REFINING EXPERT BASED EVALUATION ON THE BASIS OF A LIMITED QUANTITY OF DATA

Abstract

A techniq­ue has be­en de­ve­lo­ped to re­fi­ne ex­pert ba­sed eval­ua­ti­on of the pro­ba­bi­lity distri­bu­ti­on pa­ra­me­ter of a ran­dom va­ri­ab­le ba­sed on a li­mi­ted amo­unt of sta­tis­ti­cal da­ta. This ma­de it pos­sib­le to iden­tify the most in­for­ma­ti­ve da­ta transmis­si­on chan­nel (the most qua­li­fi­ed ex­pert) and get its re­li­ab­le as­sessment. It has be­en es­tab­lis­hed that the analysis and pro­ces­sing of a li­mi­ted amo­unt of da­ta is car­ri­ed out using well-known techniq­ues in pro­ba­bi­lity the­ory and mat­he­ma­ti­cal sta­tis­tics, whe­re sig­ni­fi­cant the­ore­ti­cal and prac­ti­cal ex­pe­ri­en­ce has be­en ac­cu­mu­la­ted. A mat­he­ma­ti­cal mo­del that descri­bes the sta­te of an ob­ject, pro­cess, or phe­no­me­non is pre­sen­ted as a po­int es­ti­ma­te of the pro­ba­bi­lity distri­bu­ti­on pa­ra­me­ter of a ran­dom va­ri­ab­le, the val­ue of which is ob­ta­ined on the ba­sis of a small sample of da­ta. The mo­dern appro­ac­hes to the sta­tis­ti­cal es­ti­ma­ti­on of a ran­dom va­ri­ab­le are analyzed, the most com­mon of which is the Ba­ye­si­an appro­ach. It is es­tab­lis­hed that the most sig­ni­fi­cant mo­ment of the Ba­ye­si­an es­ti­ma­ti­on of the unknown pa­ra­me­ter of the pro­ba­bi­lity distri­bu­ti­on of a ran­dom va­ri­ab­le is the ap­po­intment of a cer­ta­in functi­on of the a pri­ori den­sity of its distri­bu­ti­on. This functi­on sho­uld cor­res­pond to the ava­ilab­le pre­li­mi­nary in­for­ma­ti­on on the sha­pe of the a pri­ori pro­ba­bi­lity distri­bu­ti­on of this qu­an­tity. The tra­di­ti­onal appro­ach to iden­tif­ying the most in­for­ma­ti­ve chan­nel for transmit­ting da­ta on the sta­te of an ob­ject, the co­ur­se of a pro­cess or phe­no­me­non, and cut­ting off ot­hers is less re­li­ab­le. This is car­ri­ed out using the so-cal­led mec­ha­nism of re­du­cers of deg­re­es of fre­edom. Its ma­in di­sad­van­ta­ge is that in the cut-off da­ta transmis­si­on chan­nels, the­re may be so­me use­ful in­for­ma­ti­on that is not in­vol­ved in the de­ve­lop­ment of an ag­re­ed so­lu­ti­on. The­re­fo­re, it is ne­ces­sary to intro­du­ce mec­ha­nisms of discri­mi­na­tors of deg­re­es of fre­edom. They al­low all da­ta transmis­si­on chan­nels to par­ti­ci­pa­te in the de­ci­si­on-ma­king pro­cess in terms of im­por­tan­ce, which cor­res­ponds to the gre­atest deg­ree of the­ir in­for­ma­ti­on con­tent in the cur­rent sit­ua­ti­on. An il­lustra­ti­ve example of the appli­ca­ti­on of the con­si­de­red met­hods of ave­ra­ging da­ta is shown, which ref­lects the re­sults of cal­cu­la­ti­ons by ite­ra­ti­ons using the imple­men­ta­ti­on mec­ha­nisms of both re­du­cers and discri­mi­na­tors of deg­re­es of fre­edom. The­se mec­ha­nisms ref­lect the fe­atu­res of the imple­men­ta­ti­on of ite­ra­ti­ve al­go­rithms that are cha­rac­te­ris­tic of both met­hods of mat­he­ma­ti­cal sta­tis­tics and met­hods of a syner­ge­tic system of ave­ra­ging da­ta.