Index
absolute convergence criterion
accelerated bias-corrected bootstrap, see bootstrap, BCa
accelerated EM methods
ACE, see alternating conditional expectations
activation function
adaptation factor
for adaptive MCMC
adaptive importance sampling
adaptive kernel
adaptive MCMC
acceptance rate
adaptation factor
adaptive Metropolis algorithm
batching
bounded convergence
diminishing adaptation
Metropolis-within-Gibbs
random walk Metropolis-within-Gibbs
adaptive quadrature
adaptive rejection sampling
additive model
additive predictor
additivity and variance stabilization
AIC, see Akaike information criterion
AIDS
air blast pressure
Aitken acceleration
for EM algorithm
Akaike information criterion
allele
almost everywhere
almost sure convergence
alternating conditional expectations
Alzheimer's disease
AMISE, see asymptotic mean integrated squared error
amoeba method, see Nelder–Mead algorithm
annealing
antithetic bootstrap
antithetic sampling
aperiodic Markov chain
ascent algorithm
backtracking
random ascent
steepest ascent
step length
Asian option
aspiration criteria
asymptotic mean integrated squared error
asymptotically unbiased estimator
auxiliary variable methods
for Markov random fields
AVAS, see additivity and variance stabilization
average squared jumping distance
backfitting
backtracking
bagging
balanced bootstrap
balloon estimator
bandwidth
for smoothing, see smoothing, bandwidth
optimal
baseball salaries
batch method
batch times
for adaptive MCMC
Baum–Welch algorithm
Bayes factor
Bayes information criterion
Bayes' theorem
Bayesian bootstrap
Bayesian estimation
BCa
BCV, see biased cross-validation
benthic invertebrates
Bernoulli distribution
definition
simulation
beta distribution
definition
simulation
Beverton–Holt model
BFGS update
bias
bias–variance trade-off
biased cross-validation
BIC, see Bayes information criterion
“big oh” notation
binomial coefficient
binomial distribution
definition
simulation
bisection method
biweight kernel
Black–Scholes model
block bootstrap
block size
centering
circular
dependent wild
moving
nonmoving
sieve
stationary
studentizing
tapered
block size
for block bootstrap
blocks-of-blocks bootstrap
BOA software
body fat
bond variable
bootstrap
aggregating, see bagging
antithetic
asymptotics
bagging
balanced
Bayesian
BCa
bias correction
block
blocks of blocks
bumping
centering
circular block
confidence interval
consistency
dependent wild
for AR() models
for dependent data
for EM algorithm
for independent data
for regression
for smoothers
hypothesis testing
inferential methods
likelihood
moving block
nested
nonmoving block
paired
parametric
percentile method
permutation
pivot
pivoting
pseudo-data
regression
cases
residuals
sieve
stationary block
studentized, see bootstrap, t
t
tapered block
transformation-respecting
umbrella of model parameters, see bumping
variance reduction
variance-stabilizing transformation
weighted likelihood
bootstrap filter
bounded convergence
for adaptive MCMC
bowhead whales
Box–Cox transformation
bracketing methods
breast cancer
bridge sampling
BUGS software
bumping
burn-in
call option
cancer
capture–recapture
carrying capacity
CART, see tree-based methods
Cauchy distribution
definition
simulation
censored data
central limit theorem
CFTP, see coupling from the past
chi-square distribution
definition
simulation
circular block bootstrap
clinical trial
coal-mining disasters
CODA software
Colorado topography
combinatorial optimization
candidate solution
genetic algorithm
globally competitive solution
local search
particle swarm
problem complexity
simulated annealing
steepest ascent
tabu algorithm
traveling salesman problem
complexity
composite rule
confidence bands
confidence interval
bootstrap
conjugate prior distribution
consistent estimator
constant-span running-mean smoother
containment, see bounded convergence for adaptive MCMC
contraction
for Nelder–Mead method
contractive mapping
control variates
improvement to importance sampling
convergence almost surely
convergence criterion
absolute
relative
convergence in probability
convergence order
convex function
cooling schedule
copper–nickel alloy
cost–complexity pruning
coupling from the past
for Markov random fields
credible interval
cross-validation
for smoothing, see smoothing, cross-validation
for tree-based methods
crossover
cubic smoothing spline
curse of dimensionality
curve fitting, see smoothing
cusum diagnostic
CVRSS, see residual sum of squares, cross-validated
cycle
cyclic coordinate ascent, see Gauss–Seidel iteration
Darwinian natural selection
decoupling
degeneracy
delta method
density dependence
density estimation
adaptive kernel
asymptotic mean integrated squared error
balloon
bandwidth
bias–variance trade-off
biased cross-validation
choice of kernel
cross-validation
exploratory projection pursuit
integrated squared error
kernel
logspline
maximal smoothing principle
mean integrated squared error
mean squared error
multivariate
nearest neighbor
plug-in methods
product kernel
pseudo-likelihood
Sheather–Jones method
Silverman's rule of thumb
transformation
unbiased cross-validation
univariate
variable-kernel
dependent wild bootstrap
derivative-free method
detailed balance
differentiation
numerical
diminishing adaptation
for adaptive MCMC
Dirichlet distribution
definition
simulation
discrete Newton methods
distributions
Bernoulli
beta
binomial
Cauchy
chi-square
Dirichlet
exponential
gamma
lognormal
multinomial
multivariate normal
negative binomial
normal
Poisson
Student's t
uniform
Weibull
double bootstrap, see nested bootstrap
drug abuse
earthquakes
ECM algorithm
edge-recombination crossover
effective sample size
for importance sampling
for Markov chain Monte Carlo
for sequential importance sampling
EM algorithm
acceleration methods
Aitken acceleration
ascent property
bootstrapping
conditional maximization
convergence
E step
ECM
empirical information
for exponential families
generalized
gradient EM
latent data
Louis's method
M step
MCEM
missing data
missing information principle
Monte Carlo
numerical differentiation of l′(θ)
Q function
quasi-Newton acceleration
SEM
supplemented
variance estimates
empirical information
envelope
for importance sampling
for rejection sampling
for sequential importance sampling
Epanechnikov kernel
equivalent degrees of freedom
equivalent kernels
ergodic Markov chain
ergodic theorem
Euler–Maclaurin formula
European option
evolution, see peppered moths
expanding pointwise confidence bands
expansion
for Nelder–Mead method
expectation–maximization algorithm, see EM algorithm
expected Fisher information
exploratory projection pursuit
exponential distribution
definition
simulation
exponential family
EM algorithm
face recognition
feed-forward neural network
finite differences
Fisher information
expected
observed
Fisher scoring
fitness
fixed-point iteration
convergence
scaled
flour beetle
functional
functional iteration, see fixed-point iteration
fundamental polynomials
fur seal pups
GAM, see generalized additive model
gamma distribution
definition
simulation
gamma function
Gauss–Hermite quadrature
Gauss–Legendre quadrature
Gauss–Newton method
Gauss–Seidel iteration
Gaussian quadrature
approximation error
GDP
gear couplings
Gelman–Rubin statistic
GEM algorithm, see EM algorithm, generalized
generalized additive model
additive predictor
local scoring
generalized cross-validation
smoothing, see smoothing, generalized cross-validation
generalized EM, see EM algorithm, generalized
generalized linear mixed model
generalized linear model
link function
genetic algorithm
allele
binary encoding
chromosome
convergence
crossover
edge recombination
fitness
generation
genetic operators
genotype
locus
mutation
offspring
order crossover
parent
permutation chromosome
phenotype
scaled fitness
schema
selection mechanism
steady-state
tournament selection
uniform crossover
genetic map distance
genetic mapping
Gibbs sampling
blocked
cycle
diagnostics, see Markov chain Monte Carlo, diagnostics
for Markov random fields
griddy
hybrid
random scan
relationship to Metropolis–Hastings
reparameterization
globally competitive solution
gradient
gradient EM, see EM algorithm, gradient EM
greedy algorithm
griddy–Gibbs sampling
hat matrix
Hermite polynomials
Hessian matrix
hidden Markov model
hierarchical centering
highest posterior density region
Himmelblau's function
hit-and-run algorithm
HIV
hormone treatment
HPD region
human face recognition
hybrid Markov chain Monte Carlo
i.i.d.
image analysis
importance ratio
importance sampling
adaptive
choice of envelope
compared with sampling importance resampling
control variate improvement
effective sample size
envelope
importance ratio
sequential
standardized importance weights
unstandardized importance weights
importance sampling function
improper prior distribution
independence chain
industrialized countries
infrared emissions
inner product
integrated squared error
integration
Monte Carlo, see Monte Carlo integration
numerical, see numerical integration
internal node
interpolating polynomials
inverse cumulative distribution function method
IRLS, see iteratively reweighted least squares
irreducible Markov chain
ISE, see integrated squared error
iterated bootstrap, see nested bootstrap
iterated conditional modes
iteratively reweighted least squares
Jacobi polynomials
Jacobian matrix
Jeffreys prior
Jensen's inequality
k-change
kernel
adaptive
asymptotic relative efficiency
biweight
canonical
Epanechnikov
normal
product
rescaling
triangle
tricube
triweight
uniform
variable
kernel density estimation, see density estimation, kernel
kernel smoother
knot
logspline
Laguerre polynomials
Langevin Metropolis–Hastings
latent data
least squares cross-validation
leave-one-out, see cross-validation
Legendre polynomials
likelihood function
profile
line search methods
linear regression, see regression
link function
linkage
Lipschitz condition
“little oh” notation
local averaging
local regression smoother
local scoring
local search
random starts
tabu algorithm
variable-depth
locally dependent Markov random field
locally weighted regression smoother, see local regression smoother
locus
loess smoother
logistic growth model
logistic regression
lognormal distribution
definition
simulation
logspline density estimation
Louis's method
macroinvertebrates
majorization
map distance
Maple software
mark–recapture
Markov chain
aperiodic
convergence
coupling
detailed balance
ergodic
irreducible
nonnull state
recurrent state
reversible
state space
states
stationary distribution
time-homogeneous
Markov chain Monte Carlo
acceptance rate
adaptive
adaptive Metropolis algorithm
auxiliary variable methods
batch method
Bayesian estimation
burn-in
convergence
coupling from the past
cusum diagnostic
diagnostics, see burn-in, convergence, mixing, number of chains, run length
effective sample size
for Markov random fields
Gelman–Rubin statistic
Gibbs sampling
hierarchical centering
hit-and-run algorithm
hybrid strategies
image analysis
independence chain
Langevin Metropolis–Hastings
maximum likelihood
Metropolis–Hastings
Metropolis–Hastings ratio
Metropolis-within-Gibbs
mixing
Monte Carlo standard error
multiple-try Metropolis–Hastings
number of chains
perfect sampling
proposal distribution
random walk chain
reparameterization
reversible jump
run length
sample path
simulated tempering
slice sampling
software
structured Markov chain Monte Carlo
Swendsen–Wang algorithm
target distribution
Markov process
Markov random field
auxiliary variable methods
Gibbs sampling
locally dependent
perfect sampling
MARS
Martian atmosphere
Mathematica software
MATLAB language, xvi
maximal smoothing principle
maximum likelihood
MCEM algorithm, see Monte Carlo EM algorithm
MCMC, see Markov chain Monte Carlo
mean integrated squared error
mean squared error
of estimation
of prediction
Metropolis–Hastings algorithm
acceptance rate
diagnostics, see Markov chain Monte Carlo, diagnostics
multiple-try
relationship to Gibbs sampling
reparameterization
Metropolis–Hastings ratio
generalized
minorization
MISE, see mean integrated squared error
missing data
missing information principle
mixing
mixture distribution
MLE
modified Newton method
Monte Carlo EM algorithm
Monte Carlo integration
antithetic sampling
control variates
importance sampling
Markov chain Monte Carlo, see Markov chain Monte Carlo
Rao–Blackwellization
Riemann sum improvement
variance reduction
Monte Carlo maximum likelihood
moving average
moving block bootstrap
MSE, see mean squared error
MSPE, see mean squared error, of prediction
multinomial coefficient
multinomial distribution
definition
simulation
multiple integrals
multiple-try Metropolis–Hastings algorithm
multivariate adaptive regression splines
multivariate normal distribution
definition
simulation
Nadaraya–Watson estimator
natural selection
navigation, see terrain navigation
nearest neighbor density estimation
negative binomial distribution
definition
simulation
neighborhood
for local search
for Nelder–Mead method
for simulated annealing
for smoothing
for tabu algorithm
k-change
Nelder–Mead algorithm
nested bootstrap
network failure
neural network
Newton's method
convergence
discrete
modified
Newton–Côtes quadrature
Newton-like methods
backtracking
node
for numerical integration
for tree-based methods
nonmoving block bootstrap
nonlinear equations, solving, see optimization
nonlinear least squares
nonnull state
nonparametric bootstrap, see bootstrap
nonparametric density estimation, see density estimation
nonparametric regression, see smoothing
normal distribution
definition
simulation
normal kernel
normalizing constant
Norwegian paper
notation
NP problem
NP-complete problem
NP-hard problem
numerical differentiation
numerical integration
nth-degree rule
adaptive quadrature
composite rule
Gauss–Hermite quadrature
Gauss–Legendre quadrature
Gaussian quadrature
approximation error
method of undetermined coefficients
multiple integrals
Newton–Côtes quadrature
node
over infinite range
product formulas
Riemann rule
Romberg integration
approximation error
simple rule
Simpson's rule
adjoining subintervals
approximation error
singularities
software
transformations
trapezoidal rule
approximation error
notation
notation
observed Fisher information
oil spills
optimization
absolute convergence criterion
ascent algorithm
backfitting
backtracking
BFGS
bisection
bracketing methods
combinatorial, see combinatorial optimization
convergence criteria
derivative-free
discrete Newton methods
EM algorithm, see EM algorithm
Fisher scoring
fixed-point iteration
Gauss–Newton
Gauss–Seidel iteration
iterated conditional modes
iteratively reweighted least squares
majorization
minorization
multivariate
Nelder–Mead algorithm
Newton's method
Newton-like methods
order of convergence
quasi-Newton
relative convergence criterion
scaled fixed-point iteration
secant method
starting value
steepest ascent
stopping rule
univariate
optimization transfer
option pricing
order crossover
order of convergence
orthogonal polynomials
orthonormal polynomials
paper manufacture
parallel chords, method of, see fixed-point iteration
parametric bootstrap, see bootstrap, parametric
parent node
particle filter
particle swarm
path sampling
peppered moths
percentile method
perfect sampling
for Markov random fields
sandwiching
permutation bootstrap, see balanced bootstrap
permutation test
pigment moisture content
pivotal quantity
plug-in methods
pointwise confidence band
Poisson distribution
definition
simulation
polynomial algorithm
polynomials
fundamental
Hermite
interpolating
Jacobi
Laguerre
Legendre
orthogonal
orthonormal
population dynamics
carrying capacity
density dependence
population modeling
positive definite matrix
positive semidefinite matrix
positivity
posterior distribution
predictor
predictor–response data
pressure of air blast
principal curves smoother
projection index
software
span selection
principal surfaces smoother
prior distribution
conjugate
improper
Jeffreys
probability integral transform
problem complexity
product formulas
product kernel
profile likelihood
projection index
projection pursuit density estimation, see exploratory projection pursuit
projection pursuit regression
proposal distribution
for Markov chain Monte Carlo
for simulated annealing
pruning
pseudo-data
pseudo-likelihood
quadrature, see numerical integration
quasi-Newton acceleration
for EM algorithm
quasi-Newton methods
BFGS
R language
random ascent
random starts local search
random walk chain
randomization test
Rao–Blackwellization
improvement of rejection sampling
recombination
recurrent state
recursive partitioning regression, see tree-based methods
reflection
for Nelder–Mead method
regression
bootstrapping
cases
paired
residuals
logistic
recursive partitioning, see tree-based methods
variable selection
with missing data
rejection sampling
adaptive
envelope
Rao–Blackwellization improvement
squeezed
rejuvenation
relative convergence criterion
residual sum of squares
cross-validated
response
reversible jump methods
reversible Markov chain
Richardson extrapolation
Riemann rule
RJMCMC, see Markov chain Monte Carlo, reversible jump
Romberg integration
approximation error
root node
roughness
RSS, see residual sum of squares
running-line smoother
running-polynomial smoother
S-Plus language
salmon population
sample path
sample point adaptive estimator
sampling importance resampling
adaptive
choice of envelope
compared with importance sampling
standardized importance weights
scatterplot smoothing, see smoothing
score equation
score function
secant condition
secant method
convergence
self-avoiding walk
self-consistency
SEM algorithm
sensitivity analysis
sequential importance sampling
degeneracy
effective sample size
envelope
for Markov processes
rejuvenation
with resampling
sequential Monte Carlo
sexual histories
Sheather–Jones method
shrink transformation
for Nelder–Mead method
sieve block bootstrap
Silverman's rule of thumb
simple rule for integration
simplex
for Nelder–Mead method
Simpson's rule
adjoining subintervals
approximation error
Romberg improvement of
simulated annealing
as a Markov chain
constrained solution space
convergence
cooling schedule
neighborhoods
proposal distribution
temperature
simulated tempering
simulation
adaptive importance sampling
adaptive rejection sampling
approximate
bridge sampling
exact
importance sampling
inverse cumulative distribution function
path sampling
rejection sampling
sampling importance resampling
sequential Monte Carlo
squeezed rejection sampling
standard distributions
standard parametric distributions
target distribution
uniform distribution
SIR, see sampling importance resampling
slash distribution
slice sampling
smooth function model
smoothing
additive model
additivity and variance stabilization
alternating conditional expectations
bandwidth
confidence bands
constant-span running mean
cross-validation
equivalent degrees of freedom
equivalent kernels
expanding confidence bands
generalized additive model
local scoring
generalized cross-validation
kernel
linear
local averaging
local regression
locally weighted regression, see smoothing, local regression
loess
matrix
mean squared estimation error
mean squared prediction error
Nadaraya–Watson estimator
neighborhood
nonlinear
principal curves
projection index
span selection
principal surfaces
projection pursuit regression
running lines
running polynomial
span
splines
supersmoother
variable-span
software
density estimation
for Markov chain Monte Carlo
numerical integration
principal curves
tree-based methods
variable selection
span, see smoothing, span
sphering
spline smoother
split coordinate
split point
square-integrable
squeezed rejection sampling
squeezing function
standardized importance weights
state space
states
stationary block bootstrap
stationary distribution
steady-state genetic algorithm
steepest ascent
steepest ascent/mildest descent
step length
definition
for backtracking
stochastic monotonicity
stomach cancer
stream ecology
stream monitoring
strong law of large numbers
structure index
structured Markov chain Monte Carlo
Student's t distribution
definition
simulation
studentized bootstrap, see bootstrap, t
subinterval
subtree
sufficient descent
supersmoother
supplemented EM algorithm, see SEM algorithm
survival analysis
Swendsen–Wang algorithm
decoupling
symmetric nearest neighborhood
t distribution, see Student's t distribution
tabu algorithm
aspiration by influence
aspiration criteria
diversification
frequency
intensification
move attributes
recency
tabu list
tabu tenure
tapered block bootstrap
target distribution
Taylor series
delta method
for Gauss–Newton method
for Newton's method
for Simpson's rule
for trapezoidal rule
Taylor's theorem
terrain navigation
time–speed parameterization of curves
time-homogeneous Markov chain
tournament selection
tracking, see terrain navigation
transformation of random variables
trapezoidal rule
approximation error
Romberg improvement of
traveling salesman problem
tree rings
tree-based methods
classification
model uncertainty
node
internal
parent
root
pruning
software
split
split coordinate
split point
subtree
tree
triangle kernel
tricube kernel
triweight kernel
UCV, see unbiased cross-validation
unbiased cross-validation
unbiased estimator
undetermined coefficients, method of
uniform distribution
definition
simulation
uniform kernel
unit-speed parameterization
Utah serviceberry
vanishing adaptation, see diminishing adaptation
variable kernel
variable selection
variable-depth local search
variable-kernel density estimator
variable-metric method
variable-span smoother
variance reduction
antithetic sampling
control variates
for bootstrap
importance sampling
Rao–Blackwellization
Riemann sum improvement
variance-stabilizing transformation
weak law of large numbers
website for this book, xvi
Weibull distribution
definition
weighted likelihood bootstrap
whale migration
whale population dynamics
whitening
WinBUGS software
wine chemistry