Thank you very much professor, A honor count with your answer...

Best regards,

I agree with both of you... Thank you very much...

In most cases Yes!

Dear Alain Manuel Chaple Gil,

I agree with 'YES, in most cases' [Frank B. K. Twenefour]. I would say 'in general, yes".

Let us first define Statistical Inference:

"The theory, methods, and practice of forming judgments about the parameters of a population, usually on the basis of random sampling".

"Statistical inference means drawing conclusions based on data" [Duke University]

Another way of looking at this is: One cannot 'infer' that which is already 'known'. Therefore if the samples are not selected at random, meaning they were 'intentionally selected', then there is no 'inference', but rather knowledge about them to begin with; which caused someone to specifically select the samples in the first place. If this is true then the objectivity of randomness is negated and the inference is less reliable.

Random sampling allows for the deduction and assumption used in inference.

Without random sample one gets poor deduction and poor assumptions.

I hope I have offered a 'reflective' perspective on statistical inference.

Thank you Alain Manuel Chaple Gil, for your question!

Respectfully,

Jeanetta Mastron

On another note: IF anyone is looking for the 'argument' of the answers that are YES to the question, they may find their "NO" answers in the blogging of Alan Downey

"Statistical inference is only mostly wrong" March 2, 2015 - see below link

http://allendowney.blogspot.com/2015/03/statistical-inference-is-only-mostly.html

http://dictionary.reference.com/browse/statistical+inference

https://stat.duke.edu/~fab2/inference_talk.pdf

The answer is YES

Yes it can

Alain -

As Jaap said, there are design-based sampling and estimation methodologies, and model-based (regression) methodologies, but a combination too: model-assisted design-based methodologies.  This would be in the area of survey statistics, where continuous data applications dominate. See

Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.  (design-based and model-based combined)

Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. (mostly design-based except for a section under ratio estimation)

Lohr, S.L.(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.  (Comparable to Cochran)

Särndal, C.-E., Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang. 

Purely model-based methods can be used when there are good regressor data. See

 https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

This is often possible in the case of highly skewed establishment survey data, where cutoff sampling may be helpful. 

 https://www.researchgate.net/publication/261472614_Efficacy_of_Quasi-Cutoff_Sampling_and_Model-Based_Estimation_For_Establishment_Surveys_and_Related_Considerations

In any case, stratification is often useful - perhaps even more for model-based methods.

Models can be helpful with small area estimation, often using Bayesian statistics, but not in the case shown here, where we only need to borrow strength:

 https://www.researchgate.net/publication/262066356_Quasi-Cutoff_Sampling_and_Simple_Small_Area_Estimation_with_Nonresponse

Or here:

 https://www.researchgate.net/publication/261586154_Using_Prediction-Oriented_Software_for_Survey_Estimation

There is a great deal more on my ResearchGate page:

 https://www.researchgate.net/profile/James_Knaub

Much of the energy data here uses my methodologies:

 http://www.eia.gov/

Reports there, such as the Electric Power Monthly depend upon this.  See sales and revenue for a good example, and similarly under the Natural Gas Monthly.  In many other cases, there is nothing else practical that can be done. 

A major key is good regressor data for the population. 

Cheers - Jim 

Article Efficacy of Quasi-Cutoff Sampling and Model-Based Estimation...

Article Using Prediction-Oriented Software for Survey Estimation

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

Article Quasi-Cutoff Sampling and Simple Small Area Estimation with ...

Consider section 8 in the paper found here: 

https://www.researchgate.net/publication/261526501_Cutoff_vs._Design-Based_Sampling_and_Inference_For_Establishment_Surveys

That one-page section gives a little history on the development of survey sampling with regard to your question, Alain. 

Article Cutoff vs. Design-Based Sampling and Inference For Establish...

This may be of interest:

Valliant, Dorfman, and Royall (2000), Finite Population Sampling and Inference: A Prediction Approach. New York: John Wiley.

Further, even some purposeful sampling, using regression modeling, might be inferred here:

An Introduction to Model-Based Survey Sampling with Applications,

Ray Chambers and Robert Clark, 2012,  

Oxford Statistical Science Series 37

and here we see a little on purposeful sampling and a mention of cutoff sampling in particular:

Blair, E. and Blair, J.(2015), Applied Survey Sampling, Sage Publications.

and there is a great deal by others in the statistical literature.  

However, when using prediction (regression modeling), sampling above is usually done with random/balanced sampling. 

This seminar that I attended - which drew a rather large audience - may be of interest:

"2014 WSS PRESIDENT’S INVITED SEMINAR," 

WSS PRESIDENT'S INVITED LECTURE Title: On Making Inferences from Non-Probability Samples

 http://washstat.org/seminars/2014/20140326_brick.html

In that seminar, Mike Brick addressed a committee report on non-probability sampling of many types.  That report  can be found on ResearchGate:

https://www.researchgate.net/publication/273561892_Summary_Report_of_the_AAPOR_Task_Force_on_Non-probability_Sampling

Article Summary Report of the AAPOR Task Force on Non-probability Sampling

From the internet, here is a soil science paper i found that i think might be of some interest:

"Design-based and model-based sampling strategies for soil monitoring," by Dick Brus,

Soil Science Centre, Wageningen University and Research Centre, P.O. Box47, 6700 AA Wageningen, The Netherlands,

Email [email protected]

https://www.google.com/url?sa=t&source=web&rct=j&url=http://iuss.org/19th%2520WCSS/Symposium/pdf/1309.pdf&ved=0CCgQFjACOBRqFQoTCNOBi_DJpscCFU-sgAodZXsCjQ&usg=AFQjCNG6X79WG0qLmlZhVAtpxVKP5ODtRg&sig2=V6eNbgmwMaLTZJ4ZtJPvpw

PS -  Found it here: 

https://www.researchgate.net/publication/48191798_Design-based_and_model-based_sampling_strategies_for_soil_monitoring

.....

I noticed that the author, Dick J. Brus, did a great deal of related work with Jaap de Gruijter, available through each of their ResearchGate profiles. 

Article Design-based and model-based sampling strategies for soil monitoring

Professor Knaub,

Thank you very much for your interesting posts. Articles you recommend me were excellent.

Best regards.

Alain -

Thank you.  I especially found "Design-based and model-based sampling strategies for soil monitoring," by Brus to be very interesting.   It is also short, so convenient for a quick look into that application for soil science, which I expect has other applications.

As it was short, when comparing design-based to model-based sampling in this reference, he succinctly made it a tradeoff between "validity" and "efficiency," by which, I think, he essentially, or to a large extent, meant "bias" and "variance," respectively. 

In Cochran (1977), Sampling Techniques, Wiley, page 158, he discusses the source of the term, "model-unbiased," which I believe explains why MSE and variance are used interchangeably for model-based inference. But as I once saw in a preliminary paper by Galit Shmueli, I think you can think of model-failure, as resulting in the actual bias that is the result of the fact that a model is never exactly correct.  So the estimation of coefficients, and residuals are two parts of the estimated variance of the prediction error, for the model, which can be estimated simultaneously with the prediction.  But the bias comes from model-failure, which can only be studied through test data.  (I very recently suggested such a use of test data for another question on ResearchGate on omitted variable bias, which would be a reason for "model-failure."  For a look at model-failure for a simpler application, where it is generally not a problem, see the paper on that topic, at the link attached. For establishment surveys, which are highly skewed, using stratification when necessary to be sure models are applied to homogeneous, though heteroscedastic categories, model-based inference for cutoff or quasi-cutoff  [multiple attributes] sampling is extremely efficient.) 

 https://www.researchgate.net/publication/261474154_On_Model-Failure_When_Estimating_from_Cutoff_Samples

A model-based approach gives you flexibility to use your resources where they are needed, perhaps more so than a probability design, and I think that Brus hints at that, which can also be seen to happen in the attached link to a paper on sample size requirements, particularly for establishment surveys. 

 https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements

Having expended a great deal of effort developing model-based estimates for practical solutions for establishment surveys, I found the parallels with this soil sampling, space-time oriented paper, to be very interesting. 

Note that Brus states that "... randomness is introduced via the model..." which is very much like the way it can be interpreted in the usual survey statistics.

One more point: Note that with surveys, the distinction between considering design-based sampling or model-based sampling and considering design-based estimation or model-based estimation is important. You cannot use design-based estimation if you do not have a design-based (probability selection based) sample.  When someone uses model-assisted sampling,  they generally mean the survey design weights may be modified by essentially estimation techniques, which determine how the survey weights might be "calibrated" (i.e., modified).  Here is a good reference for model-assisted approaches:

Särndal, CE., Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang. 

Cheers - Jim  

Article On Model-Failure When Estimating from Cutoff Samples

Conference Paper Projected Variance for the Model-based Classical Ratio Estim...

I think James have given more valuable references. I supplement some words to supply an application in forestry. In forest inventory and monitoring (James talked about soil monitoring above), both probability sampling and purposive sampling are used in practice. The national forest inventory (NFI) in China was conducted based on systematic sampling, and the statistics or inventory results were published periodically, For the establishment of volume and biomass models applied in NFI, purposive sampling was used to select the sample trees. In other words, the sample trees were selected intentionally, not randomly. Of course, they are not selected as one pleases or at will. Some rules should be followed to serve our purpose. Sometimes, we call the volume and biomass models as "super-polulation models", which means that they can be used in any population, not limited in a population for a special probability sampling. They can be used in various scales, from regional, provincial levels to county-level, even to stand-level. Due to these reasons, the prediction errors of volume and biomass models should be much lower, for example, less than 3% or 5%.

Yes. I agree with all the above recommendation but i want to say that all the necessary conditions must be met.