Big Data

136 

Big Data: Storage, Sharing, and Security

The denominator of t

i

is equivalent to s

i

based on Equation 5.6.

∗

Therefore, (

ˆ

t

MLE

i

−t

0

i

) also

follows a normal distribution with zero mean and variance given by:

var



ˆ

t

MLE

i



=



d

s

i



2

var



ˆa

MLE

i



(5.36)

Hence, the confidence interval that can be obtained to quantify the estimation accuracy of the

MLE on source reliability. The confidence interval of the reliability estimation of source S

i

(i.e.,

ˆ

t

MLE

i

) at confidence level p is given by the following:



ˆ

t

MLE

i

−c

p



var



ˆ

t

MLE

i



,

ˆ

t

MLE

i

+ c

p



var



ˆ

t

MLE

i





(5.37)

where c

p

is the standard score (z-score) of the confidence level p. For example, for the 95%

confidence level, c

p

=