,

ܘൌܛെ܊െܟ

(5.33)

ctra intensity is thus treated as a peak only when the following

is satisfied, i.e., ݌௜൐0. Here, a peak is assumed to correspond

signal. Due to any possible variation, it may not be possible for a

ed peak to have an identical spectra analyser value, i.e., the value

the horizontal axis of a spectrum, across replicates in a spectra

wever, the spectra analyser values across replicates for a true peak

med to have a relatively small variation and this variance is

ntly smaller than the distance between true peaks. Therefore, an

t process is required when discovering peaks for a spectra data

tiple replicates. The main purpose of using an alignment process

s, i.e., removing false signals and the confusion across replicates.

r assumption for applying an alignment process to the discovered

nt peaks in a replicated spectra data set is that a peak

nding to a potential true signal should occur in most replicates.

a false signal may present in one replicate by a chance.

e analysing a single spectrum, estimating baselines and extracting

ctrum based on a spectra data with multiple replicates needs some

the t vector. The new t vector is defined as below,

ൌ1 െݎ௜ൌ1 െ

1

1 ൅expሾെߢܧ௠ሺݏ௠௜െܾ௠௜െݓ௠ሻሿ

(5.34)

a t vector is called a global aligner. In the above equation, ߢ൒1

positive number, which was set 100 as default [Lau, et al., 2012],

s for the expectation across replicates and m is used to index the

trum. The use of such a sigmoid function is to make it

able. The derivative of ݎ௜ is called an entropy and is shown

ݎ௜

ᇱൌݎ௜ሺ1 െݎ௜ሻ

(5.35)

noise threshold variable w is assumed to follow a Gamma

on. Therefore the model posterior of replicated spectra is defined