The likelihood function
was defined from the distance function and each number of data sets (T) from 1 to 10 was put into the likelihood function
Given the data measurement error [[xi].sub.i] ~ Normal(0, [[sigma].sup.2]), the likelihood function
for an individual data point at the time point t is
In this study we use the procedure in  where the maximum likelihood estimator of p is obtained by directly maximizing the profile likelihood function
. For any given value of p we find the maximum likelihood estimate of [beta], [THETA] and compute the log-likelihood function.
To obtain estimator [[??].sub.[OMEGA]] ([u.sub.i], [v.sub.i]) we form likelihood function
under population parameter space L([OMEGA]).
Since the number of samples T was known, the partial derivative of the logarithmic likelihood function
for the connection weight [W.sub.ij], the offset [a.sub.i] of the visible layer element, and the offset [b.sub.j] of the hidden layer unit could be expressed by P(h|[V.sup.(t)], [theta]) and P(v, h | [theta]).
Conversely, given ([h.sup.+.sub.u], [h.sup.-.sub.u]) and [([h.sup.+.sub.u], [h.sup.-.sub.u]) : i [member of] Ij, the same formula can be interpreted as a function of [theta], called the individual likelihood function
for one trip of a passenger.
The global likelihood functions
were constructed using 16 out of the 37 original datasets, four from each fault case, using datasets which were independent from the datasets used when constructing the local likelihood functions
In this paper, the time delay likelihood function
under the condition of multipath is deduced by using channel frequency response.
Based on this received signal model, we derive an accurate closed-form formula of the likelihood function
and propose a modified LLR calculation algorithm.
Considering that the measurements are independent of each other, the likelihood function
of the observed values [y.sub.1], [y.sub.2], ..., [y.sub.N] is
observed data at times ([t.sub.1], [t.sub.2], ..., [t.sub.n]) from the model defined by (1) and (4), and then the likelihood function
is given by
The usual practice for statistical inference is to use the natural logarithm of the likelihood function
, namely, the log-likelihood function, which is given by