Loading ...
Sorry, an error occurred while loading the content.

GEOSTATS: Nugget Effect, Jacknife, CV & Bootstrap

Expand Messages
  • Gregoire Dubois
    Dear all, I have two questions. The first one is about the use of cross-validation, jacknife and bootstrap in geostatistics while developed for independent and
    Message 1 of 2 , Sep 5, 1905
    View Source
    • 0 Attachment
      Dear all,

      I have two questions.

      The first one is about the use of cross-validation, jacknife and bootstrap in
      geostatistics while developed for independent and identically distributed
      observations. What are the consequences of the application of these techniques
      to dependent data and what can be done to adapt these techniques to
      geostatistics.

      My second question is about the nugget effect, which can be defined as

      Nugget Effect (NE) = Error Variance (EV) + Micro Variance (MV) ,

      where the error variance is the variance of the measurement errors, and the
      micro variance is the variance of the small scale structure.

      This definition is the one implemented in Surfer and follows the
      recommendation of Cressie

      CRESSIE N. (1993)
      Statistics for spatial data
      John Wiley & Sons Inc. (Revised Edition)
      (see pages 127 - 130)

      When EV = 0 and NE > 0, the estimates will honor every observation, when MV =
      0 and NE > 0, the estimates do not honor every observation. Both situations
      will have a smoothing effect.

      I have made a few tests to evaluate the relative impact of both components but
      could not see differences between EV and MV. For a given value of the NE and
      for different combinations of EV and MV, I always get the same estimates. Does
      anyone have an explanation for that ?

      I couldn't find any references to publications where both components are
      quantified in a case study and would welcome any suggestions.

      Thank you for any help

      Gregoire



      Gregoire Dubois
      Section of Earth Sciences
      Institute of Mineralogy and Petrography
      University of Lausanne
      Switzerland

      Currently detached in Italy

      http://curie.ei.jrc.it/ai-geostats.htm

      ____________________________________________________________________
      Get free email and a permanent address at http://www.netaddress.com/?N=1
      --
      *To post a message to the list, send it to ai-geostats@....
      *As a general service to list users, please remember to post a summary
      of any useful responses to your questions.
      *To unsubscribe, send email to majordomo@... with no subject and
      "unsubscribe ai-geostats" in the message body.
      DO NOT SEND Subscribe/Unsubscribe requests to the list!
    • Pierre Goovaerts
      Hello, The main difference between the Error Variance (EV) and Micro Variance (MV) is that MV=0 for h=0 and not EV. Thus, whenever h 0 both components are
      Message 2 of 2 , Apr 3 2:55 PM
      View Source
      • 0 Attachment
        Hello,

        The main difference between the Error Variance (EV) and
        Micro Variance (MV) is that MV=0 for h=0 and not EV.
        Thus, whenever h>0 both components are incorporated
        into the computation of the nugget effect.
        I am not surprised that you get similar estimates
        (at unsampled locations) if you use the same NE
        since the repartition of the nugget variance between
        Error Variance and Micro Variance won't impact the
        computation of the covariance values in your kriging
        system except for the diagonal of the left-hand-side
        kriging matrix. At sampled locations though the two
        systems will yield different estimates.

        The relative importance of the two components can be quantified
        if you have collected information about measurement errors
        (e.g. through duplicates or triplicates): many examples can
        be found in the soil science literature. An alternative is to look
        at the nugget effect of the cross variogram between two
        variables which, under the assumption that measurement errors
        of two variables are uncorrelated, can help the interpretation of
        the nugget effect of the two direct variograms (non-zero nugget
        effect on the cross variogram is due to micro-scale variation
        common to both variables), see my book. p. 102-103
        and the reference:
        Goovaerts, P. and R. Webster. 1994.
        Scale-dependent correlation between topsoil copper and cobalt
        concentrations in Scotland.
        European Journal of Soil Science, 45(1):79--95.

        Cheers,

        Pierre


        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

        ________ ________
        | \ / | Pierre Goovaerts
        |_ \ / _| Assistant professor
        __|________\/________|__ Dept of Civil & Environmental Engineering
        | | The University of Michigan
        | M I C H I G A N | EWRE Building, Room 117
        |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
        _| |_\ /_| |_
        | |\ /| | E-mail: goovaert@...
        |________| \/ |________| Phone: (734) 936-0141
        Fax: (734) 763-2275
        http://www-personal.engin.umich.edu/~goovaert/

        <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>


        On 2 Apr 2000, Gregoire Dubois wrote:

        > Dear all,
        >
        > I have two questions.
        >
        > The first one is about the use of cross-validation, jacknife and bootstrap in
        > geostatistics while developed for independent and identically distributed
        > observations. What are the consequences of the application of these techniques
        > to dependent data and what can be done to adapt these techniques to
        > geostatistics.
        >
        > My second question is about the nugget effect, which can be defined as
        >
        > Nugget Effect (NE) = Error Variance (EV) + Micro Variance (MV) ,
        >
        > where the error variance is the variance of the measurement errors, and the
        > micro variance is the variance of the small scale structure.
        >
        > This definition is the one implemented in Surfer and follows the
        > recommendation of Cressie
        >
        > CRESSIE N. (1993)
        > Statistics for spatial data
        > John Wiley & Sons Inc. (Revised Edition)
        > (see pages 127 - 130)
        >
        > When EV = 0 and NE > 0, the estimates will honor every observation, when MV =
        > 0 and NE > 0, the estimates do not honor every observation. Both situations
        > will have a smoothing effect.
        >
        > I have made a few tests to evaluate the relative impact of both components but
        > could not see differences between EV and MV. For a given value of the NE and
        > for different combinations of EV and MV, I always get the same estimates. Does
        > anyone have an explanation for that ?
        >
        > I couldn't find any references to publications where both components are
        > quantified in a case study and would welcome any suggestions.
        >
        > Thank you for any help
        >
        > Gregoire
        >
        >
        >
        > Gregoire Dubois
        > Section of Earth Sciences
        > Institute of Mineralogy and Petrography
        > University of Lausanne
        > Switzerland
        >
        > Currently detached in Italy
        >
        > http://curie.ei.jrc.it/ai-geostats.htm
        >
        > ____________________________________________________________________
        > Get free email and a permanent address at http://www.netaddress.com/?N=1
        > --
        > *To post a message to the list, send it to ai-geostats@....
        > *As a general service to list users, please remember to post a summary
        > of any useful responses to your questions.
        > *To unsubscribe, send email to majordomo@... with no subject and
        > "unsubscribe ai-geostats" in the message body.
        > DO NOT SEND Subscribe/Unsubscribe requests to the list!
        >

        --
        *To post a message to the list, send it to ai-geostats@....
        *As a general service to list users, please remember to post a summary
        of any useful responses to your questions.
        *To unsubscribe, send email to majordomo@... with no subject and
        "unsubscribe ai-geostats" in the message body.
        DO NOT SEND Subscribe/Unsubscribe requests to the list!
      Your message has been successfully submitted and would be delivered to recipients shortly.