Hi everyone,
One more month of project and one less to finish the PhD. What a stress!
Currently finishing the final piece of research work to start the worst nightmare of every PhD, writing :) Well, I already started ...let's be honest...otherwise I would be in trouble (and maybe I 'm already in trouble)...
This must be a thing of age, but 3 years sure go fast.
Well, I am still preparing to go to one of my last conferences (yes, crazy to still consider conferences, but these are progressively more important) and a couple of "extra things".
Today I'll spend some time to talk about one of the lessons I learned during all this time working with statistics and probabilistic models (or maybe this comment extends to research in general) .
This week I was thinking... this thing of the "getting up the chair and screaming YES!!!" moment must be a myth... Why?
Mainly because a real contribution comes from many almost YES moments :) its just that these years made me learn that it is not recommended to "celebrate" too soon heheh
You see the most brilliant minds in history saying that hard-work is almost everything and for sure they know it.
People are amazing identifying patterns, and that's what you spend most of your time doing in research (theoretical or experimental, even though that theoretical is a bit different).
Particularly in statistics, where there is this randomness associated, one can never celebrate too soon if something you're working on effectively "works".
Statistics is a bit tricky in this, because you can never be too confident that you have some pattern or "working" thing to in the end realize that you were just super"lucky". Having then to deal with the after-unhappiness and -disappointment ...
This is why I have the feeling that people from statistics can never get up the chair in the middle of the office and scream "YESSS!" in this moment of "heat" (at least not because of work).
You really need to be extra careful before doing any celebration... test all the things ...many times... and many times again.... and many times again... confirm the statistics... etc etc
This of course applies to all the research, whether you're in the lab, or trying to represent some physical phenomena with maths.
Nevertheless, with this feeling of "never-eureka" coming, comes preserverance and "earth-footing" which is of major importance to at least complete a PhD.
Well, not that was expecting to have it in first place... But it is funny. Movies are always better. Even more, progressively I feel that I understand less of what I am working. People say it is normal....
See you (this time don't know when I will have the strength to come here write)
Rui
ESR4 Probabilistic Optimization of the Design of Offshore Wind Turbine Towers
Saturday, 14 April 2018
Sunday, 11 February 2018
Trainning Week Trinity and University College Dublin
Hi everyone,
Quite the cold out there, no?! And what do we do? Write a blog post!
Naan that's not true, otherwise, with such a weather here I would post almost every day :)
So, we had recently the trainning week here. Very focused on business and more soft skills, such as project management or even how to manage an interview.
I am not a capitalist by nature but I have to say that business can be quite interesting and challenging.
When you're used to numbers and to analyse very difficult things as most of the things you deal with when doing a PhD in engineering you may tend to depreciate how hard it is to succeed at business. Truth is that it is really hard.
You need to have an additional set of skills (for good and bad). Lot's of people only use the good ones, lots both and lots only the bad ones. Even if you do not have any interest in business itself, the activity remains quite interesting from the psychlogical point of view.
The thing is that this is a field that I do not know yet well. I read a lot about people ( all these major nd minor new entrepeneurs), and see many things but I didn't gather enough independent tought to be able to conjecture about it.
The training week was interesting because of that. Basically, I am still chewing my opinion on business and how to deal with it. Will I keep chewing my whole life? Thats the question.
Regarding work, same as always. Finishing a PhD in 3 years is quite demanding. You can see that by the lack of activity here. I feel that I cannot wrap my mind over anything else than the PhD for now. Still 6~7 months to go. I can see the light at the end of the tunnel :) lets see if it is a good light or a train to run over me hahah
Well, working on finishing research now...to start writing (or compiling) ASAP. Stressfull.
And the random ending notice of this blog is, please travel as much as you can. This is something that is coming a lot now in new generations. And why? Go out there find it ;) Ill talk about it in my next post.
See you soon,
Rui
Friday, 1 December 2017
Reliability in the engineering world and visiting Phimeca
Hi everyone!
Here we are again.
I told you that I was going to depart in a new experience very soon, and that was no lie.
Today I am finishing a visit I did to Phimeca, in France. Phimeca is an engineering company that is committed to bring the statistical know-how to the engineering world.
Well, and that is no easy task. Imagine that you ar a more classic structure stakeholder, and someone tells your... look lets use some of our mathematical knowldege to improve this structure operation and make it more safe. You would be like , okay...hum...interesting. Where do we start?
And then: Why don't we use some polynomial chaos expansion to replicate etc etc You are like: wwooow , halt! Polynomial chaos.... that doesn't sound very safe!!! (not the right name to captivate users out of research)
Or, well, lets evaluate the probability of failure. And you as structure stakeholder are like... whatt !?! This is going to fail?! Whats this!?!
Or, this is very conservative... and you as stakeholder are like: Great!! Will never fail! Go away.. no need...
You can see more or less how challenging this can be to implement in the real world in terms of awareness.
Nevertheless, introducing statistical know-how is much more powerfull than one can imagine and is really growing.
Easy, just you take a look at all the standards and see the progressive increase in the need to assess uncertainty. It is no joke. Characterization of uncertainty really makes you robust to what's to come. If we now have huge amounts of data we can acess, why not to use it?
I think I told you before, but I used to put statistics on a second row of importance when comparing to structural analysis or fluid mechanics... But that was so wrong. Now, I am not leaving it ever. Give it a try too! You wont regret.
Well, why I came in contact with Phimeca is simple. They are high profile experts in the field of reliability and all its complex techniques. In my particular case, Kriging models, their knowledge was of great help and I can tell that I learned a lot.
But soon back home, to continue work there!
I know I said that I was going to write about thinking globally, that I always emphasise in my posts. But no inspiration today. Being busy really cuts of you capability to think more generally.
Well, I can tell you that I have been quite busy. I had a paper accepted in a Journal, finally. (so hard to get it) And, I am working in some amazing stuff (I'm a pessimist by nature, so when I say its amazing, I think it really is... ).
2018 the final year of the PhD. Things are getting busy, so that I do not have time to divagate about the world problems....which is good and bad ! They say ignorance is bliss and that's no lie :)
But let's stay brainless-less, all of us. As soon as inspiration comes I'll come with the thinking global post (more criticism on top of cynism ...basically).
Nooo, it really is important to think globally. The lost of this sight is what brought us here today (in my opinion).
See you soon,
Rui
Here we are again.
I told you that I was going to depart in a new experience very soon, and that was no lie.
Today I am finishing a visit I did to Phimeca, in France. Phimeca is an engineering company that is committed to bring the statistical know-how to the engineering world.
Well, and that is no easy task. Imagine that you ar a more classic structure stakeholder, and someone tells your... look lets use some of our mathematical knowldege to improve this structure operation and make it more safe. You would be like , okay...hum...interesting. Where do we start?
And then: Why don't we use some polynomial chaos expansion to replicate etc etc You are like: wwooow , halt! Polynomial chaos.... that doesn't sound very safe!!! (not the right name to captivate users out of research)
Or, well, lets evaluate the probability of failure. And you as structure stakeholder are like... whatt !?! This is going to fail?! Whats this!?!
Or, this is very conservative... and you as stakeholder are like: Great!! Will never fail! Go away.. no need...
You can see more or less how challenging this can be to implement in the real world in terms of awareness.
Nevertheless, introducing statistical know-how is much more powerfull than one can imagine and is really growing.
Easy, just you take a look at all the standards and see the progressive increase in the need to assess uncertainty. It is no joke. Characterization of uncertainty really makes you robust to what's to come. If we now have huge amounts of data we can acess, why not to use it?
I think I told you before, but I used to put statistics on a second row of importance when comparing to structural analysis or fluid mechanics... But that was so wrong. Now, I am not leaving it ever. Give it a try too! You wont regret.
Well, why I came in contact with Phimeca is simple. They are high profile experts in the field of reliability and all its complex techniques. In my particular case, Kriging models, their knowledge was of great help and I can tell that I learned a lot.
But soon back home, to continue work there!
I know I said that I was going to write about thinking globally, that I always emphasise in my posts. But no inspiration today. Being busy really cuts of you capability to think more generally.
Well, I can tell you that I have been quite busy. I had a paper accepted in a Journal, finally. (so hard to get it) And, I am working in some amazing stuff (I'm a pessimist by nature, so when I say its amazing, I think it really is... ).
2018 the final year of the PhD. Things are getting busy, so that I do not have time to divagate about the world problems....which is good and bad ! They say ignorance is bliss and that's no lie :)
But let's stay brainless-less, all of us. As soon as inspiration comes I'll come with the thinking global post (more criticism on top of cynism ...basically).
Nooo, it really is important to think globally. The lost of this sight is what brought us here today (in my opinion).
See you soon,
Rui
Sunday, 15 October 2017
ICSI 2017 Conference and small update
Hi all,
Here we are again ! After some time as always...
I have been crazy busy lately...I didn't even have much time to breath!
A new post. Just a small update. Last week we were threatened that the person(s) with less posts in TRUSS blogs will need to perform some irish dancing here in Dublin...so here I am posting. Not that I wouldn'te dance...but I want to save the world that terrible image...
Last month of September I was in a conference in Madeira, Funchal (by the way, very beautiful island...heheh) about structural fatigue and its analysis. For me, that I am working mainly in the way probabilistic problems are applied to physical problems but with a strong focus on the statistical part, this was very interesting. It helped me to improve my perception on how the other researchers look at the physical problem of fatigue. And more important is that I could talk with some of the big experts on fatigue and understand a bit more the topic, that is not an easy one...
Conference on your specific topic are the best but from my experience you should consider sometimes a conference on different topics in order to make your knowledge more robust.
I had the opportunity to do a presentation of a paper with a pre-assessment of the design of experiments of a OWT tower. As I don't know much about fatigue (well... not much about statistics too hahah) I felt a bit lost sometimes. But in the middle of the difficulty you can always extract positive points. And the funny part is that, this was probably the conference where I got more interest in my work. It is a bit funny... as I am strongly focused on the statistical analysis and the conference was not really directed at it (despite having lots of people working on the probabilistic part of the fatigue).
It is in fact a bit surprising that in a non-specific conference people show the most interest. I will assume that it is because I have more mature ideas now. But in some way it is an indicator of how, in research, everyone is so "interiorized" in their own topics that some interaction is lost... you know what I mean...
In work, I will be moving very soon to work on new stuff and new experiences ...but I'll come back soon with this and I'll talk a bit about thinking globally, which I believe I talked about before. But it is never to much.
See you soon,
Rui
Here we are again ! After some time as always...
I have been crazy busy lately...I didn't even have much time to breath!
A new post. Just a small update. Last week we were threatened that the person(s) with less posts in TRUSS blogs will need to perform some irish dancing here in Dublin...so here I am posting. Not that I wouldn'te dance...but I want to save the world that terrible image...
Last month of September I was in a conference in Madeira, Funchal (by the way, very beautiful island...heheh) about structural fatigue and its analysis. For me, that I am working mainly in the way probabilistic problems are applied to physical problems but with a strong focus on the statistical part, this was very interesting. It helped me to improve my perception on how the other researchers look at the physical problem of fatigue. And more important is that I could talk with some of the big experts on fatigue and understand a bit more the topic, that is not an easy one...
Conference on your specific topic are the best but from my experience you should consider sometimes a conference on different topics in order to make your knowledge more robust.
I had the opportunity to do a presentation of a paper with a pre-assessment of the design of experiments of a OWT tower. As I don't know much about fatigue (well... not much about statistics too hahah) I felt a bit lost sometimes. But in the middle of the difficulty you can always extract positive points. And the funny part is that, this was probably the conference where I got more interest in my work. It is a bit funny... as I am strongly focused on the statistical analysis and the conference was not really directed at it (despite having lots of people working on the probabilistic part of the fatigue).
It is in fact a bit surprising that in a non-specific conference people show the most interest. I will assume that it is because I have more mature ideas now. But in some way it is an indicator of how, in research, everyone is so "interiorized" in their own topics that some interaction is lost... you know what I mean...
In work, I will be moving very soon to work on new stuff and new experiences ...but I'll come back soon with this and I'll talk a bit about thinking globally, which I believe I talked about before. But it is never to much.
See you soon,
Rui
Monday, 31 July 2017
The importance of characterizing your random inputs and their influence in your probabilistic process.
Hi everyone,
So its time for a new message in the blog about work.
I told you before that I was looking at these very cool models called Kriging models. Well, I m still looking at them, but now I have been inveting some time on the analysis if their design of experiments, or, the variables that are used to create the model that, lets say, stay on our x axis (y axis will give the output, just imagine a 2D curve).
Why is it important to look at these variables before any further progress? I have the surrogate model, I have the means to compute the results, why spend some time doing tests with these variables?
Well, maybe you don't need, but lets see why it is important.
When you run an experiment some variables affect much more the output of your experiment than the other. So, if a variable is 98% responsible for the variations in your output why should you consume your time looking at the other variables. You just do it once, you quantify these relations between variables and then in future experiments you now "whats happening". This is of particular interest in the case where you're going to repeat your experiments a lot!
But do not forget, this preliminary analysis, usually called, sensitivity analysis, needs to be very well done. Otherwise you may neglect important effects. Like coupled effects or similar.
So, you spend some more time in this and in the future you just save some time. We just need to believe that the balance will be positive. And it is very likely to be.
In cases where budget and time is a limited resource (in other words, always), this can be very interesting.
I believe and I heard it many times before from big scientists that, no additional complexity should be added to the analysis if it is not needed. Or, that "simple is beautiful".
In the case of Offshore Wind Turbine Towers there are many many variables that affect the behaviour of the turbine. As a very complex technology, its analysis is time consuming, so, characterizing well the different variables that affect the turbine is important before going on loops trying to do new things. Basically, before trying intensive research !
Even more when you work on probailistic research, quantifiying uncertainty adds a new layer of complexity and effort, so this is even more important.
To analyse the influence of the different variables there are many different techniques, Screening, Sobol, Anova, KL divergence, you can find many in the literature. Also, different techniques exist to simulate experiments, as the simple Monte Carlo or the Latin Hypercube Sampling. If variables ar correlated it gets a bit more complex, but still feasible. You can find many of them in literature.
Well, all this just to tell you that despite looking a secndary task from your main topic, or boring in some way, sensitivity analysis are very relevant and they can be a milestone when you're doing research in terms of saving time and resource and in the end your skin. Its like that subject that you're never into during the university but suddendly when you start working you realise it is much harder than it looks and much more important.
I know I know, some of you will now say....I didn't need 95% of the university courses.... bu this one for sure you needed and for sure it was diluted in the many different courses and you probably never had it to its full extent.
I recomend some reaidng on the topic. Very interesting indeed!
See you soon!
So its time for a new message in the blog about work.
I told you before that I was looking at these very cool models called Kriging models. Well, I m still looking at them, but now I have been inveting some time on the analysis if their design of experiments, or, the variables that are used to create the model that, lets say, stay on our x axis (y axis will give the output, just imagine a 2D curve).
Why is it important to look at these variables before any further progress? I have the surrogate model, I have the means to compute the results, why spend some time doing tests with these variables?
Well, maybe you don't need, but lets see why it is important.
When you run an experiment some variables affect much more the output of your experiment than the other. So, if a variable is 98% responsible for the variations in your output why should you consume your time looking at the other variables. You just do it once, you quantify these relations between variables and then in future experiments you now "whats happening". This is of particular interest in the case where you're going to repeat your experiments a lot!
But do not forget, this preliminary analysis, usually called, sensitivity analysis, needs to be very well done. Otherwise you may neglect important effects. Like coupled effects or similar.
So, you spend some more time in this and in the future you just save some time. We just need to believe that the balance will be positive. And it is very likely to be.
In cases where budget and time is a limited resource (in other words, always), this can be very interesting.
I believe and I heard it many times before from big scientists that, no additional complexity should be added to the analysis if it is not needed. Or, that "simple is beautiful".
In the case of Offshore Wind Turbine Towers there are many many variables that affect the behaviour of the turbine. As a very complex technology, its analysis is time consuming, so, characterizing well the different variables that affect the turbine is important before going on loops trying to do new things. Basically, before trying intensive research !
Even more when you work on probailistic research, quantifiying uncertainty adds a new layer of complexity and effort, so this is even more important.
To analyse the influence of the different variables there are many different techniques, Screening, Sobol, Anova, KL divergence, you can find many in the literature. Also, different techniques exist to simulate experiments, as the simple Monte Carlo or the Latin Hypercube Sampling. If variables ar correlated it gets a bit more complex, but still feasible. You can find many of them in literature.
Well, all this just to tell you that despite looking a secndary task from your main topic, or boring in some way, sensitivity analysis are very relevant and they can be a milestone when you're doing research in terms of saving time and resource and in the end your skin. Its like that subject that you're never into during the university but suddendly when you start working you realise it is much harder than it looks and much more important.
I know I know, some of you will now say....I didn't need 95% of the university courses.... bu this one for sure you needed and for sure it was diluted in the many different courses and you probably never had it to its full extent.
I recomend some reaidng on the topic. Very interesting indeed!
See you soon!
Monday, 10 July 2017
ESREL2017 Conference and Renewable Energy
Hi everyone!
Just last month was the ESREL conference and I had the opportunity to participate and present some of the work that I have been developing on OWT reliability.
ESREL its quite a big conference, probably the biggest or one of the biggest in Europe about reliability.
I have to say that it was an interesting experience, met lots of interesting people. Other ITN students (working on wind turbines...wow), which makes me happy to see such an interest in reliability and addressing uncertainty for OWT. But mostly, the opportunity to interact in an international conference and present some work, reuniting some good comments, good contacts, that was great.
Here I am doing the presentation, still need to train a bit more to lose some stiffness in the stage :)
Next I will be at home, Madeira, for a Conference in September called ICSI2017. I hope at least so interesting as this one.
Okay okay, these things of conference and all is interesting, but... More than important to get yourself and your "brand" known...
It looks like in renewable energy we are going back in time (in fact in everything not only renewable energy) and we need to work together to fight some of these ideas/seeds that are being implemented slowly on people heads.
It looks like in renewable energy we are going back in time (in fact in everything not only renewable energy) and we need to work together to fight some of these ideas/seeds that are being implemented slowly on people heads.
Some time ago I saw this amazing video by Neil deGrasse Tyson (below), one of the most outreaching persons in science that always has one of those arguments in the sleeve. I think it mirrors how surprising in a negative sense is this discussion over science, global warming and everything.
I believe, and believe well applied here, that it really looks silly when you hear all these arguments that contradict some scientific facts.
It is true that science can be wrong, and it happens, but just the fact that people identify patterns in their studies, that means that something is happening there and it does not matter if it is important or not on a first phase.
Some people criticize how science is made, and on how some studies are accepted with low confidence and all that but in fact that is not true.
But be aware, things are published when patterns and occurrences show that something that is widely correlated is happening. The results show it. You, that have access the data, may be interpreting the results on your own way, maybe wrong, but the truth is that something that is widely correlated is happening. It is not just something that happened by luck in one experiment. It can start like that, but then you repeat and repeat ... and if the pattern is there...its just not a matter of luck...
Then, your results go to be reviewed by other scientits...and believe me...it is a competitive world...
It is like you work for a company, lets say for example McRui, and someones presents you a burger from Burger Rui that is undoubtedly good. Well, you will try to say that it is no good because its painful to believe that burgers better than yours may exist. But if it really is, you don't have other choice than accept it and try to improve your own burgers. Remember, science is supported on quality, not on anything else...
And that thing of fake results does not exist. See the example, one of the most prominent guys of anti-vaccination was caught in the past because of its biased results...and lost his degree. So that myth does not exist. Lie has short legs. And shorter than usual in science.
Well, there is lot to be said, but remember :
You cannot say that you do not believe on a scientific fact. That just does not make sense. You can choose to believe or not in many thing, just not on science. Its not a matter of whether you believe or not. Please stop that.
If you really don't "believe" in the global warming by human hands (apart from other effects we are indeed accelerating it) or vaccines or whatever and on the importance of the renewable energy, please go read a bit about it.
I challenge you to do some science to prove the contrary. And make it accepted by a renowned entity !
See you soon,
Rui
Monday, 29 May 2017
Applying the Kriging Models in Structural Reliability
Hi all,
I will then, as promised, talk a bit today about the Kriging surface models.
These models are nothing more than surrogate models that account for a certain level of uncertainty. They are widely used for many fields, but their initial application goes back to geostatistics.
They are an interesting tool that we don't hear much about when learning Engineering. On the other hand, if you talk with a Geologist they will know for sure about what you're talking. I share my office with some people from Geology, and they do. They are all happy when they see me working with it... it's like... "look at this Engineer in trouble with these simple Kriging" haha
Well, as I told before these are nothing more than interpolators. The image below will help you understand (courtesy of Wikipedia):
The idea of the Kriging surrogate model is to approximate a group of points in a N-dimensional space with a curve. Like you would do with a 2nd, 3nd or n degree polynomial. But in this case, we assume that the space between the points we do not know as an error which is Gaussian distributed.
Let's see, you see the red dots, these are the points that we know. If we assume a deterministic interpolation scheme we will have the red line or another line (depending on the order of the approximation) that will in the limit be the same as the trimmed blue line. For such a complex model it's hard to have exactly the blue trimmed line if we use a reasonable amount of points, so we are very likely to be induce in some kind of error in our prediction of the variation of z with x.
Where does the Kriging surface comes into play then? Well, if you assume the Kriging surface for the same set of points you will have the gray area, mixed with the red line. This means that you know that your blue trimmed lined will be, with 95% confidence, inside that area. (!! but it can be out! The Gaussian distribution tails are not bounded). So, let's say it is like a model, that fits infinite curves to a certain group of points.
With one single sample of points for all the domain of x from the Kriging:
If you're lucky you will have the exact same blue curve...well....very very lucky....
If you're not, you will end up with an approximation that is worst than the red line (which is the expected curve). If you take many many "samples of this curve" you will end with the red line, the expected curve.
Can you see the interest now? They are indeed an amazing piece of math. You can tell, well, whats the point? It's all left to the luck? Or, I'll end up with a red curve anyway?
Well, do not forget that so many things in this world follow a Gaussian distribution... and a tool like this one, which is simple and beautiful, can be widely implemented in this world for much more than just approximating curves or a couple of points.
If you have a system's output that is Gaussian distributed and depends on many variables you can use this, like I am doing. If you're not sure about your curve and you want some degrees of uncertainty, here we are :) etc etc...
I am pretty sure that you're amazed, because the first time I saw this I was like: "This is way I am not going anywhere, such a simple and beautiful tool and I couldn't even think remotely on this existing inside my ignorance" :)
It was nice to write to you all.
For those who know me... I know I know...lately it's Kriging for this, Kriging for that... Kriging for beers... Kriging tatoo...I can't avoid it. I love the concept hehe
But I know I know, extra care in the application of them, as good-sense is needed.
See you soon and I hope you find the post interesting,
Rui
I will then, as promised, talk a bit today about the Kriging surface models.
These models are nothing more than surrogate models that account for a certain level of uncertainty. They are widely used for many fields, but their initial application goes back to geostatistics.
They are an interesting tool that we don't hear much about when learning Engineering. On the other hand, if you talk with a Geologist they will know for sure about what you're talking. I share my office with some people from Geology, and they do. They are all happy when they see me working with it... it's like... "look at this Engineer in trouble with these simple Kriging" haha
Well, as I told before these are nothing more than interpolators. The image below will help you understand (courtesy of Wikipedia):
The idea of the Kriging surrogate model is to approximate a group of points in a N-dimensional space with a curve. Like you would do with a 2nd, 3nd or n degree polynomial. But in this case, we assume that the space between the points we do not know as an error which is Gaussian distributed.
Let's see, you see the red dots, these are the points that we know. If we assume a deterministic interpolation scheme we will have the red line or another line (depending on the order of the approximation) that will in the limit be the same as the trimmed blue line. For such a complex model it's hard to have exactly the blue trimmed line if we use a reasonable amount of points, so we are very likely to be induce in some kind of error in our prediction of the variation of z with x.
Where does the Kriging surface comes into play then? Well, if you assume the Kriging surface for the same set of points you will have the gray area, mixed with the red line. This means that you know that your blue trimmed lined will be, with 95% confidence, inside that area. (!! but it can be out! The Gaussian distribution tails are not bounded). So, let's say it is like a model, that fits infinite curves to a certain group of points.
With one single sample of points for all the domain of x from the Kriging:
If you're lucky you will have the exact same blue curve...well....very very lucky....
If you're not, you will end up with an approximation that is worst than the red line (which is the expected curve). If you take many many "samples of this curve" you will end with the red line, the expected curve.
Can you see the interest now? They are indeed an amazing piece of math. You can tell, well, whats the point? It's all left to the luck? Or, I'll end up with a red curve anyway?
Well, do not forget that so many things in this world follow a Gaussian distribution... and a tool like this one, which is simple and beautiful, can be widely implemented in this world for much more than just approximating curves or a couple of points.
If you have a system's output that is Gaussian distributed and depends on many variables you can use this, like I am doing. If you're not sure about your curve and you want some degrees of uncertainty, here we are :) etc etc...
I am pretty sure that you're amazed, because the first time I saw this I was like: "This is way I am not going anywhere, such a simple and beautiful tool and I couldn't even think remotely on this existing inside my ignorance" :)
It was nice to write to you all.
For those who know me... I know I know...lately it's Kriging for this, Kriging for that... Kriging for beers... Kriging tatoo...I can't avoid it. I love the concept hehe
But I know I know, extra care in the application of them, as good-sense is needed.
See you soon and I hope you find the post interesting,
Rui
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