RISK is The combination of the probability of an event and its consequences

In the case of admission to all types of risk, risk or threat have the potential to become an opportunity

Hi Marina,

I think you have to understand the difference in definition between probability and possibility first.

Probability: "the extent to which an event is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible."

Possibility: "the state or fact of being likely or possible; likelihood."

Actually, those two words are synonyms. However, there is subtle difference between the two, for example probability implies that you know the fire is highly likely to occur (to the extent which you can almost count), while possibility is much weaker meaning that the fire is likely to happen but you can't be so sure therefore it is associated with uncertain risk which has to be modeled accordingly with nonlinear stochastic trait. So your colleague is right about using possibility. Particularly, probability is more subjective, but possibility is more objective (notice the wording "favorable" and "fact").

Thus, it is possible in the future, but people don't know when/where/how? It can occur in 1/10/100/1000/100000 etc years from now at any time/place? Possibilities do not require details about the knowledge of systems versus probabilities take characteristics of systems into account to become more specific in what might happen in the future?  

Exactly, Marcel. One can predict probability but not unknown possibility of existence. Risk essentially is uncertain and unpredictable. If one could predict risk, there would be no point to model risk. I think this question is quite good due to philosophical and modeling challenges. For example, we have to first define the difference between the two and then use stochastic model to catch this uncertain risk.

Probability, definitely.

Dear I will go with @Mahfuz Judeh . It is definitely Probability. Sorry to your Professor who think it other way.

Thanks to everyone who showed interest in my question and helped me to clarify the point at issue.

Sergei, thank you for example. Juehui, Marcel, I completely agree with you.

I have understood by now the following things.

Applying the probability theory implies fulfillment of a set of conditions. Probability distribution has to be defined. Personally, I in my latest research used frequency probability of fire occurrence to calculate forest fire risk. But to use this kind of probability I needed a huge number of fire examples. And it was impossible to get them.

Possibility theory (according to Dubois and Prade) is aimed at mathematical description of uncertainty connected with incompleteness of accessible information. This theory is based on the idea of possibility measure and doesn’t require some distribution to be given.

So, I decided to switch from probability to possibility. Forest fire risk is defined now as a measure of possibility that a certain object is likely to be on fire and the value of assumed harmful consequences of a would-be fire, which accounts for the quantity assessment of the object modification level as a result of natural emergency effect. I’m going to calculate the measure of possibility using rough sets.

On top of it, this professor is going to be one of the official opponents during my doctoral thesis defending. So, I should take into consideration his opinion).

Nice discussion. As a consequence, however, lets also try to keep "prediction" from being confused with "forecasting." I found the attached just now that seems to explain prediction (as opposed to forecasting) well. So above, please substitute "forecast" for "prediction," when talking about the future. 

https://www.msu.edu/user/sw/statrev/strv203.htm

There are methods to calculate the "Relative Risk" as a measure of the association between a given condition and the occurrence of an event. That is the case of the "odds ratio". If you have a number of cases of fire under a given condition, and the number of cases of fire in the absence of such a condition, yo can calculate the Relative Risk as the association between the condition and fire in a manner well known in human genetics.

Hi Marina, Besides Sergei's method, I think you will also benefit from Bayesian approach with some modifications.

James, thank you for valuable remark about the difference between prediction and forecasting.

M. Humberto, thank you for the information about "Relative risk" and "Odds ratio". If there some correlation between "relative risk" and "Bayesian conditional probability"?

For example, I have some forest region and I have forest fire close to this region. I can calculate fire danger of this forest region (using retrospective database of fire cases and meteorological data), and I can calculate the possibility that this forest region is affected by the fire when fire is known to have happened (using the mathematical model of forest fire dynamic). I can't realize what I get multiply this two values. Something like conditional possibility?

Sergei, Juehui, thank you for being so instrumental in providing me some kind of help. Sergei, I'll try to look into the methods you proposed.

Marina, my pleasure. This is why I love RG so much for its ability to allow many scientists from different field across the world to easily share and reconcile various interesting methods.

Juehui, it seems to me, I start loving RG too)

Definitely, Marina. I got started one month ago and now I cannot stop helping others by answering all the questions, some of which outside of my field are extremely interesting and thoughts stimulating.

I would also like to thank James again for another great and intuitive reference.

Dear Roland, you helped me so much, thank you for the explanation. I downloaded the book and will look into it.

Dear Roland,

My work is concerned with decision support system for protection against natural emergencies. I'd be glad to cooperate with you. Thank you for proposal. Bye.

Depends what exactly it is you want to measure. Measuring simply the POSSIBILITY of an event may be useful in risk assessment for CATASTROPHIC events, such as a nuclear reactor failure or an airplane systemic engine failure. These are non-recoverable events. 

If you are dealing with recoverable events ---such as losing a few millions in the stock market or burning a few acres of forest--- then probabilities and costs should be integrated. 

You do not have to  downplay the fact that losing forests can be reversible but still extremely bad! You can use a probabilistic risk measure that looks at the probability and cost of extreme events. CVaR, or Conditional Value at RIsk is such a measure. It has some very nice theoretical properties that can justify its use to your professor.

In conclusion: Finance literature and insurance are perhaps the most advanced in quantifying risks that can be monetized. You can find introductory chapters in my book Practical Financial Optimization: Decision making for financial engineers. Link provided below.

Dear Stavros, thank you for your help.  I haven't been even thinking of finance literature before. I'm very interested in reading your book.

@ Dear Marina, 

Risk should be assessed as a measure of probability as it reflects the continuum between absolute certainty and impossibility. Please check the links for more information....All the best. 

http://www.economicsdiscussion.net/articles/measuring-risk-probability-of-an-outcome-explained-with-diagram/1368

http://people.stern.nyu.edu/adamodar/pdfiles/valrisk/ch4.pdf

Dear Sardar,

I appreciate your help. I will browse your literature with pleasure.

Probability is always due to possibility.

In general definition of Probability is such Probability = Number of possible event / Total number of events.

Therefore first one has to count the possibility than he / she can calculate the probability. 

Dear Mohammad,

I appreciate your answer, thank you very much!

I believe that this is getting tangled up in definitions. If your purpose is to understand which risks to address with treatment actions, you cannot simply look at likelihood, you need to look at consequences as well. I'm also not quite clear if you are defining risks in terms of initiating events, like a hazard analysis, or in more general terms.

My colleagues and I use the standard ISO 31000 to guide our work and find that it is useful to first examine the consequences of a risk and then assess the likelihood of experiencing that level of consequence. This allows for the fact that many risk descriptions are not really definitive.

For instance, if you are concerned about the risk of a fire in a location near a town, I presume you might have a case in which the fire would be confined to the forest and one in which it would affect the town or perhaps some infrastructure, such as power lines, and the likelihood of these two cases would be different. If you clarify what sort of consequences you are talking about first it is easier to assess the likelihood of each case rather than trying to assign a likelihood to the general description that includes both cases.

Our measure of risk is a combination of consequence and likelihood. In some cases these might be described and combined numerically, possibly as distributions, while in other cases they might be described using qualitative scales and combined using a lookup matrix.

I'm not sure I can point you to anything specific to your area of study but you might find it useful to look at the following papers:

http://broadleaf.com.au/resource-material/climate-change-and-risk-management/

http://broadleaf.com.au/resource-material/setting-priorities-for-risk-treatment-and-assurance-of-controls/

There is also a paper describing an organisational risk management process, which I know is quite different, but if you look at section 3.3 Risk Assessment, you will see how sound qualitative methods can be used to understand risks and set priorities for treatments if you also think about existing controls and how effective they are. It is at 

http://broadleaf.com.au/wp-content/uploads/2014/11/VCAT-risk-review-case-study.pdf

I believe it is useful to concentrate on what decisions you want to make using the analysis rather than on academic definitions. Once you know what decisions you want to make and think about how you would do it, the information you need is easier to identify and the process can be tailored to meet that need.

Dear Stephen,

Thank you for being so instrumental in providing me with the detailed information.

I consider forest fire risk as a measure of possibility that a certain object is likely to be on fire and the value of assumed harmful consequences of a would-be fire, which accounts for the quantity assessment of the object modification level as a result of natural emergency effect.

I will read the papers, you propose, with pleasure. Thank you.

Hi Marina,

I think you also need to consider modeling after the data (the kind of data available to you, that is the type of data you can get your hands on).

Richard

Hi, Richard. Thank you.

I use two types of methods in my research, namely analytical modeling and machine learning methods based on past experience in the form of statistical data describing forest fires. I use analytical modeling for fire dynamic and fire risk calculation, and  machine learning methods for decision making.

Marina, I like your comprehensive methods to modeling. I tend to take the same route when it comes to very complex and critical data. 

Richard, when it comes to semi-structured, hard formalizable problems, analytical methods don't work. You are forced to split a problem to a set of tasks and use a complex of different models and methods.

Exactly.

In public health literature the focus is on risk analysis, measured as you mentioned, probability. But I don't know can I measure possibility? Is there a definition about?

Dear Miguel,

Thank you for your question. Possibility goes in parallel with probability. Possibility theory is a simple approach to reasoning with imprecise probabilities. Possibility of some state shows if this state is plausible, or not, and to what extent. For example Zadeh interpreted the membership functions of his fuzzy sets as possibility distributions. There is no universal formula for calculation possibility. If you are interesting in this question, you can read Dubois and Prade. I attached one of their articles.

Thanks for your answer and the article. I'll read it with much interest.

I'm still inclined to ask what question you are trying to answer and whether more sophisticated or just different analytical methods will add anything to the outcome. One of the challenges of analysis that is often just allowed to happen, rather than being thought through, is how much detail and complexity is useful or even supportable with the data at hand.

When the ultimate outcome is a human decision and an analysis is really just informing and supporting that judgement, I see it as working towards a balance between the analysis and the human understanding to arrive at a point at which they are consistent with one another so the humans believe the model and the model helps explain and support their conclusions.

It's easy to be carried away into analysis that goes deeper than the data you are analysing and also to go into analysis that the ultimate decision makers don't need or don't understand.

In England, I have heard many time from my professors, lab technicians, and university security officers the convincing wisdom "It is better to be safe than to be sorry". I think that looking at risk as possibility is better than looking at it as probability since the first account will induce more precautions than the second. Please see the attached article.  

http://www.ccohs.ca/oshanswers/hsprograms/risk_assessment.html

It's fine to be safe rather than sorry if it costs you nothing to do so. Most real risk management situations involve the allocation of resources so it is necessary to understand the difference between separate risks in terms of both their potential consequences and the likelihood of experiencing those consequences.

Defining risk solely in terms of consequence or likelihood, no matter what term you use for likelihood, will never guarantee an efficient allocation of resources. Risk has to be measured in terms of the two characteristics at once, whether it is by calculating something that depends on them mathematically, such as the mean of a distribution, or using qualitative measures and lookup tables, such as the ubiquitous 5x5 consequence and likelihood matrix.

Dear Stephen,

Thank you for your answer. I was confused when the professor proposed me to use possibility to calculate risk instead of probability. I just wanted to listen opinions about the point at issue. And I appreciate everybody who answered and attached the papers. It helped me to clarify some details. Thank you.

Dear Dr. Nizar,

Thank you very much for your answer and for the link. I'll read with pleasure.

Risk is the probability of harmful consequences or expected losses (deaths, injuries, destroyed and damaged buildings, etc.) as a result of interactions between a natural hazard and local vulnerable conditions (UNDP, 2004).

Risk  is the probability of harmful consequences, or expected loss (of lives, people injured, property, livelihoods, economic activity disrupted or environment damaged) resulting from interactions between natural or human induced hazards and vulnerable/capable conditions. Conditionally risk is expressed by the equation Risk = Hazards x Vulnerability/Capacity. (UN/ISDR, 2002).

Dear Fillipe,

Thank you very much for your answer.

Dear Roland,

Thank you for your interest and for your support. I'll read your articles with pleasure, and I'm sure that I'll turn to you with questions).

In terms of forest fire risk, recently I came to the idea of consideration of two types of risk, namely the risk of ignition and the risk of burning. I consider the risk of ignition for definite forestry object as a measure of ignition probability (fire danger). But the risk of burning is much more interesting thing. It has dynamic value and is calculated providing that the fire is known to have happened. It depends on fire distribution model. And I can't look at this risk as a measure of probability. On top of it, I have specific view of fire. I digitize the forestry area by square cells, and fire is presented as a rough set of these cells. So, I look as the likelihood that the object is affected by definite fire, as a possibility. My colleague and I are preparing the article now with the explanation of these models. I'll download it here, as soon as it's published.

Dear George,

Thank you for being so instrumental. I downloaded your article. I'll have a look at it with pleasure.

Kindest regards,

Marina.

Probability is a an abstractive mathematical notion , defined for infinite number of triasl. It is not possible to calculate probability of such a rare event ( dont laugh - forest fire are  rare  it os not  everyday  event in a given forest. ) In my opinion it would be reasonable to investigate as much as possible of forest fire cases , divide them into group according to some parameters - kind of trees , external temepratures etc, and calculete probabilty ( approximated ) by the Poisson distribution.

Dear Marina,

the question of what risk is has two faces. One which seems to very well known (some probability and associated consequences). The other face seems remaining in the shade, saying that the risk is much more than PxC, since PxC is only the measure of risk - one out of many measures. Therefore, I would like to introduce you the work of professor Terje Aven from University of Stavander, he wrote numerous papers on risk related issues. His expertise is in oil and gas offshore industry. Fire is a common denominator for yours and his field :) In his papers and books you will find all existing definitions of risk. These are also listed in our recent paper, which is open access one: http://www.sciencedirect.com/science/article/pii/S0951832015000356

Good luck !

https://www.researchgate.net/publication/258835771_Decision_making_under_uncertainty_in_energy_systems_State_of_the_art

Article Decision making under uncertainty in energy systems: State of the art

Dear Maryna Zharikova These links could help you

Article Occupational health and safety risks: Towards the integratio...

Article Proposal of a risk-factor-based analytical approach for inte...

Article A new practical approach to risk management for underground ...

Dear Adel Badri,

Thank you for your help! Are your papers not open access?

Dear Maryna Zharikova

I can share them with you.

I am waiting for your requests RG online.

Dear Adel Badri,

Thank you very much. I will study your papers.