy attacks on the Gulf of Guinea is increasing even though armed robbery and piracy at the Gulf of Aden is on a gradual decline. The International Maritime Bureau (IMB) specified in (2015) that the Piracy Reporting Centre updated their records to 58 attacks by pirates, comprising of ten hijackings. With 11 attacks reported for the first quarter of 2013, and 27 attacks in 2012 (almost three times more than in 2011) along the territorial waters of Nigeria thus making her the most affected country. However, it is believed that other coastline countries and areas most affected apart from Nigeria on the Gulf of Guinea comprise Ghana, Togo, Benin and Bakassi. This is evident as pirates have increased their operations mainly petro piracy on the Ghanaian waters, which negatively affects marine transportation and maritime security. The scenario has aggravated with the discovery of oil along these coastlines. This paper gives methodological responses to maritime piracy by way of three models namely, the Ordinal Logistic Regression, Series Hazard Modelling for Maritime Transport Analysis and the Bayesain Networks. The uniqueness of these models in relation to their ability to address some of the pertinent issues associated with modern day piracy is looked at. The study was conducted as a panel analysis based on a longitudinal quasi-experimental research design with focus on piracy attacks that occurred between 2006 and 2015 culminating finally in the various forecasts based on each of the different models.

Piracy was a limited problem prior to 2009. However, piracy started being noticed during the 1990s as small armed groups began holding ships and crew members for ransom. In this scenario, those responsible for piracy activities argue that their actions are just because they are protecting Somalian fishing resources [

The effectiveness of laws covering maritime piracy internationally, especially in Articles 100 to 107, and 110 of the UN Convention on the Law of the Sea (UNCLOS) have been questioned due to ongoing attacks. There is an interesting similarity between the Articles of UNCLOS, and the Geneva Convention of the High Seas 1958 (Articles 14 to 22).UNCLOS does not bind every state, however, there are non binding states bound by the Geneva Convention. This suggests that articles regarding the Law of the Sea could be deemed the same [

The surge of pirate activities in the Gulf of Guinea (GoG) (

[

The research questions to be addressed include:

1) What are the causes of the piracy surge in the Gulf of Guinea and the obstacles to effective resolution?

2) What are the effects of oil piracy in the Gulf of Guinea on maritime transportation (concerning the effects on reputation damage to maritime transport company, insurance costs, transport price increase, extra cost on changing route, trade disruption and the loss of crude oil)?

3) What are the effects of oil piracy in the Gulf of Guinea on maritime security (considering the effects on security cost, more integration with the navy, dangers associated with sailing in unfamiliar waters, threat to crew and security equipment)?

4) What are the strategies required to manage these threats?

This study is being conducted as a longitudinal design. This type of research design was chosen because the longitudinal study allows the sample to be followed over time, which then allows for repeated observations throughout a specific time period [

Longitudinal studies are quasi-experimental research designs that involves measuring repeated observations of the same variables over time. These studies are often considered to be observational studies [

Observational longitudinal studies that do not manipulate variables are argued to be less powerful in the detection of causal relationships than experiments. On the other hand, because of the repeated observation of different variables, longitudinal studies are more powerful than cross-sectional studies because of the ability to exclude time-invariant unobserved individual differences and being able to observe the temporal order of events [

There are different uses of longitudinal studies. For instance, longitudinal data allows the duration of a variable to be analyzed effectively. Moreover, survey researchers are able to develop causal explanations that are typically only attainable through experiments [

As noted previously, the longitudinal study is a quasi-experiment, which is an empirical study, allowing for the estimation of the causal impact of an intervention on the target population, yet does not include random assignment. There are similarities between quasi-experimental research and traditional experimental design or randomized controlled trials. However, quasi-experimental designs lack the random assignment element for treatment or control, instead allowing the researcher to maintain control of the treatment condition through the use of another criteria (in this case, incidences of piracy) [

Quasi-experiments have concerns issued against them in relation to internal validity due to the difficulties that may exist in comparing treatment and control groups at baseline. However, through the use of random assignment, participants are afforded the same opportunity of assignment of the intervention or comparison group. This allows for the consideration that differences in relation to observed/unobserved characteristics to occur through chance, rather than a treatment-related systematic factor. However, randomization alone does not guarantee equivalency at baseline, making it difficult for quasi-experimental studies to demonstrate a causal link, especially in the event of uncontrollable or unaccounted for confounding variables [

Experiments that contain random assignment allow units to have the same opportunity of assignment to either the control or intervention group. The qua- si-experimental design allows for the assignment for a treatment to be based on a criteria rather than random assignment [

The effectiveness of quasi-experiments varies. However, these experiments are typically deemed very effective due to pre-post testing [

In some instances, the use of quasi-experiments are considered ineffectual by experimental purists, leading them to be called queasy experiments [

True experiments rely on random assignment in order to control for all variables. Quasi-experiments are commonly used for those studies where participants cannot be randomised. Therefore, some researchers argue that it is possible to distinguish between natural and quasi-experiment [

Internal validity considers the truth (in its approximate form) regarding inferences that are in relation to causal relationships. Since quasi-experiments focus on causal relationships, internal validity is increasingly important. As a result, internal validity occurs when the researcher attempts to control all variables that may have an impact on the results of the study. Therefore, threats to internal validity include statistical regression, historical data, and the participants themselves. In order to maintain a high internal validity, researchers consider the factors (such as outside causes) that impact the outcome [

On the other hand, external validity refers to the extent that it is possible to generalise the results of the research study’s sample to the population of interest. As a result of high external validity, this generalisation is accurate and is representative of the entire population based on the sample. Moreover, external validity is increasingly important due to statistical research due to the need for an accurate depiction of the population. As a result of low external validity, the research results are less credible. This means that it is necessary to reduce threats that may exist in relation to external validity, which is often conducted through random sampling and random assignment [

There are different advantages of quasi-experimental designs. For instance, in many cases, the use of quasi-experiments is easier to establish than true experiments due to the ability of quasi-experiments to be conducted without randomisation of participant assignment. Common usages of quasi-experiments are when it is impractical or unethical to randomise the participants, making this design beneficial for research that would otherwise be harmful to participants. For instance, the use of quasi-experiments allows ecological validity threats to be minimised, especially as natural environments do not have artificiality issues, whereas a laboratory setting does [

Despite the advantages, quasi-experimental designs have disadvantages. For instance, the estimates of impact can be contaminated through confounding variables [

For this study, a relevant quasi-experimental design is the natural experiment. It differs from the traditional quasi-experimental design (focusing on treatment) because the researcher is not manipulating a variable. The researcher does not control any variable and does not use random assignment, which allows the experimental control to occur naturally. Although this technique may appear unorthodox and/or inaccurate, it has been shown to be effective in many different studies, such as in research studies analysing sudden events (whether positive or negative) [

This particular study is using a quantitative longitudinal research design, focusing on natural experimentation through a panel analysis. The use of panel analysis is valid for this study because it is used in a wide range of disciplines, such as epidemiology, social science, and econometrics. Therefore, it can also be used in finance studies effectively. The focus of panel analysis is time series analysis [

y i t = a + b x i t + ∈ i t (1)

Equation (1): Panel Data Regression Model [

In Equation 1, y refers to the dependent variable, x refers to the independent variable, a and b refer to coefficients, i and t refer to distinct variables (such as individuals and time), and Є refers to the error variable. The assumptions of the error variable conclude whether or not the equation focuses on fixed or random effects. In the case of a fixed effects model, the error variable is non-stochastic, which renders the model to one dimension through a dummy variable. In the case of a random effects model, the error variable varies stochastically, which makes the i and t in the formula to require special treatment or the completion of an error variance matrix [

This study uses panel data, important because of the analysis of all piracy attacks globally within the time period. The time period being assessed is from 2006 to 2015. This is done in order to allow a wide range of data through a time series analysis. Moreover, the data will be obtained from the International Maritime Bureau (IMB) the Piracy Reporting Centre. Although the results will consider all countries, particular emphasis will be placed on the Gulf of Guinea. Data will be downloaded from the sources into Microsoft Excel. The data will be displayed in rows and columns, where rows are the countries and columns are the year of occurrence. The final row shows a progression of all piracy attacks throughout the time period. The data analysis was conducted using Microsoft Excel. In some instances, the RealStats resource add-in for Excel was used for enhanced statistical analysis of the data. The RealStats add-in is beneficial because it works effectively with the existing statistical techniques enabled by Microsoft Excel, yet allows for an additional layer of statistical analysis. Specifically, the use of Microsoft Excel was chosen in order to provide a transparent view of data in consideration of the models selected to analyse the data. The models chosen to analyse the data are ordinal logistic regression, series hazard modelling for maritime transport risk analysis, and Bayesian networks (BN’s) technique for maritime risk analysis.

Data AnalysisThis study uses three different data analysis techniques. The goal of these techniques is to determine the change in piracy attacks, especially in relation to the Gulf of Guinea. They include: 1) ordinal logistic regression; 2) series hazard mo- delling for maritime transport risk analysis; and 3) Bayesian networks (BN’s) technique for maritime risk analysis. Each is discussed in its own sub-section below.

Initially, Peter McCullagh established the ordinal logistic regression, which is a statistical model. The ordinal logistic regression is also known as the ordered logit model or the proportional odds model. Generally, this model is considered a regression model and is used in relation to ordinal dependent variables. It is assumed within the model that the purpose of the analysis is to determine the prediction rate for a certain response. The prediction rate is based on the responses obtained for other questions. The response options are typically set (such as through a close-ended survey/questionnaire). On the basis that these assumptions are met, the ordinal logistic regression model can be used [

It is noted that the ordinal logistic regression model can only be used with data that meets the proportional odds assumptions, which assumes that proportions allow the response to be divided into classifications (such as px, where p refers to proportion and x refers to the number of the division). This involves determining the logarithms of the odds, rather than the probability, of a particular answer. This is established through the following equation:

log log p x p y (2)

Equation (2): Proportional Odds Assumption

In this formula, px refers to the sum of the current and previous categories and py refers to the sum of all future categories. Therefore, the proportional odds assumptions argue that an arithmetic sequence can be established because the number added to each logarithm is the same. Within the model, it is suggested that the results of the assumption represent the numbered of required additions for each logarithm. These results are determined through observed variables, established through a linear combination [

ln ln ( ( Prob ( event ) ( 1 − Prob ( event ) ) (3)

Equation (3): Ordinal Logistic Regression Model

The logit is found on the left side of Equation (3) and is the log of the odds that an event will occur. This “event” is clarified as the prob (event) as established in the first equation. Therefore, the calculation is based on the ratio of occurrences of an event as compared to the number of events that do not occur. The purpose of the coefficients in the logistic regression model is to show the degree of logit changes based on the predictor values variables. For the first portion of this part of the analysis, the data is shown for all countries and considers a specific time period. Based on the data, the range of occurrences is 0 to 160, resulting in coefficients of 20 ranges (P1 through P20, with multiples of 8 for each range). A table will be constructed with the range, count, and ratio. The first column is self-explanatory and includes the range title (P1, P2, etc.) and potential number of occurrences (0 - 8, 9 - 16, etc.). The second column is also self-explanatory and includes the number of times for the entire time period that the specified number of piracy attacks occurred. The count is based on the years and is conducted for each country. The third column is the ratio column. The ratio is calculated as follows:

Ratio = Count TotalCount (4)

Equation (4): Ratio Equation for Ranges

For Equation (4), the count is found in the second column and the total count (found in the third column) is the sum of all counts from that specific range to the end of the data. For example, the total count for P3 would be from P3 to P20. Each of the ratio calculations is rounded to four decimal points.

The second portion of this analysis involves the assumptions, which are derived from Equation 1. The assumptions names compose the first column and range from 0 to 19. As noted in Equation 4, the final result is, essentially log (x/y). Therefore, the second and third columns are the numerator (x) and denominator (y) respectively. The fourth column is the result of x/y, whereas the final (fifth) column is the final output of log(x/y). Since the numerator is the probability of the event, it is the ratio as found in the first portion of the analysis. The denominator, therefore, is calculated as:

y = 1 − prob ( event ) (5)

Equation (5): Calculation for Assumption Denominator

Through the division of the numerator and denominator, the result (fourth column) is derived, which allows for the log of the result to be calculated in the fifth column. These two steps (resulting in independent tables) allow the variable to be determined in the third step. The third step, as noted, allows for the ordinal logistic model variables to be determined accurately. The table used to display these results has 5 columns. The first column identifies the variable, which ranges from 0 to 19. The second column is the logit. The logit is calculated as:

L o g i t = ln ln ( prob ( event ) 1 − prob ( event ) ) (6)

Equation (6): Calculation for Logit

Therefore, this could be considered to be ln(x/y) using the numerator and denominator in the preceding step. The third column is β, which is found from the preceding step and is log(x/y) as defined previously. The fourth column is X and refers to the count obtained in the first count for each range. In this scenario, P1 is assumption (or variable) 0. The final column is found by multiplying β and X. For the first variable (0) there is neither a logit or a X variable, and βX is assumed to be β.

The fourth step involves the use of the raw data and the RealStats add-in for Excel to conduct the binary logistic regression and the multimodal logistic regression. From the regressions, it is possible to obtain the coefficient, LL0, LL, LL1, chi square, degrees of freedom, p-value, alpha, R-sq (L), R-sq (CS), R-sq (N), and Hosmer. Moreover, the regressions provide the ROC curve (the fifth step in the analysis), which provides information regarding the p-Pred, failure rate, success rate, failure cumulative rate, success cumulative rate, FPR, TPR, and AUC.

With the previous five steps, it is evident that it is possible to predict the number of attacks that would occur using the ordinal logistic regression model. The Gulf of Guinea includes Equatorial Guinea, Ghana, Guinea, and Guinea Bissau. The total number of piracy attacks are found for each of the locations for the time period of 2006 to 2015 and totals are found for all locations for all years. Each location, as well as the total, for five final outputs, has the number of piracy attacks for the year multiplied by the β value found previously in the third step. Each of these products are rounded to one decimal point. Once the values are calculated for the β value, each location’s results (including the total of all 4 areas) is summed. In order to find the predictor, the log is found for each total for all 5 data sets, resulting in 60 logs. Once all of the logs are determined, they are totalled then the ln is found of the total logs. This final ln is the predictor that attacks will occur. The ln is rounded to the nearest whole number and is used to forecast anticipated future attacks. It is assumed that piracy attacks will increase/decrease by the predictor between 2016 to 2030. For 2016, the values are based on 2015, whereas for 2017 and after, the values are based on the previous forecasted attacks. The table constructed to show the forecasts will be for all 5 scenarios (Equatorial Guinea, Ghana, Guinea, Guinea Bissau, and total of the preceding four areas). Therefore, the first column will contain the year being considered. The second through sixth columns will have the forecasted attacks. The final (seventh) column will have the average number of forecasted attacks for the year.

The summary of steps undertaken to conduct the ordinal logistic regression analysis are:

1) Determine the range size based on total number of occurrences in order to determine the determine the coefficient rate (Px through Py), allowing for equal numbers in each range.

2) Based on the raw data, count the number of occurrences for all years and countries within a specified range.

3) Based on the count obtained from the raw data, determine the radio of occurrences divided by total occurrences based on the range being considered. This means that the total count will change for different ranges. The ratio of occurrences is then rounded to four decimal points.

4) The assumptions (considered to be 0 through 19) are determined through the ratio of occurrences, 1-ratio of occurrences, and the log. Therefore, the ration of occurrences is numerator. The valve found for 1-ratio of occurrences (also know as prob (event) is the denominator. Once the numerator and denominator are divided, the log of the result is found.

5) The variable can be determined on the previous steps. The logit is the ln of the result of the numerator and denominator (as divided in the previous step). B is log of the result (the results of the preceding step) and X is the count from the second step. The variable is found by multiplying β and X. For the first variable (0) there is neither a logit or a X variable, and β x is assumed to be β.

6) The raw data for the time period and countries is entered into the RealStats add-in for Microsoft Excel to conduct the binary logistic regression and the multimodal logistic regression in order to obtain the ROC curve, which provides information regarding the p-Pred, failure rate, success rate, failure cumulative rate, success cumulative rate, FPR, TPR, and AUC.

7) These steps allow for the forecast to be determined. In order to do is this, the predictor of occurrences must be determined. A computation of the total number of piracy attacks for the individual countries is determined. For the specified time period, the total number of piracy attacks is found for each location. The piracy attack values are multiplied by the β value and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks.

[

λ k ( t / X k ) = λ 0 ( t ) exp exp ( X k β ) (7)

Equation (7): Series Hazard Modelling for Maritime Transportation Risk Ana- lysis Formula

The Series Hazard Model is projected through the Cox Proportional Hazard model. There are slight differences. For instance, the Series Hazard Model uses failures for estimation purposes, whereas the Cox Proportional Hazard Model uses subjects for estimation purposes. However, Equation (7) can be expanded to Equation (8) as (shown below) in order to capture previous failure history for conditional independence purposes. In Equation (8), it is noted that the functions of previous failures are represented by Z (such as maritime piracy). As a result, it is possible to derive the partial likelihood function from the Series Hazard function, as shown below:

λ k ( t / X k ) = λ 0 ( t ) exp exp ( X k β + Z k y ) (8)

Equation (8): Modified Series Hazard Model

The matrix Z k y is used to measure information about failure history in order to account for the dependencies that exist across these failures. Moreover, the matrix Xk consists information that is related to a specific failure. As a result, through the completion of this model, it is assumed that failure represents the unit of observation and it is possible (even permissible) to introduce dummy variables as needed. Within the condition of this analysis, λ 0 ( is represented by FPR, (can be shown on an ROC curve), X is the total of FPR and TPB, β is represented by the AUC (can be shown on an ROC), whereas Z k y is represented by p-Pred (can also be shown on an ROC). The constructed table will have seven columns. The first contains the FPR, whereas the second column the TPR. The third column is the sum of the first two columns. The fourth and fifth columns are explained previously. All values are rounded to 4 decimal points. The sixth column contains the results of the formula (see Equation (8)). The final column is the log of the results of the formula. The final row contains the sum of these logs.

Considering the Series Hazard Model, the forecast predictor is based on the sum of logs to the power of 1 through 5 and is the absolute value of the total for the countries and years. The Gulf of Guinea includes Equatorial Guinea, Ghana, Guinea, and Guinea Bissau. The total number of piracy attacks are found for each of the locations for the time period of 2006 to 2015 and totals are found for all locations for all years. Each location, as well as the total, for five final outputs, has the number of piracy attacks for the year multiplied by the sum of logs to the power of 1 through 5 (resulting in 5 rows for each country, as well as a sixth totals row for annual data). Each of these products are rounded to one decimal point. In order to find the predictor, the log is found for each total for all 5 data sets, resulting in 60 logs. Once all of the logs are determined, they are totalled then the ln is found of the total logs. This final ln is the predictor that attacks will occur. The ln is rounded to the nearest whole number and is used to forecast anticipated future attacks. It is assumed that piracy attacks will increase/decrease by the predictor between 2016 to 2030. For 2016, the values are based on 2015, whereas for 2017 and after, the values are based on the previous forecasted attacks, as shown in the table. The table constructed to show the forecasts will be for all 5 scenarios (Equatorial Guinea, Ghana, Guinea, Guinea Bissau, and total of the preceding four areas). Therefore, the first column will contain the year being considered. The second through sixth columns will have the forecasted attacks. The final (seventh) column will have the average number of forecasted attacks for the year.

The summary of the steps undertaken to conduct the Series Hazard Model are:

1) Construct a table with seven columns. The first, second, fourth, and fifth columns contain the FPR, TPR, p-Pred, and AUC (respectively) from the ROC curve information. The third column is the sum of FPR and TPR. The sixth column is the result of Equation (7), whereas the seventh column is the log of the results. The final row in the table will have the sum of logs.

2) The sum of logs can be considered by the power of 1 through 5 in order to develop the forecast predictor. The four countries under consideration are Equatorial Guinea, Ghana, Guinea and Guinea Bissau. The number of piracy attacks is determined for each country as well as the total pirate attacks which occurred for the considered time period. The piracy attack values are multiplied by the sum of logs to the power of 1 through 5 and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks.

[

P ( V ) = ∏ i = 1 n ( V i | P a ( V i ) ) (9)

Equation (9): Bayesian Network Modelling Equation

In the final conduction of this analysis, the probability is the p-Pred and is multiplied by the values (total number of occurrences). For the constructed table, the individual rows will be summed then log (sum). If the log(sum) is deemed to be between −0.15 and 0.20, the value will be considered reliable and the predictor can be used to determine the forecast predictor. If the value is outside of this range, the log will be found of log (sum) and added to p-Pred (used in the previous model and considers the power of 1 through 5) used for the forecast model.

Considering the BN model, the forecast predictor is based on the sum of logs to the power of 1 through 5 and is the absolute value of the total for the countries and years. If the criteria (between -0.15 and 0.20) is met, no further action will be taken to the predictor. However, if the criteria are not met, the log of log (sum) will be added to the predictor. The Gulf of Guinea includes Equatorial Guinea, Ghana, Guinea, and Guinea Bissau. The total number of piracy attacks are found for each of the locations for the time period of 2006 to 2015 and totals are found for all locations for all years. Each location, as well as the total, for five final outputs, has the number of piracy attacks for the year multiplied by the sum of logs to the power of 1 through 5 (resulting in 5 rows for each country, as well as a sixth totals row for annual data). Each of these products are rounded to one decimal point. In order to find the predictor, the log is found for each total for all 5 data sets, resulting in 60 logs. Once all of the logs are determined, they are totalled then the ln is found of the total logs. This final ln is the predictor that attacks will occur. The ln is rounded to the nearest whole number and is used to forecast anticipated future attacks. It is assumed that piracy attacks will increase/decrease by the predictor between 2016 to 2030. For 2016, the values are based on 2015, whereas for 2017 and after, the values are based on the previous forecasted attacks, as shown in the table. The table constructed to show the forecasts will be for all 5 scenarios (Equatorial Guinea, Ghana, Guinea, Guinea Bissau, and total of the preceding four areas). Therefore, the first column will contain the year being considered. The second through sixth columns will have the forecasted attacks. The final (seventh) column will have the average number of forecasted attacks for the year.

The summary of steps undertaken to conduct the BN model are:

1) Construct a table which multiplies the p-Pred from the ROC curve by the values. These values are rounded to one decimal point and then summed. All rows are summed then logged. If the log is within the range of −0.15 to 0.20, nothing is done to the predictor. If the log is outside of this range, the log (sum) is then logged again, which will be added to the predictor.

2) The sum of logs can be considered by the power of 1 through 5 in order to develop the forecast predictor. The previous step is outside of the stated criteria, it is added to the forecast predictor. It is prudent to determine the total number of pirate attacks for the countries being considered. At these locations, the total number of piracy attacks for the time period is determined. The piracy attack values are multiplied by the sum of logs to the power of 1 through 5 and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks.

Methodological assumptions are those things that are accepted as true or plausible by researchers and colleagues. Therefore, methodological assumptions refer to the assumption that certain aspects of the study are true based on the population, statistical test, design, or methodology. Commonly, assumptions involve honesty and truthful responses in survey studies. For this specific study, it is assumed that the data obtained was recorded accurately and without bias. It is also assumed that the data shown in this analysis is complete. This study is limited to three statistical models. However, the selected models were deemed to be the most flexible in order to conduct the forecast for anticipated piracy attacks. The study is limited to a specific time period (2006 to 2015). The study is limited to determining the correlation and forecast of piracy attacks, not causation.

In the Gulf of Aden, piracy and armed robbery are on the decline but there is an increase in the Gulf of Guinea. Records from the Piracy Reporting Centre which was specified by the International Maritime Bureau (IMB) (2015) indicate that 58 pirates’ attacks occurred with then being hijacks. In the first quarter of 2013, 11 attacks were reported, as against 27 attacks in the years 2012, almost thrice the number in 2011, with Nigeria being the country affected the most. However, other coastlines countries suffered the surged of piracy in the Gulf of Guinea. There comprise Ghana, Togo, Benin and Bakassi. A new focus has been the Ghanaian waters where pirate activities have increased amidst the oil found in these which possess the capacity to affect maritime transportation and maritime security [

The research methodology is designed to provide a process for conducting the study. This includes steps and protocols for data collection, processing, and analysis. Based on this knowledge, the research methodology chapter is divided into seven sections. The chapter considers three separate models: 1) ordinal logistic regression; 2) series hazard modelling for maritime transport risk analysis; and 3) Bayesian networks (BN’s) technique for maritime risk analysis to analyse one set of data. The goal of the chapter was to explore the methodology used so that future researchers could reconstruct the study as desired. The study was conducted as a panel analysis based on a longitudinal quasi-experimental research design and focused on piracy attacks that occurred between 2006 and 2015.

For the ordinal logistic regression analysis, the researcher determined the range size based on total number of occurrences in order to determine the coefficient rate (Px through Py), allowing for equal numbers in each range, counted the number of occurrences for all years and countries within a specified range, and determined the ratio of occurrences divided by total occurrences based on the range being considered. The assumptions of this model were identified as 0 through 19 and were determined through the ratio of occurrences, 1-ratio of occurrences, and the log. Therefore, the ratio of occurrences is the numerator. The value found for 1-ratio of occurrences (also known as prob (event)) is the denominator. Once the numerator and denominator are divided, the log of the result is found. The logit was determined through the determination of the ln of the result of the numerator and denominator (as divided in the previous step). β is the log of the result (the results of the preceding step) and X is the count from the second step. The variable is found by multiplying β and X. For the first variable (0) there is neither a logit nor an X variable, and βX is assumed to be β. Next, the raw data for the time period and countries was entered into the RealStats add-in for Microsoft Excel to conduct the binary logistic regression and the multimodal logistic regression in order to obtain the ROC curve, which provides information regarding the p-Pred, failure rate, success rate, failure cumulative rate, success cumulative rate, FPR, TPR, and AUC. This information allowed for the forecast. In order to do this, the predictor of occurrences must be determined. As a start, pirate attacks are noted, and the total number found for Equatorial Guinea, Ghana, Guinea, and Guinea Bissau. The time period for these attacks is vital for each location hence it is important to determine the total number of attacks. The piracy attack values are multiplied by the β value and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks.

For the series hazard model, a table was constructed with seven columns where the first, second, fourth, and fifth columns contain the FPR, TPR, p-Pred, and AUC (respectively) from the ROC curve information. The third column is the sum of FPR and TPR. The sixth column is the result of Equation (7), whereas the seventh column is the log of the results. The final row in the table will have the sum of logs. The sum of logs can be considered by the power of 1 through 5 in order to develop the forecast predictor. The selected Gulf of Guinea (GoG) countries should have their total number of attacks found as well as the totals for the number of pirate attacks during that time period for these specific areas. The piracy attack values are multiplied by the sum of logs to the power of 1 through 5 and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks.

For the BN model, a table was constructed where the p-Pred (found from the ROC curve) was multiplied by the values in the raw data. These values are rounded to one decimal point and then summed. All rows are summed then logged. If the log is within the range of −0.15 to 0.20, nothing is done to the predictor. If the log is outside of this range, the log (sum) is then logged again, which will be added to the predictor. The sum of logs can be considered by the power of 1 through 5 in order to develop the forecast predictor. The previous step is outside of the stated criteria, it is added to the forecast predictor. To commence, find the total number of pirate attacks for each of the four GoG countries. The time period under consideration is of essence, and should be used for the total number of total pirate attacks in that location. The piracy attack values are multiplied by the sum of logs to the power of 1 through 5 and rounded to one decimal point, then summed to reach a final value for each location (including the total). Next, the log is found of these values and then summed. The final value is the ln of the sum of the logs, which is then rounded to the nearest number to obtain the predictor of forecasted attacks. The goal is to determine the difference in forecasts based on each of the different models.

Ofosu-Boateng, N.R.L. (2017) Methodological Responses to Contemporary Maritime Piracy in the Gulf of Guinea. Open Journal of Social Sciences, 5, 240-259. https://doi.org/10.4236/jss.2017.54022