Introducción a la Inferencia Estadistica

Introducción a la Inferencia Estadistica
Departamento de Ciencias del Mar y Biología Aplicada Jose Jacobo Zubcoff

Agenda Presentación Objetivos Metodología …

Agenda Presentación Objetivos Metodología Evaluación Comentarios After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Definiciones Inferencia Muestra x y s Aleatoria Independiente Finitas, Infinitas Población μ y σ After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Definiciones Inferencia Estadística Muestra Población x μ s σ After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Contrastes de Hipótesis
Introducción a la Inferencia Estadistica Contrastes de Hipótesis Hipótesis estadística es una afirmación respecto a alguna característica de una población. Ho : Hipótesis nula H1 : Hipótesis alternativa Errores que se pueden cometer Pueden ser unilaterales o bilaterales Conclusiones a partir de una muestra aleatoria y significativa, permite aceptar o rechazar la hipótesis nula After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Contrastes de Hipótesis
Introducción a la Inferencia Estadistica Contrastes de Hipótesis Método Enunciar la hipótesis Elegir un nivel de significación α Construir la zona de aceptación y zona de rechazo (región crítica) Verificar la hipótesis con el correspondiente estadístico Analizar los resultados

Contraste de Bondad de Ajuste
Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Oi= Frecuencia absoluta Observada x x Oi x x χ2 = Σ(Oi-Ei)2 Ei Ei = n P x x x Intervalo i-ésimo

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste H0= Adherencia de la muestra a la distribución hipotética H1= La muestra NO se ajusta a la distribución hipotética χ2 = Σ(Oi-Ei)2 Ei Rechazamos H0 si: > c χ2k-m-1,α Punto crítico c K es el numero de Intervalos m es el Nº de parámetros estimados

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 Valores X Oi E(X)=X= n π = 5 π p = X/5 = / 5 = 0.517

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 pi 0.026 0.141 0.301 0.322 0.173 0.037 Valores X Oi Pi es estimado a partir de la Esperanza de la Variable Aleatoria (la media) Luego se calculan los P(X=0) P(X=1) .... en base a la expresión de la Binomial (modelo teórico). E(X)=X= n π = 5 π p = X/5 = / 5 = 0.517

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 pi 0.026 0.141 0.301 0.322 0.173 0.037 Ei=551 pi 14.33 77.69 165.8 177.4 95.32 20.39 Valores X Oi E(X)=X= n π = 5 π p = X/5 = / 5 = 0.517 Ei > 5

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 pi 0.026 0.141 0.301 0.322 0.173 0.037 Ei=551 pi 14.33 77.69 165.8 177.4 95.32 20.39 Valores X Oi χ2 = Σ(Oi-Ei)2 Ei χ2 = ( )2 14.33 ( )2 95.32 χ2k-m-1,α = χ26-1-1,0.05 Buscar en Tabla χ2 = 3.187

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 pi 0.026 0.141 0.301 0.322 0.173 0.037 Ei=551 pi 14.33 77.69 165.8 177.4 95.32 20.39 Valores X Oi P-valor ... P-valor = P(χ2k-m-1 >3.187) χ2k-m-1,α = χ26-1-1,0.05 Buscar en Tabla χ2 = 3.187

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 1 2 3 4 5 17 81 152 180 104 pi 0.026 0.141 0.301 0.322 0.173 0.037 Ei=551 pi 14.33 77.69 165.8 177.4 95.32 20.39 Valores X Oi P-valor = P(χ2k-m-1 >3.187) en la Tabla para gl=4 0.1 < P-valor < 0.9

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 3 4 5 >=6 52 29 19 7 Valores X Oi

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 3 4 5 >=6 52 29 19 7 pi 0.4 .37 .16 .05 .01 .002 .0003 Ei= 109 pi 44.36 39.89 17.98 5.341 1.199 0.218 .0327 Valores X Oi Ei > 5

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 3 4 5 >=6 52 29 19 7 pi 0.4 .37 .16 .05 .01 .002 .0003 Ei= 109 pi 44.36 39.89 17.98 5.341 1.199 0.218 .0327 Valores X Oi Agrupar

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 >=3 52 29 19 9 pi 0.4 .37 .16 .0623 Ei= 109 pi 44.36 39.89 17.98 6.791 Valores X Oi After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 >=3 52 29 19 9 pi 0.4 .37 .16 .0623 Ei= 109 pi 44.36 39.89 17.98 6.791 Valores X Oi After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. χ2 = Σ(Oi-Ei)2 Ei χ2 = ( )2 44.36 ( )2 6.791 χ2k-m-1,α = χ24-1-1,0.05 Buscar en Tabla χ2 = 5.065

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. de Poisson 1 2 >=3 52 29 19 9 pi 0.4 .37 .16 .0623 Ei= 109 pi 44.36 39.89 17.98 6.791 Valores X Oi After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. P-valor = P(χ2k-m-1 >5.065) en la Tabla para gl=2 0.05 < P-valor < 0.1

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste P-valor = P(χ2k-m-1 > χ2expt ) 1 .90 . .10 .05 .01 Debemos hallar el p-valor y compararlo con el nivel de significación Zona de Rechazo After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. P-valor Zona de Aceptación

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste P-valor = P(χ2k-m-1 > χ2expt ) 1 .90 . .10 .05 .01 Zona de Rechazo After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. P-valor Zona de Aceptación

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Valores de X (74 valores observados en una tabla de datos) H0= Adherencia de la muestra a la distribución hipotética H1= La muestra NO se ajusta a la distribución hipotética After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. χ2 = Σ(Oi-Ei)2 Ei

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste x x x χ2 = Σ(Oi-Ei)2 Ei x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. x x

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 0.2 x x x χ2 = Σ(Oi-Ei)2 Ei x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. x x

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 0.2 0.4 x x x χ2 = Σ(Oi-Ei)2 Ei x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. x x

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Valores X (74 valores observados en una tabla de datos) Intervalos Oi pi 0.2 Ei= 74 pi After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Valores X (74 valores observados en una tabla de datos) Intervalos Oi pi 0.2 Ei= 74 pi 14.8 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste 0.2 x x x χ2 = Σ(Oi-Ei)2 Ei x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. x x P20 -k1 -k2 k2 k1

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste K1 = P80 – x s K2 = P60 – x s x = (k s) + Xmedia x = Xmedia + k s -k1 -k2 k2 k1 -K1= P20 – x s -K2= P40 – x s

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste K1 = P80 – x s K2 = P60 – x s x = (k s) + Xmedia x = Xmedia + k s -k1 -k2 k2 k1 -K1= P20 – x s Normal estándar -K2= P40 – x s

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Destipificando obtenemos los valores de la variable (Percentiles 20, 40, 60 y 80) K1 = P80 – x s P80 = x + K1 . s = 79.10 K2 = P60 – x s P60 = x + K2 . s = 72.44 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. -K2= P40 – x s P40 = x - K2 . s = 66.79 -K1= P20 – x s P20 = x - K1 . s = 60.13

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Intervalos <60.13 [60.13,66.7] [66.7, 72.44] [72.44,79.10] >79.10 Oi pi 0.2 Ei= 74 pi 14.8 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Intervalos <60.13 [60.13,66.7] [66.7, 72.44] [72.44,79.10] >79.10 Oi 18 12 14 pi 0.2 Ei= 74 pi 14.8 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. Ei > 5

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Intervalos <60.13 [60.13,66.7] [66.7, 72.44] [72.44,79.10] >79.10 Oi 18 12 14 pi 0.2 Ei= 74 pi 14.8 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. χ2 = Σ(Oi-Ei)2 Ei χ2 = ( )2 14.8 (12 – 14.8)2 14.8 χ2k-m-1,α = χ25-2-1,0.05 Buscar en Tabla χ2 = 5.991

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Ajuste a una Dist. Normal Intervalos <60.13 [60.13,66.7] [66.7, 72.44] [72.44,79.10] >79.10 Oi 18 12 14 pi 0.2 Ei= 74 pi 14.8 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. P-valor = P(χ2k-m-1 >5.991) en la Tabla para gl=2 0.1 < P-valor < 0.9

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste P-valor = P(χ2k-m-1 > χ2expt ) 1 .90 . .10 .05 .01 Zona de Rechazo After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. P-valor Zona de Aceptación

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov En una variable continua la Fc. de Distribucion es ...

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov x x x x x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov x x After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. x x x

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 ,710 ,797 … 1,066 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 0,11 ,710 0,22 ,797 0,33 … 1,066 1 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 0,11 -1,37 ,710 0,22 -1,09 ,797 0,33 -0,37 … 1,066 1 1,85 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 0,11 -1,37 0,085 ,710 0,22 -1,09 0,138 ,797 0,33 -0,37 0,355 … 1,066 1 1,85 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 0,11 -1,37 0,085 0,026 ,710 0,22 -1,09 0,138 0,0846 ,797 0,33 -0,37 0,355 0,0216 … 1,066 1 1,85 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data.

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | 0,676 0,11 -1,37 0,085 0,026 ,710 0,22 -1,09 0,138 0,0846 ,797 0,33 -0,37 0,355 0,0216 … 1,066 1 1,85 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. MAX 0,1536

Introducción a la Inferencia Estadistica Contraste de Bondad de Ajuste Método de Kolmogorov-Smirnov X Faci Zi Фi |F- Фi | |Fi-1- Фi | 0,676 0,11 -1,37 0,085 0,026 ,710 0,22 -1,09 0,138 0,0846 0,138-0,11 ,797 0,33 -0,37 0,355 0,0216 … 1,066 1 1,85 After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. MAX 0,1536

Método de Kolmogorov-Smirnov
Introducción a la Inferencia Estadistica Método de Kolmogorov-Smirnov H0= Adherencia de la muestra a la distribución hipotética H1= La muestra NO se ajusta a la distribución hipotética Rechazamos H0 si: Max(|Fi-Фi|) > c After these remarks I hope it is obvious that we consider the Data Warehouses as a perfect environment to do Data mining. Because, there is no doubt that Data Warehouses contains historical collection of all relevant data for analysis purposes and are prepared to obtain information about those data. Punto crítico c En la tabla de Kolmogorov-Smirnov

Introducción a la Inferencia Estadistica

Presentaciones similares

Presentación del tema: "Introducción a la Inferencia Estadistica"— Transcripción de la presentación:

Presentaciones similares

Sobre el proyecto

Feedback

Iniciar la sesión

Autorizarse a través de una red social:

Introducción a la Inferencia Estadistica

Presentaciones similares

Presentación del tema: "Introducción a la Inferencia Estadistica"— Transcripción de la presentación:

Presentaciones similares

Sobre el proyecto

Feedback