From 27f926a0f01c3fa8e25e81093160f4c07309dbaa Mon Sep 17 00:00:00 2001 From: Walmes Zeviani <walmes@ufpr.br> Date: Fri, 25 Nov 2016 15:20:17 -0200 Subject: [PATCH] Adiciona trabalho 2. --- README.md | 6 +++++ scripts/trab2.Rmd | 65 ++++++++++++++++++++++++++++++++++------------ scripts/trab2.pdf | Bin 0 -> 148947 bytes 3 files changed, 55 insertions(+), 16 deletions(-) create mode 100644 scripts/trab2.pdf diff --git a/README.md b/README.md index 82797e4..05be7bc 100644 --- a/README.md +++ b/README.md @@ -189,6 +189,12 @@ distribuições de probabilidade. 7. Trabalho para ser feito em duplas com entrega para o dia 23/09 às 22h00. +### Atividade 2 - Métodos Computacionalmente Intensivos + +O documento [trab2.pdf](./scripts/trab2.pdf) contém a lista de +atividades. O trabalho deve ser realizado individualmente ou em +duplas. Deve ser impresso e entregue até dia 09/12 + ## Notas <!------------------------------------------- --> diff --git a/scripts/trab2.Rmd b/scripts/trab2.Rmd index cd9be1b..95ef6fb 100644 --- a/scripts/trab2.Rmd +++ b/scripts/trab2.Rmd @@ -7,11 +7,33 @@ output: highlight: haddock --- -1. TODO questão teórica. +1. Bootstrap, Jackknife, Testes de Aleatorização e Monte Carlo são +considerados métodos computacionalmente intensivos de inferência +estatística. Estes métodos são utilizados em uma grande variedade de de +problemas, desde testes de hipóteses e intervalos de confiança à cálculo +de integrais. Descreva a ideia fundamental de cada método e destaque as +semelhanças e diferenças entre eles, produzindo uma visão geral e +estruturada deles. **** -2. Apresente e implemente um teste de aleatorização TODO. +2. Ratos foram aleatoriamente divididos em dois grupos de 24 animais. O +experimento mediu o desempenho para percorrer labirintos dos ratos que +cresceram ao som de Mozart e Anthrax (rock). Os resultados, em minutos, +para percorrer o labirinto estão fragmento de código abaixo. Apresente e +implemente um teste de aleatorização para a mediana para comparar os +estilos musicais no desempenho dos ratos no labirinto. + +```{r, eval = FALSE} +# Tempo para percorrer o labirinto. +y <- c(444, 219, 347, 327, 431, 333, 310, 341, 206, 203, NA, 267, 275, + 297, 215, 305, 262, 259, 225, 306, 343, 315, 407, 422, 101, 162, + 152, 153, 132, 191, 106, 180, 099, 120, 134, 078, 123, 121, 065, + 067, 068, 048, 076, 197, 121, 119, 086, 113) +# Ratos que cresceram com Mozart (1) e Anthrax (2). +g <- rep(1:2, each = 24) +plot(y ~ g) +``` **** @@ -39,15 +61,27 @@ by(data = iris, **** -4. Faça uma avaliação entre dois modelos de regressão para -ajuste aos dados hipsométricos de altura e diâmentro à altura do peito -(DAP) de árvores em um cultivo florestal. - +4. Os modelos hisométricos são fundamentais para os levantamentos +florestais (estimar o volume de madeira em uma floresta). Uma amostra de +árvores é realizada para determinação da altura total (H) e do diâmetro +à altura do peito (DAP). Um modelo que relacione altura e DAP +normalmente é ajustado como etapa para determinação do volume. Dois +modelos podem ser aplicados: * Linear: $\hat{h} = \beta_0 + \beta_1 d + \beta_2 \sqrt{d}$. * Não linear: $\hat{h} = \theta_0 + \theta_a (1 - \exp\{-\theta_k d\})$. +em que $h$ é a altura e $d$ é o DAP. + +Para o modelo não linear, obtenha: i) a distribuição de probabilidade +empírica dos parâmentros, ii) a variância das estimativas de cada +parâmetro e iii) uma estimativa de vício para cada parâmetro. Descreva +os resultados. + +Para os dois modelos, obtenha a distribuição do valor predito para uma +árvore de DAP = 20. Descreva os resultados. + ```{r, eval = FALSE} dap <- read.table("http://www.leg.ufpr.br/~walmes/data/dap.txt", header = TRUE, sep = "\t") @@ -56,29 +90,28 @@ dap <- dap[complete.cases(dap), ] names(dap) <- c("d", "h") rownames(dap) <- NULL -plot(h ~ d, - data = dap, - xlab = "Diâmetro à altura do peito (cm)", - ylab = "Altura (m)") - m0 <- lm(h ~ d + sqrt(d), data = dap) -summary(m0) n0 <- nls(h ~ b0 + ba * (1 - exp(-bk * d)), data = dap, start = list(b0 = 0, ba = 40, bk = 0.05)) -summary(n0) -``` -Defina a medida de ajuste TODO. +plot(h ~ d, + data = dap, + xlab = "Diâmetro à altura do peito (cm)", + ylab = "Altura (m)") +curve(cbind(1, x, sqrt(x)) %*% coef(m0), add = TRUE, col = 2) +with(as.list(coef(n0)), + curve(b0 + ba * (1 - exp(-bk * x)), add = TRUE, col = 4)) +``` **** 5. Avalie, por simulação Monte Carlo, a qualidade de dois estimadores baseados na distribuição de frequência da amostra. O estimador A é a moda determinada pelo histograma e o estimador B é a moda determinada -pelo ponto de máximo da densidade kernel gaussiana. A matéria abaixo +pelo ponto de máximo da densidade *kernel* gaussiana. A matéria abaixo apresenta a funções para ambos os estimadores. 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