ID Shortcut Theorem Author Date
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