loading

Logout succeed

Logout succeed. See you again!

ebook img

Parameter es*ma*on in Physiological models using WinBUGS Aris PDF

pages87 Pages
release year2009
file size2.11 MB
languageEnglish

Preview Parameter es*ma*on in Physiological models using WinBUGS Aris

Parameter
es)ma)on
in
Physiological
models
using
WinBUGS
 Aris
Dokoumetzidis
 University
of
Athens Structure
 1.
Introduc)on
and
the
basics
of
WinBUGS
 • Introduc*on
to
WinBUGS

 • Familiarisa*on
with
the
interface
 • Winbugs
language:
models,
priors,
ini*al
values
 • Running
Winbugs
and
the
format
of
the
results
 • Chain
convergence
and
diagnos*cs
 • Running
a
simple
BUGS
mode
 2.
FiEng
models
to
kine)c
data
 • Running
a
pharmacokine*c
model
 • Using
scripts
and
interfacing
WinBugs
from
other
programmes
 • FiCng
ODE
models
to
data Structure
 3.
Hierarchical
models
 • FiCng
popula*on
models
to
kine*c
data
 • Descrip*ve
covariates

 • Mul*‐level
hierarchical
models
 4.
Informa)ve
Priors
 • Defining
informa*ve
priors
from
previous
WinBUGS
runs

 • Defining
informa*ve
priors
from
literature
 6.
Model
comparison WinBUGS
 BUGS:
Bayesian
inference
Using
Gibbs
Sampling
 A
computer
programme
to
perform
Bayesian
inference
of
parametric
models
using
 Markov
Chain
Monte
Carlo
(MCMC)
method.

 Different
versions:
WinBUGS,
OpenBUGS
(same
but
open
source),

 Unix
command
line
based
versions.
 Can
be
run
on
Linux
and
Mac
through
WINE
 Also
interfaces
from
Matlab,
S‐Plus,
R
and
other
 Winbugs
developed
on
a
plaTorm
called
Blackbox
(Omeron,
Switzerland)
using
a
 language
called
Component
Pascal
which
is
a
non‐ANSI
Pascal
dialect. MCMC
 Markov
Chain
Monte
Carlo
method
creates
random
samples
such
that
aVer
enough
 itera*ons
the
chain
converges
to
a
sta*onary
distribu*on
which
is
the
joint
 distribu*on
of
all
stochas*c
parameters.
 (Markov
chain
is
a
series
of
states
with
memory
1,
i.e.
each
state
depends
only
on
the
 previous
step)
 Gibbs
sampling:

The
chain
is
updated
by
sampling,
for
each
variable,
from
its
full
 condi*onal
distribu*on
where
all
other
variables
are
considered
known
and
are
given
 the
values
of
the
previous
state
of
the
chain.
 Metropolis
–
Has)ngs:

Used
when
the
distribu*on
is
not
of
known
form
like
in
 nonlinear
systems.
 For
each
variable
a
new
value
is
generated
from
a
proposal
distribu*on
which
is
then
 compared
with
the
old
value.
The
new
value
is
accepted
with
a
probability
so
that
the
 draws
are
actually
simula*ng
from
the
posterior
distribu*on.
If
a
value
is
rejected
 then
the
variable
retains
its
old
value. WinBUGS
interface Running
WinBUGS
 • Fit
parametric
models
to
data
and
obtain
parameter
es*mates
 • Parameter
es*mates
typically
are
point
es*mates
and
uncertainty
 • In
WinBUGS
the
output
is
a
chain
of
samples
from
a
nonparametric
 distribu*on
represen*ng
the
posterior
distribu*on
 • With
descrip*ve
sta*s*cs
on
the
chains,
meaningful
output

is
 calculated

 • Also
being
Bayesian
one
has
to
set
priors
in
the
form
of
parametric
 distribu*ons Running
WinBUGS
 BUGS
model
 model { for (i in 1:n.ind) { for (j in ... Priors
 y
 t si n e d .
 b ro run
model
 posteriors
 p value
 Data
 n
 o * a r t n e c n o c *me
 Ini*al
values WinBUGS
Language
 Used
to
define
the
model
and
the
priors.
 Not
really
a
full
featured
programming
language
 Can
do:
 • Assignments
of
variables.
So
called
logical
nodes:
a <- b • Defini*on
of
stochas*c
variables
(nodes):
a ~ dnorm(mu,tau) • For‐loops:
for( i in 1:N ) { <commands> } • Evaluate
algebraic
formulas
(but
big
ones
are
slow,
these
need
to
be
hardcoded
 and
be
called
as
func*ons):
a <- b + (exp(d) – 1)
 • No
“if”
statement
but
a
“step”
func*on
can
poten*ally
serve
the
“if“
 func*onality
for
certain
cases.
e.g.
to
define
branched
expressions
 • Supports
indices
and
tables:
x[i, j, k]


or

y[1:5, 1:5] or
 z[]
means
all
values
of
z
and z[,3] means
the
3rd
column
 • A
defini*on
of
the
data
as
a
stochas*c
node
is
always
present Data
 Data
in
WinBUGS
are
inserted
as
mul*dimensional
matrices
or
vectors
in
2
formats
 Rectangular
array
 a[] b[] 1 1.2 2 1.6 3 0.12 END S‐Plus
format
 list( a = c(1, 2, 3), b = c(1.2, 1.6, 0.12), m = structure(.Data=c(1,2,3,4,5,6,NA,8,9),.Dim=c(3, 3)) )

See more

The list of books you might like