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Words: 12k
Articles: 558
Table of contents
12k
558
Kullback-Leibler divergence
Probability and statistics
45
1
Gibbs inequality
Kullback-Leibler divergence
26
Probability theory
Probability and statistics
7k
297
Probability space
Probability theory
33
1
Event
Probability space
9
Uniform random point in a disk
Probability theory
61
1
Origin in a triangle of three radial random points
Uniform random point in a disk
42
Independent sigma-algebras
Probability theory
120
4
Independent events
Independent sigma-algebras
19
Independence extended from generating pi-systems
Independent sigma-algebras
41
Tail sigma-algebra
Independent sigma-algebras
39
1
Kolmogorov zero-one law
Tail sigma-algebra
15
Product measure
Probability theory
21
Random variable
Probability theory
51
2
Independent random variables
Random variable
37
1
Independent and identically distributed random variables
Independent random variables
15
Queueing theory
Probability theory
129
3
Poisson arrivals see time averages
Queueing theory
39
M-G-1 queue
Queueing theory
50
Little law
Queueing theory
40
Convergence of random variables
Probability theory
329
13
Convergence in distribution
Convergence of random variables
44
Almost sure convergence
Convergence of random variables
33
1
Strong law of large numbers
Almost sure convergence
12
Cramer-Wold theorem
Convergence of random variables
36
Convergence in probability
Convergence of random variables
82
3
Bounded-metric characterization of convergence in probability
Convergence in probability
23
Almost-sure subsequence from convergence in probability
Convergence in probability
21
Independent rare-event counterexample to almost-sure convergence
Convergence in probability
23
Convergence in Lp from convergence in probability and an Lr bound
Convergence of random variables
38
Central limit theorem
Convergence of random variables
56
2
Self-normalized central limit theorem with a second-moment denominator
Central limit theorem
37
Multivariate central limit theorem
Central limit theorem
19
Poisson limit theorem
Convergence of random variables
23
Simple symmetric random walk
Probability theory
21
Martingale
Probability theory
518
20
Symmetric signs forced by the martingale property
Martingale
35
Supermartingale
Martingale
39
1
Supermartingale majorant bound
Supermartingale
25
Stopping time
Martingale
116
3
Stopped martingale in discrete time
Stopping time
81
1
Discounted symmetric random-walk exit transform
Stopped martingale in discrete time
35
Optional sampling theorem for a supermartingale
Stopping time
19
Predictable process
Martingale
219
8
Martingale transform
Predictable process
186
6
Recovery of a martingale-transform integrand by conditional covariance
Martingale transform
14
Stopped martingale
Martingale transform
23
Reflection principle for simple symmetric random walk
Martingale transform
74
1
Point probability for the maximum of simple symmetric random walk
Reflection principle for simple symmetric random walk
29
Predictable representation in a Rademacher filtration
Martingale transform
58
1
Stopped martingale isometry in a Rademacher filtration
Predictable representation in a Rademacher filtration
31
Predictable compensator of a discrete supermartingale
Predictable process
13
Doob decomposition in discrete time
Martingale
24
Snell envelope
Martingale
72
2
Complementarity for the Snell envelope compensator
Snell envelope
19
Optimal stopping time from the compensator
Snell envelope
28
Borel-Cantelli lemmas
Probability theory
102
2
Tail-sum formula for expectation
Borel-Cantelli lemmas
31
Extremes of independent exponential variables
Borel-Cantelli lemmas
38
Stochastic process
Probability theory
420
18
Gaussian process
Stochastic process
24
Brownian motion
Stochastic process
380
16
Brownian bridge
Brownian motion
22
Exponential Brownian martingale
Brownian motion
103
3
Risk-neutral measure for the Black-Scholes model
Exponential Brownian martingale
72
2
Power payoff in the Black-Scholes model
Risk-neutral measure for the Black-Scholes model
9
Brownian time reversal for fixed-strike lookback extrema
Risk-neutral measure for the Black-Scholes model
37
Gaussian-process characterization of Brownian motion
Brownian motion
15
Time inversion of Brownian motion
Brownian motion
26
Brownian motion with drift
Brownian motion
59
3
Finite-horizon maximum of Brownian motion with negative drift
Brownian motion with drift
20
Infinite-horizon crossing probability for Brownian motion with negative drift
Brownian motion with drift
5
Last passage time above a level for Brownian motion with negative drift
Brownian motion with drift
20
Brownian reflection principle
Brownian motion
25
Cameron-Martin theorem for a linear drift
Brownian motion
23
Brownian transition semigroup
Brownian motion
44
1
Brownian compensator martingale
Brownian transition semigroup
26
Exponential test-function characterization of Brownian motion
Brownian motion
42
Characteristic-function convergence theorem
Probability theory
15
Poisson process
Probability theory
276
8
Poisson thinning
Poisson process
67
2
Binomial thinning conditional on a total
Poisson thinning
21
Infinite-server queue transient distribution
Poisson thinning
27
Kolmogorov forward equation for a Poisson process
Poisson process
20
Poisson process conditional arrival times
Poisson process
42
Number of one Poisson type before another
Poisson process
37
Exponential formula for a marked Poisson sum
Poisson process
45
Age of a Poisson process
Poisson process
38
Fokker-Planck equation
Probability theory
27
1
Fokker-Planck probability current
Fokker-Planck equation
14
Wald identity
Probability theory
20
Poisson point process
Probability theory
382
9
Superposition theorem for Poisson point processes
Poisson point process
44
Campbell theorem
Poisson point process
44
Non-homogeneous Poisson point process
Poisson point process
50
1
Intensity function of a point process
Non-homogeneous Poisson point process
15
Mapping theorem for Poisson point processes
Poisson point process
145
2
Radial volume transform of a homogeneous Poisson point process
Mapping theorem for Poisson point processes
85
1
Kth-nearest-neighbour distance in a homogeneous Poisson point process
Radial volume transform of a homogeneous Poisson point process
43
Independent marking theorem for Poisson point processes
Poisson point process
47
Poisson thinning theorem
Poisson point process
29
Order statistic
Probability theory
12
1
Order symmetry of independent random variables
Order statistic
12
Probability distribution
Probability theory
1k
56
Beta distribution
Probability distribution
14
Cumulative distribution function
Probability distribution
72
1
Uniform convergence of distribution functions to a continuous limit
Cumulative distribution function
43
Cauchy distribution
Probability distribution
78
2
Stability of the Cauchy distribution
Cauchy distribution
21
Stable distribution
Cauchy distribution
30
Probability generating function
Probability distribution
28
Probability mass function
Probability distribution
26
Quantile function
Probability distribution
93
2
Inverse transform sampling
Quantile function
27
Quantile coupling for convergence in distribution
Quantile function
51
Discrete probability distribution
Probability distribution
300
11
Geometric distribution
Discrete probability distribution
67
1
Coupon collector problem
Geometric distribution
43
Negative binomial distribution
Discrete probability distribution
70
1
Negative binomial stopping argument
Negative binomial distribution
38
Binomial distribution
Discrete probability distribution
13
Multinomial distribution
Discrete probability distribution
16
Poisson distribution
Discrete probability distribution
122
4
Poisson central limit theorem
Poisson distribution
17
Poisson-multinomial conditioning
Poisson distribution
75
1
Poisson trick
Poisson-multinomial conditioning
64
Normal approximation to the Poisson distribution
Poisson distribution
20
Continuous probability distribution
Probability distribution
397
15
Probability density function
Continuous probability distribution
24
Gamma distribution
Continuous probability distribution
77
2
Erlang distribution
Gamma distribution
28
Sampling an integer-shape gamma distribution
Gamma distribution
35
Exponential distribution
Continuous probability distribution
139
4
Memorylessness of the exponential distribution
Exponential distribution
23
Uniform ratio of independent exponential variables
Exponential distribution
24
Competing exponential clocks
Exponential distribution
41
Geometric sum of exponential variables
Exponential distribution
33
Uniform distribution
Continuous probability distribution
111
3
Sum of two independent uniform variables
Uniform distribution
26
Uniform split of a random total
Uniform distribution
73
1
Exponential characterization by a uniform random split
Uniform split of a random total
49
Laplace distribution
Continuous probability distribution
32
1
Laplace regression
Laplace distribution
20
Symmetric distribution
Probability distribution
18
Median
Probability distribution
14
Moment-generating function
Probability distribution
14
Joint distribution function
Probability distribution
18
Normal distribution
Probability distribution
88
5
Half-normal distribution
Normal distribution
12
Log-normal distribution
Normal distribution
22
Gaussian integration by parts
Normal distribution
20
Standard normal distribution
Normal distribution
25
1
Standard normal distribution function
Standard normal distribution
12
Chi-squared distribution
Probability distribution
39
1
Chi-squared stochastic ordering
Chi-squared distribution
25
Weibull distribution
Probability distribution
9
Characteristic function of a uniform distribution
Probability distribution
22
1
Small-argument sine product asymptotic
Characteristic function of a uniform distribution
14
Variance of a uniform distribution
Probability distribution
12
Exponential survival probability
Probability distribution
17
Expected value
Probability theory
158
10
Variance
Expected value
92
5
Variance additivity for independent random variables
Variance
7
Standard deviation
Variance
12
Covariance
Variance
59
2
Covariance matrix
Covariance
37
1
Correlation coefficient
Covariance matrix
8
Indicator random variable
Expected value
Tail-sum formula
Expected value
16
Linearity of expectation
Expected value
11
Variance of a sample mean
Expected value
18
Probability inequality
Probability theory
123
6
Chebyshev inequality
Probability inequality
16
First moment method
Probability inequality
33
Second moment method
Probability inequality
25
Markov inequality
Probability inequality
31
1
Exponential Markov bound
Markov inequality
19
Union bound
Probability inequality
7
Conditional probability
Probability theory
43
2
Bayes theorem
Conditional probability
19
Conditional distribution
Conditional probability
15
Random partition
Probability theory
55
3
Restricted-growth string
Random partition
15
Singleton block
Random partition
10
Exchangeable random partition
Random partition
15
Random path in a binary tree
Probability theory
18
Markov chain
Probability theory
2k
97
Birth-death chain
Markov chain
21
Product Markov chain
Markov chain
34
Transition matrix
Markov chain
11
Irreducible Markov chain
Markov chain
17
Aperiodic Markov chain
Markov chain
25
Recurrent state
Markov chain
14
Transient state
Markov chain
14
First return time
Markov chain
31
1
Mean recurrence time
First return time
21
Preservation under enlargement of transition support
Markov chain
55
Running minimum of an independent sequence is Markov
Markov chain
22
Overlapping moving sum need not be Markov
Markov chain
38
Reversible Markov chain
Markov chain
27
1
Detailed balance
Reversible Markov chain
15
Hitting probability
Markov chain
78
1
Harmonic hitting probability for the balanced-difference urn
Hitting probability
59
Expected hitting time
Markov chain
26
Expected occupation count before absorption
Markov chain
80
1
Four-state reflecting absorbing random walk
Expected occupation count before absorption
53
Conditional hitting time
Markov chain
23
Periodic Markov chain
Markov chain
18
Lazy Markov chain
Markov chain
14
Convergence to an invariant distribution
Markov chain
12
Recurrent Markov chain
Markov chain
79
4
Positive recurrent state
Recurrent Markov chain
13
Null recurrent state
Recurrent Markov chain
13
Recurrence criterion by return probabilities
Recurrent Markov chain
15
Biased random walk hitting probability
Recurrent Markov chain
23
Random walk on a graph
Markov chain
216
7
Simple random walk
Random walk on a graph
16
Simple random walk on the integer line
Random walk on a graph
90
2
Expected visits to the origin by a simple random walk
Simple random walk on the integer line
27
Simultaneous returns of independent simple random walks
Simple random walk on the integer line
38
Stationary distribution of a graph random walk
Random walk on a graph
12
Biased random walk
Random walk on a graph
84
1
Reflected biased random walk on the nonnegative integers
Biased random walk
73
Gambler's ruin
Markov chain
58
1
Expected duration of symmetric gambler's ruin
Gambler's ruin
42
Strong Markov property
Markov chain
71
1
Two-state excursion visit law
Strong Markov property
42
Stationary cycle occupation formula
Markov chain
41
Markov property
Markov chain
18
Continuous-time Markov chain
Markov chain
1k
48
Martingale problem for a continuous-time Markov chain
Continuous-time Markov chain
26
Q-matrix
Continuous-time Markov chain
22
Transition semigroup of a continuous-time Markov chain
Continuous-time Markov chain
38
1
Kolmogorov equations
Transition semigroup of a continuous-time Markov chain
17
Markov jump-process generator
Continuous-time Markov chain
34
Holding-time reversal along a fixed CTMC jump path
Continuous-time Markov chain
47
Recurrence equivalence for a CTMC and its fixed-time skeleton
Continuous-time Markov chain
40
Jump chain
Continuous-time Markov chain
163
5
Reflected nearest-neighbour random walk
Jump chain
42
Invariant-measure transfer between a jump chain and a CTMC
Jump chain
74
2
Slow holding rates destroy positive recurrence
Invariant-measure transfer between a jump chain and a CTMC
30
Fast holding rates create continuous-time positive recurrence
Invariant-measure transfer between a jump chain and a CTMC
18
Nonexplosion from recurrent visits to a slow state
Jump chain
29
Explosion of a continuous-time Markov chain
Continuous-time Markov chain
74
2
Explosion by summable holding times
Explosion of a continuous-time Markov chain
25
Explosion of an upward-biased walk with geometrically increasing rates
Explosion of a continuous-time Markov chain
38
Invariant distribution of a continuous-time Markov chain
Continuous-time Markov chain
38
1
Invariant distribution of an explosive chain
Invariant distribution of a continuous-time Markov chain
27
Batch-birth linear-death process
Continuous-time Markov chain
60
1
Moments of a batch-birth linear-death process
Batch-birth linear-death process
27
Birth-death process
Continuous-time Markov chain
719
27
Yule process
Birth-death process
108
2
Mean population of a Yule process
Yule process
31
Conditional Yule birth times
Yule process
44
Extinction probability of a linear birth-death process
Birth-death process
25
Detailed balance for a birth-death process
Birth-death process
35
Birth-death master equation
Birth-death process
60
3
First-moment equation of a birth-death process
Birth-death master equation
15
Factorial moment
Birth-death master equation
29
1
Poisson factorial moments
Factorial moment
17
Poisson moment closure for a birth-death process
Birth-death process
31
Diffusion approximation of a birth-death process
Birth-death process
75
2
Linear noise approximation
Diffusion approximation of a birth-death process
27
Mean drift from a Fokker--Planck equation
Diffusion approximation of a birth-death process
24
Birth-death recurrence classification
Birth-death process
30
M-M-1 queue
Birth-death process
195
7
M-M-1 queue with state-dependent admission
M-M-1 queue
46
Positive recurrence of an M-M-1 queue
M-M-1 queue
15
Stationary distribution of an M-M-1 queue
M-M-1 queue
14
Burke theorem
M-M-1 queue
20
M-M-1 queue with Bernoulli feedback
M-M-1 queue
54
1
Poisson output theorem for a feedback queue
M-M-1 queue with Bernoulli feedback
32
Mean busy period of an M-M-1 queue
M-M-1 queue
24
M-M-infinity queue
Birth-death process
144
4
Stationary distribution of an M-M-infinity queue
M-M-infinity queue
22
Burke theorem for an M-M-infinity queue
M-M-infinity queue
32
Transient distribution of an M-M-infinity queue
M-M-infinity queue
25
Mean busy period of an M-M-infinity queue
M-M-infinity queue
27
Finite Markov chain
Markov chain
Communicating class
Markov chain
65
3
Communicating states
Communicating class
20
Closed communicating class
Communicating class
16
Transient communicating class
Communicating class
29
Stationary distribution
Markov chain
8
Renewal process
Probability theory
325
11
Renewal-reward theorem
Renewal process
24
Renewal counting law of large numbers
Renewal process
18
Renewal interval containing a fixed time
Renewal process
145
3
Size-biased distribution
Renewal interval containing a fixed time
43
Exponential renewal interval limit
Renewal interval containing a fixed time
41
Stochastic length bias of a renewal interval
Renewal interval containing a fixed time
43
Residual lifetime process
Renewal process
116
4
Renewal excess limit theorem
Residual lifetime process
76
1
Exponential first interarrival in a renewal superposition containing a Poisson process
Renewal excess limit theorem
53
Residual lifetime Markov chain
Residual lifetime process
13
Equilibrium residual-life distribution
Residual lifetime process
16
Law of total variance
Probability theory
13
Characteristic function
Probability theory
32
1
Characteristic function of a sum of independent variables
Characteristic function
16
Variance normalization
Probability theory
21
Information theory
Probability and statistics
662
31
Alphabet
Information theory
17
Conditional entropy
Information theory
57
2
Conditioning reduces entropy
Conditional entropy
18
Entropy of a sum of independent finite-group variables
Conditional entropy
28
Mutual information
Information theory
61
2
Chain rule for mutual information
Mutual information
10
Incremental information in a twofold binary repetition code
Mutual information
40
Channel capacity
Information theory
74
3
Weakly symmetric channel capacity
Channel capacity
65
2
Binary symmetric channel capacity
Weakly symmetric channel capacity
15
Ternary symmetric channel capacity
Weakly symmetric channel capacity
19
Information entropy
Information theory
23
1
Binary entropy
Information entropy
6
Huffman coding
Information theory
213
7
Huffman sibling property
Huffman coding
24
Optimal prefix code
Huffman coding
149
4
Expected codeword length
Optimal prefix code
17
Probability monotonicity of optimal prefix-code lengths
Optimal prefix code
37
Deepest sibling property of an optimal prefix code
Optimal prefix code
64
Nonunique optimal prefix code
Optimal prefix code
16
Huffman codeword length bounds
Huffman coding
20
Bernoulli source
Information theory
13
Information rate
Information theory
85
2
Reliable source encoding at a rate
Information rate
37
Information rate under fixed-length blocking
Information rate
34
Asymptotic equipartition property
Information theory
20
Shannon noiseless coding theorem
Information theory
13
Unicity distance
Information theory
86
3
Key equivocation
Unicity distance
17
Source redundancy in cryptanalysis
Unicity distance
23
Infinite unicity distance from a source symmetry
Unicity distance
24
Statistical modelling
Probability and statistics
3k
131
Unbiased estimator
Statistical modelling
20
Heteroscedastic
Statistical modelling
12
Akaike information criterion
Statistical modelling
117
3
Mallows Cp
Akaike information criterion
98
2
Bias-variance decomposition for linear prediction
Mallows Cp
36
Unbiased prediction-error identity for ordinary least squares
Mallows Cp
40
Shape parameter
Statistical modelling
16
Exponential family
Statistical modelling
169
8
Natural parameter of an exponential family
Exponential family
17
Cumulant function of an exponential family
Exponential family
43
2
Exponential-family derivative identities
Cumulant function of an exponential family
11
Mean parameter of an exponential family
Cumulant function of an exponential family
12
Inverse Gaussian distribution
Exponential family
29
Exponential-family deviance
Exponential family
15
Negative binomial exponential family
Exponential family
26
Exponential dispersion family
Exponential family
26
Generalized linear model
Statistical modelling
486
20
Linear predictor
Generalized linear model
17
Link function
Generalized linear model
14
Binomial regression
Generalized linear model
23
Pearson dispersion estimator
Generalized linear model
15
Canonical link function
Generalized linear model
40
1
Poisson canonical link
Canonical link function
22
Poisson regression
Generalized linear model
17
Poisson exposure model
Generalized linear model
98
3
Estimators for a Poisson exposure model
Poisson exposure model
51
1
Variance comparison for Poisson exposure estimators
Estimators for a Poisson exposure model
29
Normal-approximation tests for a Poisson exposure model
Poisson exposure model
18
Logistic regression
Generalized linear model
177
6
Bernoulli logistic-regression model
Logistic regression
41
1
Fitted-mean balance for logistic regression with an intercept
Bernoulli logistic-regression model
31
Logistic loss
Logistic regression
50
1
Positive semidefinite quadratic-form classifier
Logistic loss
31
Grouped-binomial logistic regression
Logistic regression
23
Reference level in a regression factor
Logistic regression
50
Probit regression
Generalized linear model
31
Iteratively reweighted least squares
Generalized linear model
17
Independent Poisson conditioning
Statistical modelling
16
Normal linear model
Statistical modelling
583
25
Cochran's theorem
Normal linear model
24
Linear regression
Normal linear model
140
4
Design matrix
Linear regression
23
Regression coefficient
Linear regression
20
Interaction term
Linear regression
26
Attenuation bias from classical measurement error
Linear regression
46
R linear-model formula
Normal linear model
53
1
Degrees of freedom of a factor predictor
R linear-model formula
24
Hat matrix
Normal linear model
25
Normal linear-model confidence ellipsoid
Normal linear model
48
1
Cook's distance
Normal linear-model confidence ellipsoid
34
Multicollinearity
Normal linear model
31
Ordinary least squares estimators
Normal linear model
69
1
Residual sum of squares in simple linear regression
Ordinary least squares estimators
52
Gauss-Markov theorem
Normal linear model
14
Weighted least squares
Normal linear model
47
2
Generalized least squares
Weighted least squares
32
1
Whitening transformation
Generalized least squares
20
Normal equation
Normal linear model
9
Consistency of least squares
Normal linear model
21
One-way normal linear model
Normal linear model
91
4
Cell-means parametrization
One-way normal linear model
41
1
Linear contrast of cell means
Cell-means parametrization
21
Full-dominance mean constraint
One-way normal linear model
12
Additive allele-count model
One-way normal linear model
18
Regression leverage
Statistical modelling
12
Risk ratio
Statistical modelling
28
1
Drug efficacy as a risk reduction
Risk ratio
17
Odds ratio
Statistical modelling
27
Log-linear model
Statistical modelling
86
2
Saturated log-linear model
Log-linear model
20
Equal-efficacy Poisson log-linear model
Log-linear model
49
Maximum-likelihood estimator
Statistical modelling
114
5
Likelihood function
Maximum-likelihood estimator
26
Log-likelihood
Maximum-likelihood estimator
26
Binomial proportion maximum-likelihood estimator
Maximum-likelihood estimator
8
Exponential distribution rate estimator
Maximum-likelihood estimator
19
Asymptotic normality of a maximum likelihood estimator
Maximum-likelihood estimator
17
Logistic distribution
Statistical modelling
12
Gaussian conditional expectation
Statistical modelling
12
Linear discriminant analysis
Statistical modelling
14
Quadratic discriminant analysis
Statistical modelling
22
Bootstrapping (statistics)
Statistical modelling
15
Risk function
Statistical modelling
110
5
Mean squared error
Risk function
49
2
Bias-variance decomposition of mean squared error
Mean squared error
10
Affine shrinkage estimator for a binomial proportion
Mean squared error
27
Admissible estimator
Risk function
24
Minimax estimator
Risk function
13
Cramer-Rao bound
Statistical modelling
16
Score function
Statistical modelling
161
8
Mean-zero score identity
Score function
12
Fisher information matrix
Score function
139
6
Tensorization of Fisher information
Fisher information matrix
36
Fisher information in a stationary Gaussian autoregressive location model
Fisher information matrix
23
Fisher scoring
Fisher information matrix
43
1
Binomial-proportion Fisher scoring
Fisher scoring
28
Information identity
Fisher information matrix
7
Normal location-scale score
Fisher information matrix
15
Statistical hypothesis testing
Statistical modelling
698
30
Null hypothesis
Statistical hypothesis testing
22
Significance level
Statistical hypothesis testing
21
P-value
Statistical hypothesis testing
26
Joint hypothesis test
Statistical hypothesis testing
26
Power function of a statistical test
Statistical hypothesis testing
28
Uniformly most powerful test
Statistical hypothesis testing
53
1
Crossing-power obstruction to a uniformly most powerful test
Uniformly most powerful test
25
Pearson chi-squared goodness-of-fit test
Statistical hypothesis testing
54
1
Pearson chi-squared test of independence
Pearson chi-squared goodness-of-fit test
22
Wald test
Statistical hypothesis testing
158
4
Multivariate Wald statistic
Wald test
57
1
Wald statistic for linear restrictions
Multivariate Wald statistic
28
Wald and likelihood-ratio asymptotic equivalence
Wald test
51
Two-sided Gaussian p-value
Wald test
27
Likelihood-ratio test
Statistical hypothesis testing
123
5
Likelihood ratio
Likelihood-ratio test
14
Generalized likelihood-ratio test
Likelihood-ratio test
93
3
Analysis of deviance for nested generalized linear models
Generalized likelihood-ratio test
32
Likelihood-ratio test for equality of two normal means
Generalized likelihood-ratio test
17
Nested likelihood-ratio rejection regions
Generalized likelihood-ratio test
24
Score test
Statistical hypothesis testing
87
5
Restricted maximum-likelihood estimator
Score test
16
Score test under a simple null
Score test
30
1
Quadratic form of a standard normal vector
Score test under a simple null
7
Residual sum of squares in a normal sample
Score test
21
1
Chi-square central limit theorem
Residual sum of squares in a normal sample
11
Neyman-Pearson lemma
Statistical hypothesis testing
86
3
Monotone likelihood ratio
Neyman-Pearson lemma
60
2
Karlin-Rubin theorem
Monotone likelihood ratio
39
1
Uniformly most powerful upper-tail test for a logistic location
Karlin-Rubin theorem
17
Grouped exponential observation
Statistical modelling
39
1
Asymptotic information loss from grouping
Grouped exponential observation
19
Augmented Markov chain
Probability and statistics
Bayesian normal model
Probability and statistics
42
1
Normal-normal conjugacy with known observation variance
Bayesian normal model
42
Branching-process extinction criterion
Probability and statistics
Cauchy-Schwarz inequality
Probability and statistics
Cover time
Probability and statistics
Expected energy
Probability and statistics
F-test
Probability and statistics
20
1
Nested-model F-test
F-test
20
Galton-Watson process
Probability and statistics
61
2
Galton-Watson extinction fixed point
Galton-Watson process
21
Quadratic Galton-Watson extinction bound
Galton-Watson process
20
Gaussian tail bound
Probability and statistics
14
Gronwall inequality
Probability and statistics
23
1
Discrete Gronwall inequality
Gronwall inequality
23
Kac's lemma
Probability and statistics
36
Markov additive process
Probability and statistics
18
Multiple hypothesis testing
Probability and statistics
Multivariate normal distribution
Probability and statistics
136
9
Multivariate normal density
Multivariate normal distribution
12
Linear image of a multivariate normal vector
Multivariate normal distribution
26
Independence of uncorrelated jointly normal variables
Multivariate normal distribution
14
Bivariate normal distribution
Multivariate normal distribution
62
3
Maximum-likelihood covariance estimator for centered Gaussian data
Bivariate normal distribution
28
1
Asymptotic covariance of the bivariate Gaussian covariance estimator
Maximum-likelihood covariance estimator for centered Gaussian data
19
Conditional distribution of a bivariate normal variable
Bivariate normal distribution
8
Uncorrelated jointly normal variables are independent
Multivariate normal distribution
10
Orthogonal projection of a Gaussian vector
Multivariate normal distribution
12
Paley-Zygmund inequality
Probability and statistics
Pivotal quantity
Probability and statistics
Rao-Blackwell theorem
Probability and statistics
70
1
Rao-Blackwell estimator of a squared normal mean
Rao-Blackwell theorem
34
Regression residual
Probability and statistics
Sufficient statistic
Probability and statistics
136
4
Normal sample sum with known variance
Sufficient statistic
34
Minimal sufficient statistic
Sufficient statistic
56
1
Likelihood-ratio criterion for minimal sufficiency
Minimal sufficient statistic
24
Fisher-Neyman factorization theorem
Sufficient statistic
23
Weierstrass M-test
Probability and statistics
Monte Carlo method
Probability and statistics
144
3
Rejection sampling
Monte Carlo method
52
Importance sampling
Monte Carlo method
70
1
Self-normalized importance sampling
Importance sampling
32
Statistical inference
Probability and statistics
1k
48
Kolmogorov-Smirnov theorem
Statistical inference
26
Bias of a kernel density estimator
Statistical inference
39
Standard error
Statistical inference
21
Wilks theorem
Statistical inference
31
Chi-squared test of independence
Statistical inference
22
Statistical decision theory
Statistical inference
324
10
Bayes classifier
Statistical decision theory
112
2
Gaussian Bayes classifier
Bayes classifier
30
Uniqueness of a Bayes classifier
Bayes classifier
47
Risk of a decision rule
Statistical decision theory
19
Bayes risk
Statistical decision theory
58
1
Least favorable prior
Bayes risk
29
Minimax decision rule
Statistical decision theory
119
3
Equalizer rule
Minimax decision rule
72
1
Minimax Gaussian Bayes classifier from equal class errors
Equalizer rule
41
Constant-risk limit-of-Bayes-risk criterion
Minimax decision rule
38
Student t confidence interval
Statistical inference
53
1
Student t confidence interval for a centered regression intercept
Student t confidence interval
39
Bayesian statistics
Statistical inference
432
19
Prior probability
Bayesian statistics
16
Bayesian posterior
Bayesian statistics
210
8
Point-null mixture prior
Bayesian posterior
118
3
Marginal likelihood for a Gaussian point-null mixture
Point-null mixture prior
80
2
Posterior probability of a Gaussian point null
Marginal likelihood for a Gaussian point-null mixture
65
1
Jeffreys-Lindley paradox for a Gaussian point null
Posterior probability of a Gaussian point null
54
Improper prior
Bayesian posterior
26
Poisson-gamma conjugacy
Bayesian posterior
29
Gamma-exponential conjugacy
Bayesian posterior
11
Beta-binomial conjugacy
Bayesian posterior
16
Bayes estimator
Bayesian statistics
83
4
Bayes estimator under squared error loss
Bayes estimator
11
Bayes estimator under parameter-weighted squared error
Bayes estimator
27
Bayes estimator under reciprocal weighted quadratic loss
Bayes estimator
22
Posterior expected loss
Bayes estimator
16
Markov chain Monte Carlo
Bayesian statistics
111
3
Gibbs sampler
Markov chain Monte Carlo
86
2
Stationarity of the two-coordinate Gibbs sampler
Gibbs sampler
23
Normal mean-precision Gibbs sampler
Gibbs sampler
43
Jackknife bias correction
Statistical inference
61
1
Sample variance
Jackknife bias correction
28
Asymptotic normality
Statistical inference
119
5
Slutsky theorem
Asymptotic normality
14
Sandwich covariance matrix
Asymptotic normality
15
Delta method
Asymptotic normality
34
1
Asymptotic distribution of the Gaussian sample correlation
Delta method
18
Endpoint asymptotics of the symmetric-uniform maximum likelihood estimator
Asymptotic normality
39
Asymptotic relative efficiency
Statistical inference
12
Wald confidence interval
Statistical inference
20
Linear least-squares projection
Probability and statistics
32
1
Schur complement covariance
Linear least-squares projection
15
Ancestors
(3)
Area of mathematics
Mathematics
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