P1-P5 Aleksandra Dacko #7

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a-dacko wants to merge 6 commits into gerkovink:main from a-dacko:P_ADacko

Practicals/Aleksandra Dacko/P1/P1_Dacko.Rmd

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+    ---
+    title: "P1_Dacko"
+    author: "Aleksandra Dacko"
+    date: "9/14/2022"
+    output: html_document
+    ---
+    ```{r setup, include=FALSE}
+    knitr::opts_chunk$set(echo = TRUE)
+    ```
+    ```{r, warning=FALSE}
+    library(future)
+    library(tidyverse)
+    library(furrr)
+    library(DT)
+    library(ggplot2)
+    ```
+    ## Exercises for the first practical
+    ### a), b)
+    ```{r}
+    plan(multisession,workers=3)
+    NEW<-1:100 %>% future_map( function(x){
+      x <- rnorm(5000,mean=0,sd=1)
+      M <- mean(x)
+      AB<-M-0
+      DF <- length(x) - 1
+      SE <- 1 / sqrt(length(x))
+      QT<-(qt(.975, DF) * SE)
+      return(c(mean=M,
+             bias=AB,
+             std_err=SE,
+             lower=M-QT,
+             upper=M+QT,
+             cov = M - QT < 0 & 0 < M + QT))},.options = furrr_options(seed = 123),.progress = TRUE
+      ) %>% do.call("rbind", .) %>% as_tibble
+    NEW
+    ```
+    ```{r}
+    NEW%>% colMeans()
+    ```
+    ### c)
+    ```{r}
+    limits <- aes(ymax = NEW$upper, ymin = NEW$lower)
+    NEW %>% mutate(covered_by_95_CI = as.factor(cov)) %>%
+    ggplot(aes(y=mean, x=1:100, colour = covered_by_95_CI)) +
+      geom_hline(aes(yintercept = 0), color = "black", size = 2) +
+      geom_pointrange(limits) +
+      xlab("Simulations") +
+      ylab("Means and 95% Confidence Intervals")+ggtitle("The Simulation study of the 95% confidence intervals")+scale_color_manual(labels = c("not covered (4/100)","covered (96/100)"), values = c("maroon","lightseagreen"))
+    ```
+    ### d)
+    ```{r}
+    NEW %>% round(4) %>% filter((lower>0 & upper>0 )| (lower<0 & upper<0) ) %>%select(-cov) %>% DT::datatable()
+    ```

Practicals/Aleksandra Dacko/P1/P1_Dacko.html

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Practicals/Aleksandra Dacko/P1/my_other_puppies.jpg

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Practicals/Aleksandra Dacko/P2/P2_Dacko.Rmd

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+    ---
+    title: "P2_ADacko"
+    author: "Aleksandra Dacko"
+    date: "11/1/2022"
+    output: html_document
+    ---
+    # This is my function simulating the multilevel hidden markov model observations and state sequence.
+    ```{r setup, include=FALSE}
+    knitr::opts_chunk$set(echo = TRUE)
+    require(mHMMbayes)
+    ```
+    ### Specify conditions
+    ```{r}
+    n_t <- 100
+    n <- 10
+    m <- 2
+    n_dep <- 1
+    q_emiss <- 3
+    gamma <- matrix(c(0.8, 0.2,
+.3, 0.7), ncol = m, byrow = TRUE)
+    emiss_distr <- list(matrix(c(0.5, 0.5, 0.0,
+.1, 0.1, 0.8), nrow = m, ncol = q_emiss, byrow = TRUE))
+    ```
+    ### Run the simulation function
+    ```{r}
+    set.seed(1234)
+    data1 <- sim_mHMM(n_t = n_t, n = n, gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
+                      gamma = gamma, emiss_distr = emiss_distr, var_gamma = .5, var_emiss = .5)
+    ```
+    ### Run mhmm() function over the sumulated data set
+    ```{r, results='hide'}
+    out_2st_sim <- mHMM(s_data = data1$obs,
+                     gen = list(m = m, n_dep = n_dep, q_emiss = q_emiss),
+                     start_val = c(list(gamma), emiss_distr),
+                     mcmc = list(J = 100, burn_in = 10))
+    ```
+    ### Plot the gamma estimations and obtain the group-level gamma estimations
+    ```{r}
+    plot(out_2st_sim)
+    obtain_gamma(out_2st_sim)
+    ```
+    ### Add the session informations
+    ```{r}
+    sessionInfo()
+    ```

Practicals/Aleksandra Dacko/P2/P2_Dacko.html

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Practicals/Aleksandra Dacko/P3/Presentation_P3.zip

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Practicals/Aleksandra Dacko/P4/P4.Rproj

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+    Version: 1.0
+    RestoreWorkspace: Default
+    SaveWorkspace: Default
+    AlwaysSaveHistory: Default
+    EnableCodeIndexing: Yes
+    UseSpacesForTab: Yes
+    NumSpacesForTab: 2
+    Encoding: UTF-8
+    RnwWeave: Sweave
+    LaTeX: pdfLaTeX

Practicals/Aleksandra Dacko/P5/P5.Rproj

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+    Version: 1.0
+    RestoreWorkspace: Default
+    SaveWorkspace: Default
+    AlwaysSaveHistory: Default
+    EnableCodeIndexing: Yes
+    UseSpacesForTab: Yes
+    NumSpacesForTab: 2
+    Encoding: UTF-8
+    RnwWeave: Sweave
+    LaTeX: pdfLaTeX

Practicals/Aleksandra Dacko/P5/bh.Rmd

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+    ---
+    title: "Fibonacci sequence"
+    author: "Aleksandra Dacko"
+    date: "1/3/2023"
+    output: ioslides_presentation
+    logo: "images/logo.png"
+    bibliography: "references.bib"
+    ---
+    <style>
+    div.footnotes {
+      position: absolute;
+      bottom: 0;
+      margin-bottom: 25px;
+      margin-left: 40px;
+      width: 80%;
+      font-size: 0.6em;
+    }
+    </style>
+    <script src="https://ajax.googleapis.com/ajax/libs/jquery/3.1.1/jquery.min.js"></script>
+    <script>
+      $(document).ready(function() {
+        $('slide:not(.backdrop):not(.title-slide)').append('<div class=\"footnotes\">');
+        $('footnote').each(function(index) {
+          var text  = $(this).html();
+          var fnNum = (index+1).toString().sup();
+          $(this).html(text + fnNum);
+          var footnote   = fnNum + ': ' + $(this).attr('content') + '<br/>';
+          var oldContent = $(this).parents('slide').children('div.footnotes').html();
+          var newContent = oldContent + footnote;
+          $(this).parents('slide').children('div.footnotes').html(newContent);
+        });
+      });
+    </script>
+    <style>
+    ```{r setup, include=FALSE}
+    knitr::opts_chunk$set(echo = FALSE)
+    ```
+    ## R Markdown
+    This is an R Markdown presentation. Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see <http://rmarkdown.rstudio.com>.
+    When you click the **Knit** button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document.
+    ## Slide with Bullets
+    - Bullet 1
+    - Bullet 2
+    - Bullet 3
+    ## Slide with R Output
+    ```{r cars, echo = TRUE}
+    summary(cars)
+    ```
+    ## Slide with Plot
+    ```{r pressure}
+    plot(pressure)
+    ```

Practicals/Aleksandra Dacko/P5/bh.html

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Practicals/Aleksandra Dacko/P5/citations.csv

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+    Authors,Title,Publication,Volume,Number,Pages,Year,Publisher
+    "Falcon, Sergio; Plaza, Ángel; ",The k-Fibonacci sequence and the Pascal 2-triangle,"Chaos, Solitons & Fractals",33,1,38-49,2007,Elsevier
+    "Horadam, AF; ",A generalized Fibonacci sequence,The American Mathematical Monthly,68,5,455-459,1961,Taylor & Francis
+    "Waddill, Marcellus E; Sacks, Louis; ",Another generalized Fibonacci sequence,The Fibonacci Quarterly,5,3,209-222,1967,Citeseer
+    "Catarino, Paula; ",On some identities for k-Fibonacci sequence,Int. J. Contemp. Math. Sci,9,1,37-42,2014,
+    "Park, Andrew E; Fernandez, John J; Schmedders, Karl; Cohen, Mark S; ",The Fibonacci sequence: relationship to the human hand,The journal of hand surgery,28,1,157-160,2003,Elsevier
+    "Edson, Marcia; Yayenie, Omer; ",A New Generalization of Fibonacci Sequence & Extended Binet's Formula,,,,,2009,Walter de Gruyter GmbH & Co. KG
+    "Scott, Tony C; Marketos, Pan; ",On the origin of the Fibonacci Sequence,MacTutor History of Mathematics,23,,,2014,
+    "Yayenie, Omer; ",A note on generalized Fibonacci sequences,Applied Mathematics and Computation,217,12,5603-5611,2011,Elsevier
+    "Atanassov, K; Atanassova, L; Sasselov, D; ",A new perspective to the generalization of the Fibonacci sequence,The Fibonacci Quarterly,23,1,21-28,1985,
+    "Viswanath, Divakar; ",Random Fibonacci sequences and the number 1.13198824…,Mathematics of Computation,69,231,1131-1155,2000,
+    "Bravo, Jhon J; Luca, Florian; ",Powers of two in generalized Fibonacci sequences,Revista Colombiana de Matemáticas,46,1,67-79,2012,Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
+    "Falcon, Sergio; Plaza, Ángel; ",On k-Fibonacci sequences and polynomials and their derivatives,"Chaos, Solitons & Fractals",39,3,1005-1019,2009,Elsevier
+    "Jun, Wang; ",k-step Fibonacci sequence modulo m,Utilitas Mathematica,71,,,2006,
+    "Wilcox, Howard J; ",Fibonacci sequences of period n in groups,Fibonacci Quart,24,4,356-361,1986,
+    "Gupta, VK; Panwar, Yashwant K; Sikhwal, Omprakash; ",Generalized Fibonacci Sequences,Theoretical Mathematics and Applications,2,2,115-124,2012,

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