P0 |
-temp- |
Proof Template |
StatProofBook |
2019-09-27 |

P1 |
mvn-ltt |
Linear transformation theorem for the multivariate normal distribution |
JoramSoch |
2019-08-27 |

P2 |
mlr-ols |
Ordinary least squares for multiple linear regression |
JoramSoch |
2019-09-27 |

P3 |
lme-anc |
Partition of the log model evidence into accuracy and complexity |
JoramSoch |
2019-09-27 |

P4 |
bayes-th |
Bayes’ theorem |
JoramSoch |
2019-09-27 |

P5 |
mse-bnv |
Partition of the mean squared error into bias and variance |
JoramSoch |
2019-11-27 |

P6 |
ng-kl |
Kullback-Leibler divergence for the normal-gamma distribution |
JoramSoch |
2019-12-06 |

P7 |
glm-mle |
Maximum likelihood estimation for the general linear model |
JoramSoch |
2019-12-06 |

P8 |
rsq-der |
Derivation of R² and adjusted R² |
JoramSoch |
2019-12-06 |

P9 |
blr-prior |
Conjugate prior distribution for Bayesian linear regression |
JoramSoch |
2020-01-03 |

P10 |
blr-post |
Posterior distribution for Bayesian linear regression |
JoramSoch |
2020-01-03 |

P11 |
blr-lme |
Log model evidence for Bayesian linear regression |
JoramSoch |
2020-01-03 |

P12 |
bayes-rule |
Bayes’ rule |
JoramSoch |
2020-01-06 |

P13 |
lme-der |
Derivation of the log model evidence |
JoramSoch |
2020-01-06 |

P14 |
rsq-mll |
Relationship between R² and maximum log-likelihood |
JoramSoch |
2020-01-08 |

P15 |
norm-mean |
Mean of the normal distribution |
JoramSoch |
2020-01-09 |

P16 |
norm-med |
Median of the normal distribution |
JoramSoch |
2020-01-09 |

P17 |
norm-mode |
Mode of the normal distribution |
JoramSoch |
2020-01-09 |

P18 |
norm-var |
Variance of the normal distribution |
JoramSoch |
2020-01-09 |

P19 |
dmi-mce |
Relation of mutual information to marginal and conditional entropy |
JoramSoch |
2020-01-13 |

P20 |
dmi-mje |
Relation of mutual information to marginal and joint entropy |
JoramSoch |
2020-01-13 |

P21 |
dmi-jce |
Relation of mutual information to joint and conditional entropy |
JoramSoch |
2020-01-13 |

P22 |
bern-mean |
Mean of the Bernoulli distribution |
JoramSoch |
2020-01-16 |

P23 |
bin-mean |
Mean of the binomial distribution |
JoramSoch |
2020-01-16 |

P24 |
cat-mean |
Mean of the categorical distribution |
JoramSoch |
2020-01-16 |

P25 |
mult-mean |
Mean of the multinomial distribution |
JoramSoch |
2020-01-16 |

P26 |
matn-mvn |
Equivalence of matrix-normal distribution and multivariate normal distribution |
JoramSoch |
2020-01-20 |

P27 |
poiss-mle |
Maximum likelihood estimation for Poisson-distributed data |
JoramSoch |
2020-01-20 |

P28 |
beta-mome |
Method of moments for beta-distributed data |
JoramSoch |
2020-01-22 |

P29 |
bin-prior |
Conjugate prior distribution for binomial observations |
JoramSoch |
2020-01-23 |

P30 |
bin-post |
Posterior distribution for binomial observations |
JoramSoch |
2020-01-24 |

P31 |
bin-lme |
Log model evidence for binomial observations |
JoramSoch |
2020-01-24 |

P32 |
bic-der |
Derivation of the Bayesian information criterion |
JoramSoch |
2020-01-26 |

P33 |
norm-pdf |
Probability density function of the normal distribution |
JoramSoch |
2020-01-27 |

P34 |
mvn-pdf |
Probability density function of the multivariate normal distribution |
JoramSoch |
2020-01-27 |

P35 |
mvn-marg |
Marginal distributions of the multivariate normal distribution |
JoramSoch |
2020-01-29 |

P36 |
ng-marg |
Marginal distributions of the normal-gamma distribution |
JoramSoch |
2020-01-29 |

P37 |
cuni-pdf |
Probability density function of the continuous uniform distribution |
JoramSoch |
2020-01-31 |

P38 |
cuni-cdf |
Cumulative distribution function of the continuous uniform distribution |
JoramSoch |
2020-01-02 |

P39 |
cuni-qf |
Quantile function of the continuous uniform distribution |
JoramSoch |
2020-01-02 |

P40 |
mlr-ols2 |
Ordinary least squares for multiple linear regression |
JoramSoch |
2020-02-03 |

P41 |
poissexp-prior |
Conjugate prior distribution for the Poisson distribution with exposure values |
JoramSoch |
2020-02-04 |

P42 |
poissexp-post |
Posterior distribution for the Poisson distribution with exposure values |
JoramSoch |
2020-02-04 |

P43 |
poissexp-lme |
Log model evidence for the Poisson distribution with exposure values |
JoramSoch |
2020-02-04 |

P44 |
ng-pdf |
Probability density function of the normal-gamma distribution |
JoramSoch |
2020-02-07 |

P45 |
gam-pdf |
Probability density function of the gamma distribution |
JoramSoch |
2020-02-08 |

P46 |
exp-pdf |
Probability density function of the exponential distribution |
JoramSoch |
2020-02-08 |

P47 |
exp-mean |
Mean of the exponential distribution |
JoramSoch |
2020-02-10 |

P48 |
exp-cdf |
Cumulative distribution function of the exponential distribution |
JoramSoch |
2020-02-11 |

P49 |
exp-med |
Median of the exponential distribution |
JoramSoch |
2020-02-11 |

P50 |
exp-qf |
Quantile function of the exponential distribution |
JoramSoch |
2020-02-12 |

P51 |
exp-mode |
Mode of the exponential distribution |
kantundpeterpan |
2020-02-12 |

P52 |
mean-nonneg |
Non-negativity of the expected value |
JoramSoch |
2020-02-13 |

P53 |
mean-lin |
Linearity of the expected value |
JoramSoch |
2020-02-13 |

P54 |
mean-mono |
Monotonicity of the expected value |
JoramSoch |
2020-02-17 |

P55 |
mean-mult |
(Non-)Multiplicativity of the expected value |
JoramSoch |
2020-02-17 |

P56 |
ci-wilks |
Construction of confidence intervals using Wilks’ theorem |
JoramSoch |
2020-02-19 |

P57 |
ent-nonneg |
Non-negativity of the Shannon entropy |
JoramSoch |
2020-02-19 |

P58 |
cmi-mcde |
Relation of continuous mutual information to marginal and conditional differential entropy |
JoramSoch |
2020-02-21 |

P59 |
cmi-mjde |
Relation of continuous mutual information to marginal and joint differential entropy |
JoramSoch |
2020-02-21 |

P60 |
cmi-jcde |
Relation of continuous mutual information to joint and conditional differential entropy |
JoramSoch |
2020-02-21 |

P61 |
resvar-bias |
Maximum likelihood estimator of variance is biased |
JoramSoch |
2020-02-24 |

P62 |
resvar-unb |
Construction of unbiased estimator for variance |
JoramSoch |
2020-02-25 |

P63 |
snr-rsq |
Relationship between signal-to-noise ratio and R² |
JoramSoch |
2020-02-26 |

P64 |
lbf-lme |
Log Bayes factor in terms of log model evidences |
JoramSoch |
2020-02-27 |

P65 |
lfe-lme |
Log family evidences in terms of log model evidences |
JoramSoch |
2020-02-27 |

P66 |
pmp-lme |
Posterior model probabilities in terms of log model evidences |
JoramSoch |
2020-02-27 |

P67 |
bma-lme |
Bayesian model averaging in terms of log model evidences |
JoramSoch |
2020-02-27 |

P68 |
dent-neg |
Differential entropy can be negative |
JoramSoch |
2020-03-02 |

P69 |
exp-gam |
Exponential distribution is a special case of gamma distribution |
JoramSoch |
2020-03-02 |

P70 |
matn-pdf |
Probability density function of the matrix-normal distribution |
JoramSoch |
2020-03-02 |

P71 |
norm-mgf |
Moment-generating function of the normal distribution |
JoramSoch |
2020-03-03 |

P72 |
logreg-lonp |
Log-odds and probability in logistic regression |
JoramSoch |
2020-03-03 |

P73 |
pmp-lbf |
Posterior model probability in terms of log Bayes factor |
JoramSoch |
2020-03-03 |

P74 |
pmp-bf |
Posterior model probabilities in terms of Bayes factors |
JoramSoch |
2020-03-03 |

P75 |
mlr-mat |
Transformation matrices for ordinary least squares |
JoramSoch |
2020-03-09 |

P76 |
mlr-pss |
Partition of sums of squares for multiple linear regression |
JoramSoch |
2020-03-09 |

P77 |
mlr-wls |
Weighted least squares for multiple linear regression |
JoramSoch |
2020-03-11 |

P78 |
mlr-mle |
Maximum likelihood estimation for multiple linear regression |
JoramSoch |
2020-03-11 |

P79 |
mult-prior |
Conjugate prior distribution for multinomial observations |
JoramSoch |
2020-03-11 |

P80 |
mult-post |
Posterior distribution for multinomial observations |
JoramSoch |
2020-03-11 |

P81 |
mult-lme |
Log model evidence for multinomial observations |
JoramSoch |
2020-03-11 |

P82 |
cuni-mean |
Mean of the continuous uniform distribution |
JoramSoch |
2020-03-16 |

P83 |
cuni-med |
Median of the continuous uniform distribution |
JoramSoch |
2020-03-16 |

P84 |
cuni-med |
Mode of the continuous uniform distribution |
JoramSoch |
2020-03-16 |

P85 |
norm-cdf |
Cumulative distribution function of the normal distribution |
JoramSoch |
2020-03-20 |

P86 |
norm-cdfwerf |
Expression of the cumulative distribution function of the normal distribution without the error function |
JoramSoch |
2020-03-20 |

P87 |
norm-qf |
Quantile function of the normal distribution |
JoramSoch |
2020-03-20 |

P88 |
mvn-cond |
Conditional distributions of the multivariate normal distribution |
JoramSoch |
2020-03-20 |

P89 |
jl-lfnprior |
Joint likelihood is the product of likelihood function and prior density |
JoramSoch |
2020-05-05 |

P90 |
post-jl |
Posterior density is proportional to joint likelihood |
JoramSoch |
2020-05-05 |

P91 |
ml-jl |
Marginal likelihood is a definite integral of the joint likelihood |
JoramSoch |
2020-05-05 |

P92 |
mvn-kl |
Kullback-Leibler divergence for the multivariate normal distribution |
JoramSoch |
2020-05-05 |

P93 |
gam-kl |
Kullback-Leibler divergence for the gamma distribution |
JoramSoch |
2020-05-05 |

P94 |
beta-pdf |
Probability density function of the beta distribution |
JoramSoch |
2020-05-05 |

P95 |
dir-pdf |
Probability density function of the Dirichlet distribution |
JoramSoch |
2020-05-05 |

P96 |
bern-pmf |
Probability mass function of the Bernoulli distribution |
JoramSoch |
2020-05-11 |

P97 |
bin-pmf |
Probability mass function of the binomial distribution |
JoramSoch |
2020-05-11 |

P98 |
cat-pmf |
Probability mass function of the categorical distribution |
JoramSoch |
2020-05-11 |

P99 |
mult-pmf |
Probability mass function of the multinomial distribution |
JoramSoch |
2020-05-11 |

P100 |
mvn-dent |
Differential entropy of the multivariate normal distribution |
JoramSoch |
2020-05-14 |

P101 |
norm-dent |
Differential entropy of the normal distribution |
JoramSoch |
2020-05-14 |

P102 |
poiss-pmf |
Probability mass function of the Poisson distribution |
JoramSoch |
2020-05-14 |

P103 |
mean-nnrvar |
Expected value of a non-negative random variable |
JoramSoch |
2020-05-18 |

P104 |
var-mean |
Partition of variance into expected values |
JoramSoch |
2020-05-19 |

P105 |
logreg-pnlo |
Probability and log-odds in logistic regression |
JoramSoch |
2020-05-19 |

P106 |
glm-ols |
Ordinary least squares for the general linear model |
JoramSoch |
2020-05-19 |

P107 |
glm-wls |
Weighted least squares for the general linear model |
JoramSoch |
2020-05-19 |

P108 |
gam-mean |
Mean of the gamma distribution |
JoramSoch |
2020-05-19 |

P109 |
gam-var |
Variance of the gamma distribution |
JoramSoch |
2020-05-19 |

P110 |
gam-logmean |
Logarithmic expectation of the gamma distribution |
JoramSoch |
2020-05-25 |

P111 |
norm-snorm |
Relationship between normal distribution and standard normal distribution |
JoramSoch |
2020-05-26 |

P112 |
gam-sgam |
Relationship between gamma distribution and standard gamma distribution |
JoramSoch |
2020-05-26 |

P113 |
kl-ent |
Relation of discrete Kullback-Leibler divergence to Shannon entropy |
JoramSoch |
2020-05-27 |

P114 |
kl-dent |
Relation of continuous Kullback-Leibler divergence to differential entropy |
JoramSoch |
2020-05-27 |

P115 |
kl-inv |
Invariance of the Kullback-Leibler divergence under parameter transformation |
JoramSoch |
2020-05-28 |

P116 |
kl-add |
Additivity of the Kullback-Leibler divergence for independent distributions |
JoramSoch |
2020-05-31 |

P117 |
kl-nonneg |
Non-negativity of the Kullback-Leibler divergence |
JoramSoch |
2020-05-31 |

P118 |
cov-mean |
Partition of covariance into expected values |
JoramSoch |
2020-06-02 |

P119 |
cov-corr |
Relationship between covariance and correlation |
JoramSoch |
2020-06-02 |

P120 |
covmat-mean |
Partition of a covariance matrix into expected values |
JoramSoch |
2020-06-06 |

P121 |
covmat-corrmat |
Relationship between covariance matrix and correlation matrix |
JoramSoch |
2020-06-06 |

P122 |
precmat-corrmat |
Relationship between precision matrix and correlation matrix |
JoramSoch |
2020-06-06 |

P123 |
var-nonneg |
Non-negativity of the variance |
JoramSoch |
2020-06-06 |

P124 |
var-const |
Variance of constant is zero |
JoramSoch |
2020-06-27 |

P126 |
var-inv |
Invariance of the variance under addition of a constant |
JoramSoch |
2020-07-07 |

P127 |
var-scal |
Scaling of the variance upon multiplication with a constant |
JoramSoch |
2020-07-07 |

P128 |
var-sum |
Variance of the sum of two random variables |
JoramSoch |
2020-07-07 |

P129 |
var-lincomb |
Variance of the linear combination of two random variables |
JoramSoch |
2020-07-07 |

P130 |
var-add |
Additivity of the variance for independent random variables |
JoramSoch |
2020-07-07 |

P131 |
mean-qf |
Expectation of a quadratic form |
JoramSoch |
2020-07-13 |

P132 |
lfe-der |
Derivation of the log family evidence |
JoramSoch |
2020-07-13 |

P133 |
blr-pp |
Posterior probability of the alternative hypothesis for Bayesian linear regression |
JoramSoch |
2020-07-17 |

P134 |
blr-pcr |
Posterior credibility region against the omnibus null hypothesis for Bayesian linear regression |
JoramSoch |
2020-07-17 |

P135 |
mlr-idem |
Projection matrix and residual-forming matrix are idempotent |
JoramSoch |
2020-07-22 |

P136 |
mlr-wls2 |
Weighted least squares for multiple linear regression |
JoramSoch |
2020-07-22 |

P137 |
lbf-der |
Derivation of the log Bayes factor |
JoramSoch |
2020-07-22 |

P138 |
mean-lotus |
Law of the unconscious statistician |
JoramSoch |
2020-07-22 |

P139 |
pmp-der |
Derivation of the posterior model probability |
JoramSoch |
2020-07-28 |

P140 |
duni-pmf |
Probability mass function of the discrete uniform distribution |
JoramSoch |
2020-07-28 |

P141 |
duni-cdf |
Cumulative distribution function of the discrete uniform distribution |
JoramSoch |
2020-07-28 |

P142 |
duni-qf |
Quantile function of the discrete uniform distribution |
JoramSoch |
2020-07-28 |

P143 |
bma-der |
Derivation of Bayesian model averaging |
JoramSoch |
2020-08-03 |

P144 |
matn-trans |
Transposition of a matrix-normal random variable |
JoramSoch |
2020-08-03 |

P145 |
matn-ltt |
Linear transformation theorem for the matrix-normal distribution |
JoramSoch |
2020-08-03 |

P146 |
ng-cond |
Conditional distributions of the normal-gamma distribution |
JoramSoch |
2020-08-05 |

P147 |
kl-nonsymm |
Non-symmetry of the Kullback-Leibler divergence |
JoramSoch |
2020-08-11 |

P148 |
kl-conv |
Convexity of the Kullback-Leibler divergence |
JoramSoch |
2020-08-11 |

P149 |
ent-conc |
Concavity of the Shannon entropy |
JoramSoch |
2020-08-11 |

P150 |
entcross-conv |
Convexity of the cross-entropy |
JoramSoch |
2020-08-11 |

P151 |
poiss-mean |
Mean of the Poisson distribution |
JoramSoch |
2020-08-19 |

P152 |
norm-fwhm |
Full width at half maximum for the normal distribution |
JoramSoch |
2020-08-19 |

P153 |
mom-mgf |
Moment in terms of moment-generating function |
JoramSoch |
2020-08-19 |

P154 |
mgf-ltt |
Linear transformation theorem for the moment-generating function |
JoramSoch |
2020-08-19 |

P155 |
mgf-lincomb |
Moment-generating function of linear combination of independent random variables |
JoramSoch |
2020-08-19 |

P156 |
bf-sddr |
Savage-Dickey density ratio for computing Bayes factors |
tomfaulkenberry |
2020-08-26 |

P157 |
bf-ep |
Encompassing prior method for computing Bayes factors |
tomfaulkenberry |
2020-09-02 |

P158 |
cov-ind |
Covariance of independent random variables |
JoramSoch |
2020-09-03 |

P159 |
mblr-prior |
Conjugate prior distribution for multivariate Bayesian linear regression |
JoramSoch |
2020-09-03 |

P160 |
mblr-post |
Posterior distribution for multivariate Bayesian linear regression |
JoramSoch |
2020-09-03 |

P161 |
mblr-lme |
Log model evidence for multivariate Bayesian linear regression |
JoramSoch |
2020-09-03 |

P162 |
wald-pdf |
Probability density function of the Wald distribution |
tomfaulkenberry |
2020-09-04 |

P163 |
bf-trans |
Transitivity of Bayes Factors |
tomfaulkenberry |
2020-09-07 |

P164 |
gibbs-ineq |
Gibbs’ inequality |
JoramSoch |
2020-09-09 |

P165 |
logsum-ineq |
Log sum inequality |
JoramSoch |
2020-09-09 |

P166 |
kl-nonneg2 |
Non-negativity of the Kullback-Leibler divergence |
JoramSoch |
2020-09-09 |

P167 |
momcent-1st |
First central moment is zero |
JoramSoch |
2020-09-09 |

P168 |
wald-mgf |
Moment-generating function of the Wald distribution |
tomfaulkenberry |
2020-09-13 |

P169 |
wald-mean |
Mean of the Wald distribution |
tomfaulkenberry |
2020-09-13 |

P170 |
wald-var |
Variance of the Wald distribution |
tomfaulkenberry |
2020-09-13 |

P171 |
momraw-1st |
First raw moment is mean |
JoramSoch |
2020-10-08 |

P172 |
momraw-2nd |
Relationship between second raw moment, variance and mean |
JoramSoch |
2020-10-08 |

P173 |
momcent-2nd |
Second central moment is variance |
JoramSoch |
2020-10-08 |

P174 |
chi2-gam |
Chi-squared distribution is a special case of gamma distribution |
kjpetrykowski |
2020-10-12 |

P175 |
chi2-mom |
Moments of the chi-squared distribution |
kjpetrykowski |
2020-10-13 |

P176 |
norm-snorm2 |
Relationship between normal distribution and standard normal distribution |
JoramSoch |
2020-10-15 |

P177 |
gam-sgam2 |
Relationship between gamma distribution and standard gamma distribution |
JoramSoch |
2020-10-15 |

P178 |
gam-cdf |
Cumulative distribution function of the gamma distribution |
JoramSoch |
2020-10-15 |

P179 |
gam-xlogx |
Expected value of x times ln(x) for a gamma distribution |
JoramSoch |
2020-10-15 |

P180 |
norm-snorm3 |
Relationship between normal distribution and standard normal distribution |
JoramSoch |
2020-10-22 |

P181 |
dir-ep |
Exceedance probabilities for the Dirichlet distribution |
JoramSoch |
2020-10-22 |

P182 |
dir-mle |
Maximum likelihood estimation for Dirichlet-distributed data |
JoramSoch |
2020-10-22 |

P183 |
cdf-sifct |
Cumulative distribution function of a strictly increasing function of a random variable |
JoramSoch |
2020-10-29 |

P184 |
pmf-sifct |
Probability mass function of a strictly increasing function of a discrete random variable |
JoramSoch |
2020-10-29 |

P185 |
pdf-sifct |
Probability density function of a strictly increasing function of a continuous random variable |
JoramSoch |
2020-10-29 |

P186 |
cdf-sdfct |
Cumulative distribution function of a strictly decreasing function of a random variable |
JoramSoch |
2020-11-06 |

P187 |
pmf-sdfct |
Probability mass function of a strictly decreasing function of a discrete random variable |
JoramSoch |
2020-11-06 |

P188 |
pdf-sdfct |
Probability density function of a strictly decreasing function of a continuous random variable |
JoramSoch |
2020-11-06 |

P189 |
cdf-pmf |
Cumulative distribution function in terms of probability mass function of a discrete random variable |
JoramSoch |
2020-11-12 |

P190 |
cdf-pdf |
Cumulative distribution function in terms of probability density function of a continuous random variable |
JoramSoch |
2020-11-12 |

P191 |
pdf-cdf |
Probability density function is first derivative of cumulative distribution function |
JoramSoch |
2020-11-12 |

P192 |
qf-cdf |
Quantile function is inverse of strictly monotonically increasing cumulative distribution function |
JoramSoch |
2020-11-12 |

P193 |
norm-kl |
Kullback-Leibler divergence for the normal distribution |
JoramSoch |
2020-11-19 |

P194 |
gam-qf |
Quantile function of the gamma distribution |
JoramSoch |
2020-11-19 |

P195 |
beta-cdf |
Cumulative distribution function of the beta distribution |
JoramSoch |
2020-11-19 |

P196 |
norm-gi |
Gaussian integral |
JoramSoch |
2020-11-25 |

P197 |
chi2-pdf |
Probability density function of the chi-squared distribution |
JoramSoch |
2020-11-25 |

P198 |
beta-mgf |
Moment-generating function of the beta distribution |
JoramSoch |
2020-11-25 |

P199 |
dent-inv |
Invariance of the differential entropy under addition of a constant |
JoramSoch |
2020-12-02 |

P200 |
dent-add |
Addition of the differential entropy upon multiplication with a constant |
JoramSoch |
2020-12-02 |

P201 |
ug-prior |
Conjugate prior distribution for the univariate Gaussian |
JoramSoch |
2021-03-03 |

P202 |
ug-post |
Posterior distribution for the univariate Gaussian |
JoramSoch |
2021-03-03 |

P203 |
ug-lme |
Log model evidence for the univariate Gaussian |
JoramSoch |
2021-03-03 |

P204 |
ug-ttest1 |
One-sample t-test for independent observations |
JoramSoch |
2021-03-12 |

P205 |
ug-ttest2 |
Two-sample t-test for independent observations |
JoramSoch |
2021-03-12 |

P206 |
ug-ttestp |
Paired t-test for dependent observations |
JoramSoch |
2021-03-12 |

P207 |
ugkv-mle |
Maximum likelihood estimation for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P208 |
ugkv-ztest1 |
One-sample z-test for independent observations |
JoramSoch |
2021-03-24 |

P209 |
ugkv-ztest2 |
Two-sample z-test for independent observations |
JoramSoch |
2021-03-24 |

P210 |
ugkv-ztestp |
Paired z-test for dependent observations |
JoramSoch |
2021-03-24 |

P211 |
ugkv-prior |
Conjugate prior distribution for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P212 |
ugkv-post |
Posterior distribution for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P213 |
ugkv-lme |
Log model evidence for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P214 |
ugkv-anc |
Accuracy and complexity for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P215 |
ugkv-lbf |
Log Bayes factor for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P216 |
ugkv-lbfmean |
Expectation of the log Bayes factor for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P217 |
ugkv-cvlme |
Cross-validated log model evidence for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P218 |
ugkv-cvlbf |
Cross-validated log Bayes factor for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P219 |
ugkv-cvlbfmean |
Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance |
JoramSoch |
2021-03-24 |

P220 |
cdf-pit |
Probability integral transform using cumulative distribution function |
JoramSoch |
2021-04-07 |

P221 |
cdf-itm |
Inverse transformation method using cumulative distribution function |
JoramSoch |
2021-04-07 |

P222 |
cdf-dt |
Distributional transformation using cumulative distribution function |
JoramSoch |
2021-04-07 |

P223 |
ug-mle |
Maximum likelihood estimation for the univariate Gaussian |
JoramSoch |
2021-04-16 |

P224 |
poissexp-mle |
Maximum likelihood estimation for the Poisson distribution with exposure values |
JoramSoch |
2021-04-16 |

P225 |
poiss-prior |
Conjugate prior distribution for Poisson-distributed data |
JoramSoch |
2020-04-21 |

P226 |
poiss-post |
Posterior distribution for Poisson-distributed data |
JoramSoch |
2020-04-21 |

P227 |
poiss-lme |
Log model evidence for Poisson-distributed data |
JoramSoch |
2020-04-21 |

P228 |
beta-mean |
Mean of the beta distribution |
JoramSoch |
2021-04-29 |

P229 |
beta-var |
Variance of the beta distribution |
JoramSoch |
2021-04-29 |

P230 |
poiss-var |
Variance of the Poisson distribution |
JoramSoch |
2021-04-29 |

P231 |
mvt-f |
Relationship between multivariate t-distribution and F-distribution |
JoramSoch |
2021-05-04 |

P232 |
nst-t |
Relationship between non-standardized t-distribution and t-distribution |
JoramSoch |
2021-05-11 |

P233 |
norm-chi2 |
Relationship between normal distribution and chi-squared distribution |
JoramSoch |
2021-05-20 |

P234 |
norm-t |
Relationship between normal distribution and t-distribution |
JoramSoch |
2021-05-27 |

P235 |
norm-lincomb |
Linear combination of independent normal random variables |
JoramSoch |
2021-06-02 |

P236 |
mvn-ind |
Necessary and sufficient condition for independence of multivariate normal random variables |
JoramSoch |
2021-06-02 |

P237 |
ng-mean |
Mean of the normal-gamma distribution |
JoramSoch |
2021-07-08 |

P238 |
ng-dent |
Differential entropy of the normal-gamma distribution |
JoramSoch |
2021-07-08 |

P239 |
gam-dent |
Differential entropy of the gamma distribution |
JoramSoch |
2021-07-14 |

P240 |
ug-anc |
Accuracy and complexity for the univariate Gaussian |
JoramSoch |
2021-07-14 |

P241 |
prob-ind |
Probability under statistical independence |
JoramSoch |
2021-07-23 |

P242 |
prob-exc |
Probability under mutual exclusivity |
JoramSoch |
2021-07-23 |

P243 |
prob-mon |
Monotonicity of probability |
JoramSoch |
2021-07-30 |

P244 |
prob-emp |
Probability of the empty set |
JoramSoch |
2021-07-30 |

P245 |
prob-comp |
Probability of the complement |
JoramSoch |
2021-07-30 |

P246 |
prob-range |
Range of probability |
JoramSoch |
2021-07-30 |

P247 |
prob-add |
Addition law of probability |
JoramSoch |
2021-07-30 |

P248 |
prob-tot |
Law of total probability |
JoramSoch |
2021-08-08 |

P249 |
prob-exh |
Probability of exhaustive events |
JoramSoch |
2021-08-08 |

P250 |
norm-maxent |
Normal distribution maximizes differential entropy for fixed variance |
JoramSoch |
2020-08-25 |

P251 |
norm-extr |
Extreme points of the probability density function of the normal distribution |
JoramSoch |
2020-08-25 |

P252 |
norm-infl |
Inflection points of the probability density function of the normal distribution |
JoramSoch |
2020-08-26 |

P253 |
pmf-invfct |
Probability mass function of an invertible function of a random vector |
JoramSoch |
2021-08-30 |

P254 |
pdf-invfct |
Probability density function of an invertible function of a continuous random vector |
JoramSoch |
2021-08-30 |

P255 |
pdf-linfct |
Probability density function of a linear function of a continuous random vector |
JoramSoch |
2021-08-30 |

P256 |
cdf-sumind |
Cumulative distribution function of a sum of independent random variables |
JoramSoch |
2021-08-30 |

P257 |
pmf-sumind |
Probability mass function of a sum of independent discrete random variables |
JoramSoch |
2021-08-30 |

P258 |
pdf-sumind |
Probability density function of a sum of independent continuous random variables |
JoramSoch |
2021-08-30 |

P259 |
cf-fct |
Characteristic function of a function of a random variable |
JoramSoch |
2021-09-22 |

P260 |
mgf-fct |
Moment-generating function of a function of a random variable |
JoramSoch |
2021-09-22 |

P261 |
dent-addvec |
Addition of the differential entropy upon multiplication with invertible matrix |
JoramSoch |
2021-10-07 |

P262 |
dent-noninv |
Non-invariance of the differential entropy under change of variables |
JoramSoch |
2021-10-07 |

P263 |
t-pdf |
Probability density function of the t-distribution |
JoramSoch |
2021-10-12 |

P264 |
f-pdf |
Probability density function of the F-distribution |
JoramSoch |
2021-10-12 |

P265 |
tglm-dist |
Distribution of the transformed general linear model |
JoramSoch |
2021-10-21 |

P266 |
tglm-para |
Equivalence of parameter estimates from the transformed general linear model |
JoramSoch |
2021-10-21 |

P267 |
iglm-dist |
Distribution of the inverse general linear model |
JoramSoch |
2021-10-21 |

P268 |
iglm-blue |
Best linear unbiased estimator for the inverse general linear model |
JoramSoch |
2021-10-21 |

P269 |
cfm-para |
Parameters of the corresponding forward model |
JoramSoch |
2021-10-21 |

P270 |
cfm-exist |
Existence of a corresponding forward model |
JoramSoch |
2021-10-21 |

P271 |
slr-ols |
Ordinary least squares for simple linear regression |
JoramSoch |
2021-10-27 |

P272 |
slr-olsmean |
Expectation of parameter estimates for simple linear regression |
JoramSoch |
2021-10-27 |

P273 |
slr-olsvar |
Variance of parameter estimates for simple linear regression |
JoramSoch |
2021-10-27 |

P274 |
slr-meancent |
Effects of mean-centering on parameter estimates for simple linear regression |
JoramSoch |
2021-10-27 |

P275 |
slr-comp |
The regression line goes through the center of mass point |
JoramSoch |
2021-10-27 |

P276 |
slr-ressum |
The sum of residuals is zero in simple linear regression |
JoramSoch |
2021-10-27 |

P277 |
slr-rescorr |
The residuals and the covariate are uncorrelated in simple linear regression |
JoramSoch |
2021-10-27 |

P278 |
slr-resvar |
Relationship between residual variance and sample variance in simple linear regression |
JoramSoch |
2021-10-27 |

P279 |
slr-corr |
Relationship between correlation coefficient and slope estimate in simple linear regression |
JoramSoch |
2021-10-27 |

P280 |
slr-rsq |
Relationship between coefficient of determination and correlation coefficient in simple linear regression |
JoramSoch |
2021-10-27 |

P281 |
slr-mlr |
Simple linear regression is a special case of multiple linear regression |
JoramSoch |
2021-11-09 |

P282 |
slr-olsdist |
Distribution of parameter estimates for simple linear regression |
JoramSoch |
2021-11-09 |

P283 |
slr-proj |
Projection of a data point to the regression line |
JoramSoch |
2021-11-09 |

P284 |
slr-sss |
Sums of squares for simple linear regression |
JoramSoch |
2021-11-09 |

P285 |
slr-mat |
Transformation matrices for simple linear regression |
JoramSoch |
2021-11-09 |

P286 |
slr-wls |
Weighted least squares for simple linear regression |
JoramSoch |
2021-11-16 |

P287 |
slr-mle |
Maximum likelihood estimation for simple linear regression |
JoramSoch |
2021-11-16 |

P288 |
slr-ols2 |
Ordinary least squares for simple linear regression |
JoramSoch |
2021-11-16 |

P289 |
slr-wls2 |
Weighted least squares for simple linear regression |
JoramSoch |
2021-11-16 |

P290 |
slr-mle2 |
Maximum likelihood estimation for simple linear regression |
JoramSoch |
2021-11-16 |

P291 |
mean-tot |
Law of total expectation |
JoramSoch |
2021-11-26 |

P292 |
var-tot |
Law of total variance |
JoramSoch |
2021-11-26 |

P293 |
cov-tot |
Law of total covariance |
JoramSoch |
2021-11-26 |

P294 |
dir-kl |
Kullback-Leibler divergence for the Dirichlet distribution |
JoramSoch |
2021-12-02 |

P295 |
wish-kl |
Kullback-Leibler divergence for the Wishart distribution |
JoramSoch |
2021-12-02 |

P296 |
matn-kl |
Kullback-Leibler divergence for the matrix-normal distribution |
JoramSoch |
2021-12-02 |

P297 |
matn-samp |
Sampling from the matrix-normal distribution |
JoramSoch |
2021-12-07 |

P298 |
mean-tr |
Expected value of the trace of a matrix |
JoramSoch |
2021-12-07 |

P299 |
corr-z |
Correlation coefficient in terms of standard scores |
JoramSoch |
2021-12-14 |

P300 |
corr-range |
Correlation always falls between -1 and +1 |
JoramSoch |
2021-12-14 |

P301 |
bern-var |
Variance of the Bernoulli distribution |
JoramSoch |
2022-01-20 |

P302 |
bin-var |
Variance of the binomial distribution |
JoramSoch |
2022-01-20 |

P303 |
bern-varrange |
Range of the variance of the Bernoulli distribution |
JoramSoch |
2022-01-27 |

P304 |
bin-varrange |
Range of the variance of the binomial distribution |
JoramSoch |
2022-01-27 |

P305 |
mlr-mll |
Maximum log-likelihood for multiple linear regression |
JoramSoch |
2022-02-04 |

P306 |
lognorm-med |
Median of the log-normal distribution |
majapavlo |
2022-02-07 |

P307 |
mlr-aic |
Akaike information criterion for multiple linear regression |
JoramSoch |
2022-02-11 |

P308 |
mlr-bic |
Bayesian information criterion for multiple linear regression |
JoramSoch |
2022-02-11 |

P309 |
mlr-aicc |
Corrected Akaike information criterion for multiple linear regression |
JoramSoch |
2022-02-11 |

P310 |
lognorm-pdf |
Probability density function of the log-normal distribution |
majapavlo |
2022-02-13 |

P311 |
lognorm-mode |
Mode of the log-normal distribution |
majapavlo |
2022-02-13 |

P312 |
mlr-dev |
Deviance for multiple linear regression |
JoramSoch |
2022-03-01 |

P313 |
blr-dic |
Deviance information criterion for multiple linear regression |
JoramSoch |
2022-03-01 |

P314 |
lme-pnp |
Log model evidence in terms of prior and posterior distribution |
JoramSoch |
2022-03-11 |

P315 |
aicc-mll |
Corrected Akaike information criterion in terms of maximum log-likelihood |
JoramSoch |
2022-03-11 |

P316 |
aicc-aic |
Corrected Akaike information criterion converges to uncorrected Akaike information criterion when infinite data are available |
JoramSoch |
2022-03-18 |

P317 |
mle-bias |
Maximum likelihood estimation can result in biased estimates |
JoramSoch |
2022-03-18 |

P318 |
pval-h0 |
The p-value follows a uniform distribution under the null hypothesis |
JoramSoch |
2022-03-18 |

P319 |
prob-exh2 |
Probability of exhaustive events |
JoramSoch |
2022-03-27 |

P320 |
slr-olscorr |
Parameter estimates for simple linear regression are uncorrelated after mean-centering |
JoramSoch |
2022-04-14 |

P321 |
norm-probstd |
Probability of normal random variable being within standard deviations from its mean |
JoramSoch |
2022-05-08 |

P322 |
mult-cov |
Covariance matrix of the multinomial distribution |
adkipnis |
2022-05-11 |

P323 |
nw-pdf |
Probability density function of the normal-Wishart distribution |
JoramSoch |
2022-05-14 |

P324 |
ng-nw |
Normal-gamma distribution is a special case of normal-Wishart distribution |
JoramSoch |
2022-05-20 |

P325 |
lognorm-cdf |
Cumulative distribution function of the log-normal distribution |
majapavlo |
2022-06-29 |

P326 |
lognorm-qf |
Quantile function of the log-normal distribution |
majapavlo |
2022-07-09 |

P327 |
nw-mean |
Mean of the normal-Wishart distribution |
JoramSoch |
2022-07-14 |

P328 |
gam-wish |
Gamma distribution is a special case of Wishart distribution |
JoramSoch |
2022-07-14 |

P329 |
mlr-glm |
Multiple linear regression is a special case of the general linear model |
JoramSoch |
2022-07-21 |

P330 |
mvn-matn |
Multivariate normal distribution is a special case of matrix-normal distribution |
JoramSoch |
2022-07-31 |

P331 |
norm-mvn |
Normal distribution is a special case of multivariate normal distribution |
JoramSoch |
2022-08-19 |

P332 |
t-mvt |
t-distribution is a special case of multivariate t-distribution |
JoramSoch |
2022-08-25 |

P333 |
mvt-pdf |
Probability density function of the multivariate t-distribution |
JoramSoch |
2022-09-02 |

P334 |
bern-ent |
Entropy of the Bernoulli distribution |
JoramSoch |
2022-09-02 |

P335 |
bin-ent |
Entropy of the binomial distribution |
JoramSoch |
2022-09-02 |

P336 |
cat-ent |
Entropy of the categorical distribution |
JoramSoch |
2022-09-09 |

P337 |
mult-ent |
Entropy of the multinomial distribution |
JoramSoch |
2022-09-09 |

P338 |
cat-cov |
Covariance matrix of the categorical distribution |
JoramSoch |
2022-09-09 |

P339 |
mvn-mean |
Mean of the multivariate normal distribution |
JoramSoch |
2022-09-15 |

P340 |
mvn-cov |
Covariance matrix of the multivariate normal distribution |
JoramSoch |
2022-09-15 |

P341 |
matn-mean |
Mean of the matrix-normal distribution |
JoramSoch |
2022-09-15 |

P342 |
matn-cov |
Covariance matrices of the matrix-normal distribution |
JoramSoch |
2022-09-15 |

P343 |
matn-marg |
Marginal distributions for the matrix-normal distribution |
JoramSoch |
2022-09-15 |

P344 |
matn-dent |
Differential entropy for the matrix-normal distribution |
JoramSoch |
2022-09-22 |

P345 |
ng-cov |
Covariance and variance of the normal-gamma distribution |
JoramSoch |
2022-09-22 |

P346 |
ng-samp |
Sampling from the normal-gamma distribution |
JoramSoch |
2022-09-22 |

P347 |
covmat-inv |
Invariance of the covariance matrix under addition of constant vector |
JoramSoch |
2022-09-22 |

P348 |
covmat-scal |
Scaling of the covariance matrix upon multiplication with constant matrix |
JoramSoch |
2022-09-22 |

P349 |
covmat-sum |
Covariance matrix of the sum of two random vectors |
JoramSoch |
2022-09-26 |

P350 |
covmat-symm |
Symmetry of the covariance matrix |
JoramSoch |
2022-09-26 |

P351 |
covmat-psd |
Positive semi-definiteness of the covariance matrix |
JoramSoch |
2022-09-26 |

P352 |
cov-var |
Self-covariance equals variance |
JoramSoch |
2022-09-26 |

P353 |
cov-symm |
Symmetry of the covariance |
JoramSoch |
2022-09-26 |

P354 |
lognorm-mean |
Mean of the log-normal distribution |
majapavlo |
2022-10-02 |

P355 |
lognorm-var |
Variance of the log-normal distribution |
majapavlo |
2022-10-02 |

P356 |
beta-chi2 |
Relationship between chi-squared distribution and beta distribution |
JoramSoch |
2022-10-07 |

P357 |
betabin-mome |
Method of moments for beta-binomial data |
JoramSoch |
2022-10-07 |

P358 |
bin-margcond |
Marginal distribution of a conditional binomial distribution |
JoramSoch |
2022-10-07 |

P359 |
mean-prodsqr |
Square of expectation of product is less than or equal to product of expectation of squares |
JoramSoch |
2022-10-11 |

P360 |
pgf-mean |
Probability-generating function is expectation of function of random variable |
JoramSoch |
2022-10-11 |

P361 |
pgf-zero |
Value of the probability-generating function for argument zero |
JoramSoch |
2022-10-11 |

P362 |
pgf-one |
Value of the probability-generating function for argument one |
JoramSoch |
2022-10-11 |

P363 |
bin-pgf |
Probability-generating function of the binomial distribution |
JoramSoch |
2022-10-11 |

P364 |
betabin-pmf |
Probability mass function of the beta-binomial distribution |
JoramSoch |
2022-10-20 |

P365 |
betabin-pmfitogf |
Expression of the probability mass function of the beta-binomial distribution using only the gamma function |
JoramSoch |
2022-10-20 |

P366 |
betabin-cdf |
Cumulative distribution function of the beta-binomial distribution |
JoramSoch |
2022-10-22 |

P367 |
me-der |
Derivation of the model evidence |
JoramSoch |
2022-10-20 |

P368 |
fe-der |
Derivation of the family evidence |
JoramSoch |
2022-10-20 |

P369 |
anova1-ols |
Ordinary least squares for one-way analysis of variance |
JoramSoch |
2022-11-06 |

P370 |
anova1-f |
F-test for main effect in one-way analysis of variance |
JoramSoch |
2022-11-06 |

P371 |
anova2-ols |
Ordinary least squares for two-way analysis of variance |
JoramSoch |
2022-11-06 |

P372 |
anova2-fme |
F-test for main effect in two-way analysis of variance |
JoramSoch |
2022-11-10 |

P373 |
anova2-fia |
F-test for interaction in two-way analysis of variance |
JoramSoch |
2022-11-11 |

P374 |
anova2-fgm |
F-test for grand mean in two-way analysis of variance |
JoramSoch |
2022-11-11 |

P375 |
anova1-repara |
Reparametrization for one-way analysis of variance |
JoramSoch |
2022-11-15 |

P376 |
anova1-pss |
Partition of sums of squares in one-way analysis of variance |
JoramSoch |
2022-11-15 |

P377 |
anova1-fols |
F-statistic in terms of ordinary least squares estimates in one-way analysis of variance |
JoramSoch |
2022-11-15 |

P378 |
anova2-cochran |
Application of Cochran’s theorem to two-way analysis of variance |
JoramSoch |
2022-11-16 |

P379 |
anova2-pss |
Partition of sums of squares in two-way analysis of variance |
JoramSoch |
2022-11-16 |

P380 |
anova2-fols |
F-statistics in terms of ordinary least squares estimates in two-way analysis of variance |
JoramSoch |
2022-11-16 |

P381 |
bin-mle |
Maximum likelihood estimation for binomial observations |
JoramSoch |
2022-11-23 |

P382 |
bin-mll |
Maximum log-likelihood for binomial observations |
JoramSoch |
2022-11-24 |

P383 |
bin-lbf |
Log Bayes factor for binomial observations |
JoramSoch |
2022-11-25 |

P384 |
bin-pp |
Posterior probability of the alternative model for binomial observations |
JoramSoch |
2022-11-26 |

P385 |
mult-mle |
Maximum likelihood estimation for multinomial observations |
JoramSoch |
2022-12-02 |

P386 |
mult-mll |
Maximum log-likelihood for multinomial observations |
JoramSoch |
2022-12-02 |

P387 |
mult-lbf |
Log Bayes factor for multinomial observations |
JoramSoch |
2022-12-02 |

P388 |
mult-pp |
Posterior probability of the alternative model for multinomial observations |
JoramSoch |
2022-12-02 |

P389 |
mlr-wlsdist |
Distributions of estimated parameters, fitted signal and residuals in multiple linear regression upon weighted least squares |
JoramSoch |
2022-12-13 |

P390 |
mlr-rssdist |
Distribution of residual sum of squares in multiple linear regression with weighted least squares |
JoramSoch |
2022-12-13 |

P391 |
mlr-t |
t-test for multiple linear regression using contrast-based inference |
JoramSoch |
2022-12-13 |

P392 |
mlr-f |
F-test for multiple linear regression using contrast-based inference |
JoramSoch |
2022-12-13 |

P393 |
mlr-ind |
Independence of estimated parameters and residuals in multiple linear regression |
JoramSoch |
2022-12-13 |

P394 |
mvn-indprod |
Independence of products of multivariate normal random vector |
JoramSoch |
2022-12-13 |

P395 |
mvn-chi2 |
Relationship between multivariate normal distribution and chi-squared distribution |
JoramSoch |
2022-12-20 |

P396 |
cuni-var |
Variance of the continuous uniform distribution |
JoramSoch |
2022-12-20 |

P397 |
cuni-dent |
Differential entropy of the continuous uniform distribution |
JoramSoch |
2022-12-20 |

P398 |
resvar-biasp |
Maximum likelihood estimator of variance in multiple linear regression is biased |
JoramSoch |
2022-12-21 |

P399 |
mlr-symm |
Projection matrix and residual-forming matrix are symmetric |
JoramSoch |
2022-12-22 |

P400 |
mlr-olsdist |
Distributions of estimated parameters, fitted signal and residuals in multiple linear regression upon ordinary least squares |
JoramSoch |
2022-12-23 |

P401 |
exp-var |
Variance of the exponential distribution |
majapavlo |
2023-01-23 |

P402 |
exg-pdf |
Probability density function of the ex-Gaussian distribution |
tomfaulkenberry |
2023-04-18 |

P403 |
exp-mgf |
Moment-generating function of the exponential distribution |
tomfaulkenberry |
2023-04-19 |

P404 |
exg-mgf |
Moment-generating function of the ex-Gaussian distribution |
tomfaulkenberry |
2023-04-19 |

P405 |
exg-mean |
Mean of the ex-Gaussian distribution |
tomfaulkenberry |
2023-04-19 |

P406 |
exg-var |
Variance of the ex-Gaussian distribution |
tomfaulkenberry |
2023-04-19 |

P407 |
skew-mean |
Partition of skewness into expected values |
tomfaulkenberry |
2023-04-20 |

P408 |
exg-skew |
Skewness of the ex-Gaussian distribution |
tomfaulkenberry |
2023-04-21 |

P409 |
exp-skew |
Skewness of the exponential distribution |
tomfaulkenberry |
2023-04-24 |

P410 |
duni-ent |
Entropy of the discrete uniform distribution |
JoramSoch |
2023-08-11 |

P411 |
duni-maxent |
Discrete uniform distribution maximizes entropy for finite support |
JoramSoch |
2023-08-18 |

P412 |
cuni-maxent |
Continuous uniform distribution maximizes differential entropy for fixed range |
JoramSoch |
2023-08-25 |

P413 |
post-ind |
Combined posterior distributions in terms of individual posterior distributions obtained from conditionally independent data |
JoramSoch |
2023-09-01 |

P414 |
lme-mean |
Equivalence of operations for model evidence and log model evidence |
JoramSoch |
2023-09-08 |

P415 |
lfe-approx |
Approximation of log family evidences based on log model evidences |
JoramSoch |
2023-09-15 |

P416 |
bvn-pdf |
Probability density function of the bivariate normal distribution |
JoramSoch |
2023-09-22 |

P417 |
bvn-pdfcorr |
Probability density function of the bivariate normal distribution in terms of correlation coefficient |
JoramSoch |
2023-09-29 |

P418 |
mlr-olstr |
Ordinary least squares for multiple linear regression with two regressors |
JoramSoch |
2023-10-06 |

P419 |
bern-kl |
Kullback-Leibler divergence for the Bernoulli distribution |
JoramSoch |
2023-10-13 |

P420 |
bin-kl |
Kullback-Leibler divergence for the binomial distribution |
JoramSoch |
2023-10-20 |

P421 |
wald-skew |
Skewness of the Wald distribution |
tomfaulkenberry |
2023-10-24 |

P422 |
cuni-kl |
Kullback-Leibler divergence for the continuous uniform distribution |
JoramSoch |
2023-10-27 |

P423 |
wald-mome |
Method of moments for Wald-distributed data |
tomfaulkenberry |
2023-10-30 |

P424 |
exg-mome |
Method of moments for ex-Gaussian-distributed data |
tomfaulkenberry |
2023-10-30 |

P425 |
duni-kl |
Kullback-Leibler divergence for the discrete uniform distribution |
JoramSoch |
2023-11-17 |

P426 |
gam-scal |
Scaling of a random variable following the gamma distribution |
JoramSoch |
2023-11-24 |

P427 |
bin-map |
Maximum-a-posteriori estimation for binomial observations |
JoramSoch |
2023-12-01 |

P428 |
mult-map |
Maximum-a-posteriori estimation for multinomial observations |
JoramSoch |
2023-12-08 |

P429 |
bin-test |
Binomial test |
JoramSoch |
2023-12-16 |

P430 |
mult-test |
Multinomial test |
JoramSoch |
2023-12-23 |

P431 |
blr-anc |
Accuracy and complexity for Bayesian linear regression |
JoramSoch |
2024-01-12 |

P432 |
blrkc-prior |
Conjugate prior distribution for Bayesian linear regression with known covariance |
JoramSoch |
2024-01-19 |

P433 |
blrkc-post |
Posterior distribution for Bayesian linear regression with known covariance |
JoramSoch |
2024-01-19 |

P434 |
blrkc-lme |
Log model evidence for Bayesian linear regression with known covariance |
JoramSoch |
2024-01-19 |

P435 |
blrkc-anc |
Accuracy and complexity for Bayesian linear regression with known covariance |
JoramSoch |
2024-01-19 |

P436 |
mvn-mgf |
Moment-generating function of the multivariate normal distribution |
JoramSoch |
2024-02-16 |

P437 |
gam-mgf |
Moment-generating function of the gamma distribution |
JoramSoch |
2024-02-23 |

P438 |
lpsr-spsr |
The log probability scoring rule is a strictly proper scoring rule |
KarahanS |
2024-02-28 |

P439 |
resvar-unbp |
Construction of unbiased estimator for variance in multiple linear regression |
JoramSoch |
2024-03-08 |

P440 |
rsq-resvar |
Expression of R² in terms of residual variances |
JoramSoch |
2024-03-08 |

P441 |
rsq-test |
Statistical significance test for the coefficient of determinantion based on an omnibus F-test |
JoramSoch |
2024-03-08 |

P442 |
fstat-rsq |
Relationship between F-statistic and R² |
JoramSoch |
2024-03-15 |

P443 |
fstat-mll |
Relationship between F-statistic and maximum log-likelihood |
JoramSoch |
2024-03-28 |

P444 |
snr-mll |
Relationship between signal-to-noise ratio and maximum log-likelihood |
JoramSoch |
2024-03-28 |

P445 |
bsr-spsr |
Brier scoring rule is strictly proper scoring rule |
KarahanS |
2024-03-28 |

P446 |
blr-posterr |
Expression of the noise precision posterior for Bayesian linear regression using prediction and parameter errors |
JoramSoch |
2024-04-05 |

P447 |
blr-postind |
Combined posterior distribution for Bayesian linear regression when analyzing conditionally independent data sets |
JoramSoch |
2024-04-12 |

P448 |
blr-map |
Maximum-a-posteriori estimation for Bayesian linear regression |
JoramSoch |
2024-04-19 |

P449 |
blr-lbf |
Log Bayes factor for Bayesian linear regression |
JoramSoch |
2024-04-26 |

P450 |
mlr-tsingle |
Specific t-test for single regressor in multiple linear regression |
JoramSoch |
2024-05-03 |

P451 |
slr-tint |
Statistical test for intercept parameter in simple linear regression model |
JoramSoch |
2024-05-10 |

P452 |
slr-tslo |
Statistical test for slope parameter in simple linear regression model |
JoramSoch |
2024-05-17 |

P453 |
slr-fcomp |
Statistical test for comparing simple linear regression models with and without slope parameter |
JoramSoch |
2024-05-24 |

P454 |
mlr-fomnibus |
Omnibus F-test for multiple regressors in multiple linear regression |
JoramSoch |
2024-05-31 |

P455 |
glm-llr |
Log-likelihood ratio for the general linear model |
JoramSoch |
2024-06-07 |

P456 |
glm-mll |
Maximum log-likelihood for the general linear model |
JoramSoch |
2024-06-14 |

P457 |
glm-mi |
Mutual information of dependent and independent variables in the general linear model |
JoramSoch |
2024-06-21 |

P458 |
glm-llrmi |
Equivalence of log-likelihood ratio and mutual information for the general linear model |
JoramSoch |
2024-06-21 |

P459 |
iglm-llrs |
Equivalence of log-likelihood ratios for regular and inverse general linear model |
JoramSoch |
2024-06-28 |

P460 |
ug-fev |
F-test for equality of variances in two independent samples |
JoramSoch |
2024-07-05 |

P461 |
slr-pss |
Partition of sums of squares for simple linear regression |
JoramSoch |
2024-07-12 |

P462 |
mlr-ols3 |
Ordinary least squares for multiple linear regression |
JoramSoch |
2024-07-18 |

P463 |
mlr-llr |
Log-likelihood ratio for multiple linear regression |
JoramSoch |
2024-07-25 |

P464 |
prob-emp2 |
Probability of the empty set |
JoramSoch |
2024-08-08 |

P465 |
prob-mon2 |
Monotonicity of probability |
JoramSoch |
2024-08-08 |

P466 |
cdf-probexc |
Exceedance probability for a random variable in terms of cumulative distribution function |
JoramSoch |
2024-09-06 |

P467 |
postpred-jl |
Posterior predictive distribution is a marginal distribution of the joint likelihood |
aloctavodia |
2024-09-11 |

P468 |
mean-wlln |
Weak law of large numbers |
JoramSoch |
2024-09-13 |

P469 |
mean-mse |
The expected value minimizes the mean squared error |
salbalkus |
2024-09-13 |

P470 |
ind-self |
Self-independence of random event |
JoramSoch |
2024-09-20 |

P471 |
med-mae |
The median minimizes the mean absolute error |
salbalkus |
2024-09-23 |

P472 |
corr-ind |
Independent random variables are uncorrelated |
JoramSoch |
2024-09-27 |

P473 |
norm-corrind |
Normally distributed and uncorrelated does not imply independent |
JoramSoch |
2024-10-04 |