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R/ch2.html
275
R/ch2.html
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@ -241,12 +241,12 @@ Probability and Likelihood
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<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a> gt<span class="sc">::</span><span class="fu">cols_width</span>(<span class="fu">everything</span>() <span class="sc">~</span> <span class="fu">px</span>(<span class="dv">100</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="cell-output-display">
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<div id="gqllsnwjsv" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
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<div id="ujjornjsef" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
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<style>html {
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font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
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}
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#gqllsnwjsv .gt_table {
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#ujjornjsef .gt_table {
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display: table;
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border-collapse: collapse;
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margin-left: auto;
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@ -271,7 +271,7 @@ Probability and Likelihood
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border-left-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_heading {
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#ujjornjsef .gt_heading {
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background-color: #FFFFFF;
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text-align: center;
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border-bottom-color: #FFFFFF;
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@ -283,7 +283,7 @@ Probability and Likelihood
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border-right-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_title {
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#ujjornjsef .gt_title {
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color: #333333;
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font-size: 125%;
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font-weight: initial;
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@ -295,7 +295,7 @@ Probability and Likelihood
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border-bottom-width: 0;
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}
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#gqllsnwjsv .gt_subtitle {
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#ujjornjsef .gt_subtitle {
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color: #333333;
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font-size: 85%;
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font-weight: initial;
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@ -307,13 +307,13 @@ Probability and Likelihood
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border-top-width: 0;
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}
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#gqllsnwjsv .gt_bottom_border {
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#ujjornjsef .gt_bottom_border {
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border-bottom-style: solid;
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border-bottom-width: 2px;
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border-bottom-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_col_headings {
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#ujjornjsef .gt_col_headings {
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border-top-style: solid;
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border-top-width: 2px;
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border-top-color: #D3D3D3;
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@ -328,7 +328,7 @@ Probability and Likelihood
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border-right-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_col_heading {
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#ujjornjsef .gt_col_heading {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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@ -348,7 +348,7 @@ Probability and Likelihood
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overflow-x: hidden;
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}
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#gqllsnwjsv .gt_column_spanner_outer {
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#ujjornjsef .gt_column_spanner_outer {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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@ -360,15 +360,15 @@ Probability and Likelihood
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padding-right: 4px;
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}
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#gqllsnwjsv .gt_column_spanner_outer:first-child {
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#ujjornjsef .gt_column_spanner_outer:first-child {
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padding-left: 0;
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}
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#gqllsnwjsv .gt_column_spanner_outer:last-child {
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#ujjornjsef .gt_column_spanner_outer:last-child {
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padding-right: 0;
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}
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#gqllsnwjsv .gt_column_spanner {
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#ujjornjsef .gt_column_spanner {
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border-bottom-style: solid;
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border-bottom-width: 2px;
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border-bottom-color: #D3D3D3;
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@ -380,7 +380,7 @@ Probability and Likelihood
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width: 100%;
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}
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#gqllsnwjsv .gt_group_heading {
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#ujjornjsef .gt_group_heading {
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padding-top: 8px;
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padding-bottom: 8px;
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padding-left: 5px;
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@ -405,7 +405,7 @@ Probability and Likelihood
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vertical-align: middle;
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}
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#gqllsnwjsv .gt_empty_group_heading {
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#ujjornjsef .gt_empty_group_heading {
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padding: 0.5px;
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color: #333333;
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background-color: #FFFFFF;
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@ -420,15 +420,15 @@ Probability and Likelihood
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vertical-align: middle;
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}
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#gqllsnwjsv .gt_from_md > :first-child {
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#ujjornjsef .gt_from_md > :first-child {
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margin-top: 0;
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}
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#gqllsnwjsv .gt_from_md > :last-child {
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#ujjornjsef .gt_from_md > :last-child {
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margin-bottom: 0;
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}
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#gqllsnwjsv .gt_row {
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#ujjornjsef .gt_row {
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padding-top: 8px;
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padding-bottom: 8px;
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padding-left: 5px;
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@ -447,7 +447,7 @@ Probability and Likelihood
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overflow-x: hidden;
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}
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#gqllsnwjsv .gt_stub {
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#ujjornjsef .gt_stub {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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@ -460,7 +460,7 @@ Probability and Likelihood
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padding-right: 5px;
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}
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#gqllsnwjsv .gt_stub_row_group {
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#ujjornjsef .gt_stub_row_group {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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@ -474,11 +474,11 @@ Probability and Likelihood
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vertical-align: top;
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}
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#gqllsnwjsv .gt_row_group_first td {
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#ujjornjsef .gt_row_group_first td {
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border-top-width: 2px;
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}
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#gqllsnwjsv .gt_summary_row {
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#ujjornjsef .gt_summary_row {
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color: #333333;
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background-color: #FFFFFF;
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text-transform: inherit;
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@ -488,16 +488,16 @@ Probability and Likelihood
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padding-right: 5px;
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}
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#gqllsnwjsv .gt_first_summary_row {
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#ujjornjsef .gt_first_summary_row {
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border-top-style: solid;
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border-top-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_first_summary_row.thick {
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#ujjornjsef .gt_first_summary_row.thick {
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border-top-width: 2px;
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}
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#gqllsnwjsv .gt_last_summary_row {
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#ujjornjsef .gt_last_summary_row {
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padding-top: 8px;
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padding-bottom: 8px;
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padding-left: 5px;
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@ -507,7 +507,7 @@ Probability and Likelihood
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border-bottom-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_grand_summary_row {
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#ujjornjsef .gt_grand_summary_row {
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color: #333333;
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background-color: #FFFFFF;
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text-transform: inherit;
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@ -517,7 +517,7 @@ Probability and Likelihood
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padding-right: 5px;
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}
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#gqllsnwjsv .gt_first_grand_summary_row {
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#ujjornjsef .gt_first_grand_summary_row {
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padding-top: 8px;
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padding-bottom: 8px;
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padding-left: 5px;
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@ -527,11 +527,11 @@ Probability and Likelihood
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border-top-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_striped {
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#ujjornjsef .gt_striped {
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background-color: rgba(128, 128, 128, 0.05);
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}
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#gqllsnwjsv .gt_table_body {
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#ujjornjsef .gt_table_body {
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border-top-style: solid;
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border-top-width: 2px;
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border-top-color: #D3D3D3;
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@ -540,7 +540,7 @@ Probability and Likelihood
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border-bottom-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_footnotes {
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#ujjornjsef .gt_footnotes {
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color: #333333;
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background-color: #FFFFFF;
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border-bottom-style: none;
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@ -554,7 +554,7 @@ Probability and Likelihood
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border-right-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_footnote {
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#ujjornjsef .gt_footnote {
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margin: 0px;
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font-size: 90%;
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padding-left: 4px;
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@ -563,7 +563,7 @@ Probability and Likelihood
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padding-right: 5px;
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}
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#gqllsnwjsv .gt_sourcenotes {
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#ujjornjsef .gt_sourcenotes {
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color: #333333;
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background-color: #FFFFFF;
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border-bottom-style: none;
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@ -577,7 +577,7 @@ Probability and Likelihood
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border-right-color: #D3D3D3;
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}
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#gqllsnwjsv .gt_sourcenote {
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#ujjornjsef .gt_sourcenote {
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font-size: 90%;
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padding-top: 4px;
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padding-bottom: 4px;
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@ -585,64 +585,64 @@ Probability and Likelihood
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padding-right: 5px;
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}
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#gqllsnwjsv .gt_left {
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#ujjornjsef .gt_left {
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text-align: left;
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}
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#gqllsnwjsv .gt_center {
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#ujjornjsef .gt_center {
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text-align: center;
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}
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#gqllsnwjsv .gt_right {
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#ujjornjsef .gt_right {
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text-align: right;
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font-variant-numeric: tabular-nums;
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}
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#gqllsnwjsv .gt_font_normal {
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#ujjornjsef .gt_font_normal {
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font-weight: normal;
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}
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#gqllsnwjsv .gt_font_bold {
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#ujjornjsef .gt_font_bold {
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font-weight: bold;
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}
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#gqllsnwjsv .gt_font_italic {
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#ujjornjsef .gt_font_italic {
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font-style: italic;
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}
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#gqllsnwjsv .gt_super {
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#ujjornjsef .gt_super {
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font-size: 65%;
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}
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#gqllsnwjsv .gt_footnote_marks {
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#ujjornjsef .gt_footnote_marks {
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font-style: italic;
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font-weight: normal;
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font-size: 75%;
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vertical-align: 0.4em;
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}
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#gqllsnwjsv .gt_asterisk {
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#ujjornjsef .gt_asterisk {
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font-size: 100%;
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vertical-align: 0;
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}
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#gqllsnwjsv .gt_indent_1 {
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#ujjornjsef .gt_indent_1 {
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text-indent: 5px;
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}
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#gqllsnwjsv .gt_indent_2 {
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#ujjornjsef .gt_indent_2 {
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text-indent: 10px;
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}
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#gqllsnwjsv .gt_indent_3 {
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#ujjornjsef .gt_indent_3 {
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text-indent: 15px;
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}
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#gqllsnwjsv .gt_indent_4 {
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#ujjornjsef .gt_indent_4 {
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text-indent: 20px;
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}
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#gqllsnwjsv .gt_indent_5 {
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#ujjornjsef .gt_indent_5 {
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text-indent: 25px;
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}
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</style>
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@ -851,12 +851,12 @@ Baye’s Rule
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<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a> gt<span class="sc">::</span><span class="fu">cols_width</span>(<span class="fu">everything</span>() <span class="sc">~</span> <span class="fu">px</span>(<span class="dv">100</span>))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="cell-output-display">
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<div id="roxupfdiiw" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
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<div id="pnxskxfvyw" style="overflow-x:auto;overflow-y:auto;width:auto;height:auto;">
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<style>html {
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font-family: -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, Oxygen, Ubuntu, Cantarell, 'Helvetica Neue', 'Fira Sans', 'Droid Sans', Arial, sans-serif;
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}
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#roxupfdiiw .gt_table {
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#pnxskxfvyw .gt_table {
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display: table;
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border-collapse: collapse;
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margin-left: auto;
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@ -881,7 +881,7 @@ Baye’s Rule
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border-left-color: #D3D3D3;
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}
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#roxupfdiiw .gt_heading {
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#pnxskxfvyw .gt_heading {
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background-color: #FFFFFF;
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text-align: center;
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border-bottom-color: #FFFFFF;
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@ -893,7 +893,7 @@ Baye’s Rule
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border-right-color: #D3D3D3;
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}
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#roxupfdiiw .gt_title {
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#pnxskxfvyw .gt_title {
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color: #333333;
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font-size: 125%;
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font-weight: initial;
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@ -905,7 +905,7 @@ Baye’s Rule
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border-bottom-width: 0;
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}
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#roxupfdiiw .gt_subtitle {
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#pnxskxfvyw .gt_subtitle {
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color: #333333;
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font-size: 85%;
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font-weight: initial;
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@ -917,13 +917,13 @@ Baye’s Rule
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border-top-width: 0;
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}
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#roxupfdiiw .gt_bottom_border {
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#pnxskxfvyw .gt_bottom_border {
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border-bottom-style: solid;
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border-bottom-width: 2px;
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border-bottom-color: #D3D3D3;
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}
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#roxupfdiiw .gt_col_headings {
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#pnxskxfvyw .gt_col_headings {
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border-top-style: solid;
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border-top-width: 2px;
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border-top-color: #D3D3D3;
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@ -938,7 +938,7 @@ Baye’s Rule
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border-right-color: #D3D3D3;
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}
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#roxupfdiiw .gt_col_heading {
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#pnxskxfvyw .gt_col_heading {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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@ -958,7 +958,7 @@ Baye’s Rule
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overflow-x: hidden;
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}
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#roxupfdiiw .gt_column_spanner_outer {
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#pnxskxfvyw .gt_column_spanner_outer {
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color: #333333;
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background-color: #FFFFFF;
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font-size: 100%;
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padding-right: 4px;
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}
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#roxupfdiiw .gt_column_spanner_outer:first-child {
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#pnxskxfvyw .gt_column_spanner_outer:first-child {
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padding-left: 0;
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}
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#roxupfdiiw .gt_column_spanner_outer:last-child {
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#pnxskxfvyw .gt_column_spanner_outer:last-child {
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padding-right: 0;
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}
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#roxupfdiiw .gt_column_spanner {
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#pnxskxfvyw .gt_column_spanner {
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border-bottom-style: solid;
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border-bottom-width: 2px;
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border-bottom-color: #D3D3D3;
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@ -990,7 +990,7 @@ Baye’s Rule
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width: 100%;
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}
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#roxupfdiiw .gt_group_heading {
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#pnxskxfvyw .gt_group_heading {
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padding-top: 8px;
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padding-bottom: 8px;
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padding-left: 5px;
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@ -1015,7 +1015,7 @@ Baye’s Rule
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vertical-align: middle;
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}
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#roxupfdiiw .gt_empty_group_heading {
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||||
#pnxskxfvyw .gt_empty_group_heading {
|
||||
padding: 0.5px;
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
|
|
@ -1030,15 +1030,15 @@ Baye’s Rule
|
|||
vertical-align: middle;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_from_md > :first-child {
|
||||
#pnxskxfvyw .gt_from_md > :first-child {
|
||||
margin-top: 0;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_from_md > :last-child {
|
||||
#pnxskxfvyw .gt_from_md > :last-child {
|
||||
margin-bottom: 0;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_row {
|
||||
#pnxskxfvyw .gt_row {
|
||||
padding-top: 8px;
|
||||
padding-bottom: 8px;
|
||||
padding-left: 5px;
|
||||
|
|
@ -1057,7 +1057,7 @@ Baye’s Rule
|
|||
overflow-x: hidden;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_stub {
|
||||
#pnxskxfvyw .gt_stub {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
font-size: 100%;
|
||||
|
|
@ -1070,7 +1070,7 @@ Baye’s Rule
|
|||
padding-right: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_stub_row_group {
|
||||
#pnxskxfvyw .gt_stub_row_group {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
font-size: 100%;
|
||||
|
|
@ -1084,11 +1084,11 @@ Baye’s Rule
|
|||
vertical-align: top;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_row_group_first td {
|
||||
#pnxskxfvyw .gt_row_group_first td {
|
||||
border-top-width: 2px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_summary_row {
|
||||
#pnxskxfvyw .gt_summary_row {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
text-transform: inherit;
|
||||
|
|
@ -1098,16 +1098,16 @@ Baye’s Rule
|
|||
padding-right: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_first_summary_row {
|
||||
#pnxskxfvyw .gt_first_summary_row {
|
||||
border-top-style: solid;
|
||||
border-top-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_first_summary_row.thick {
|
||||
#pnxskxfvyw .gt_first_summary_row.thick {
|
||||
border-top-width: 2px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_last_summary_row {
|
||||
#pnxskxfvyw .gt_last_summary_row {
|
||||
padding-top: 8px;
|
||||
padding-bottom: 8px;
|
||||
padding-left: 5px;
|
||||
|
|
@ -1117,7 +1117,7 @@ Baye’s Rule
|
|||
border-bottom-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_grand_summary_row {
|
||||
#pnxskxfvyw .gt_grand_summary_row {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
text-transform: inherit;
|
||||
|
|
@ -1127,7 +1127,7 @@ Baye’s Rule
|
|||
padding-right: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_first_grand_summary_row {
|
||||
#pnxskxfvyw .gt_first_grand_summary_row {
|
||||
padding-top: 8px;
|
||||
padding-bottom: 8px;
|
||||
padding-left: 5px;
|
||||
|
|
@ -1137,11 +1137,11 @@ Baye’s Rule
|
|||
border-top-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_striped {
|
||||
#pnxskxfvyw .gt_striped {
|
||||
background-color: rgba(128, 128, 128, 0.05);
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_table_body {
|
||||
#pnxskxfvyw .gt_table_body {
|
||||
border-top-style: solid;
|
||||
border-top-width: 2px;
|
||||
border-top-color: #D3D3D3;
|
||||
|
|
@ -1150,7 +1150,7 @@ Baye’s Rule
|
|||
border-bottom-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_footnotes {
|
||||
#pnxskxfvyw .gt_footnotes {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
border-bottom-style: none;
|
||||
|
|
@ -1164,7 +1164,7 @@ Baye’s Rule
|
|||
border-right-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_footnote {
|
||||
#pnxskxfvyw .gt_footnote {
|
||||
margin: 0px;
|
||||
font-size: 90%;
|
||||
padding-left: 4px;
|
||||
|
|
@ -1173,7 +1173,7 @@ Baye’s Rule
|
|||
padding-right: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_sourcenotes {
|
||||
#pnxskxfvyw .gt_sourcenotes {
|
||||
color: #333333;
|
||||
background-color: #FFFFFF;
|
||||
border-bottom-style: none;
|
||||
|
|
@ -1187,7 +1187,7 @@ Baye’s Rule
|
|||
border-right-color: #D3D3D3;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_sourcenote {
|
||||
#pnxskxfvyw .gt_sourcenote {
|
||||
font-size: 90%;
|
||||
padding-top: 4px;
|
||||
padding-bottom: 4px;
|
||||
|
|
@ -1195,64 +1195,64 @@ Baye’s Rule
|
|||
padding-right: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_left {
|
||||
#pnxskxfvyw .gt_left {
|
||||
text-align: left;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_center {
|
||||
#pnxskxfvyw .gt_center {
|
||||
text-align: center;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_right {
|
||||
#pnxskxfvyw .gt_right {
|
||||
text-align: right;
|
||||
font-variant-numeric: tabular-nums;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_font_normal {
|
||||
#pnxskxfvyw .gt_font_normal {
|
||||
font-weight: normal;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_font_bold {
|
||||
#pnxskxfvyw .gt_font_bold {
|
||||
font-weight: bold;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_font_italic {
|
||||
#pnxskxfvyw .gt_font_italic {
|
||||
font-style: italic;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_super {
|
||||
#pnxskxfvyw .gt_super {
|
||||
font-size: 65%;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_footnote_marks {
|
||||
#pnxskxfvyw .gt_footnote_marks {
|
||||
font-style: italic;
|
||||
font-weight: normal;
|
||||
font-size: 75%;
|
||||
vertical-align: 0.4em;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_asterisk {
|
||||
#pnxskxfvyw .gt_asterisk {
|
||||
font-size: 100%;
|
||||
vertical-align: 0;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_indent_1 {
|
||||
#pnxskxfvyw .gt_indent_1 {
|
||||
text-indent: 5px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_indent_2 {
|
||||
#pnxskxfvyw .gt_indent_2 {
|
||||
text-indent: 10px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_indent_3 {
|
||||
#pnxskxfvyw .gt_indent_3 {
|
||||
text-indent: 15px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_indent_4 {
|
||||
#pnxskxfvyw .gt_indent_4 {
|
||||
text-indent: 20px;
|
||||
}
|
||||
|
||||
#roxupfdiiw .gt_indent_5 {
|
||||
#pnxskxfvyw .gt_indent_5 {
|
||||
text-indent: 25px;
|
||||
}
|
||||
</style>
|
||||
|
|
@ -1272,11 +1272,11 @@ Baye’s Rule
|
|||
</thead>
|
||||
<tbody class="gt_table_body">
|
||||
<tr><td class="gt_row gt_left">fake</td>
|
||||
<td class="gt_row gt_right">3967</td>
|
||||
<td class="gt_row gt_right">0.3967</td></tr>
|
||||
<td class="gt_row gt_right">4011</td>
|
||||
<td class="gt_row gt_right">0.4011</td></tr>
|
||||
<tr><td class="gt_row gt_left">real</td>
|
||||
<td class="gt_row gt_right">6033</td>
|
||||
<td class="gt_row gt_right">0.6033</td></tr>
|
||||
<td class="gt_row gt_right">5989</td>
|
||||
<td class="gt_row gt_right">0.5989</td></tr>
|
||||
</tbody>
|
||||
|
||||
|
||||
|
|
@ -1313,8 +1313,8 @@ Baye’s Rule
|
|||
# Groups: usage [2]
|
||||
usage fake real
|
||||
<chr> <int> <int>
|
||||
1 no 2891 5910
|
||||
2 yes 1076 123</code></pre>
|
||||
1 no 2942 5856
|
||||
2 yes 1069 133</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell">
|
||||
|
|
@ -1341,8 +1341,8 @@ Baye’s Rule
|
|||
<pre><code># A tibble: 2 × 3
|
||||
type total prop
|
||||
<chr> <int> <dbl>
|
||||
1 fake 1076 0.897
|
||||
2 real 123 0.103</code></pre>
|
||||
1 fake 1069 0.889
|
||||
2 real 133 0.111</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
|
|
@ -1586,6 +1586,81 @@ Important
|
|||
<p>this has been mentioned before but its an important message to drive home. Note that the reason why thes values sum to a value greater than 1 is that they are <strong>not</strong> probabilities, they are likelihoods. We are determining how likely each value of <span class="math inline">\(\pi\)</span> is given that we have observed <span class="math inline">\(Y = 1\)</span>.</p>
|
||||
</div>
|
||||
</div>
|
||||
<p>We can formalize the likelihood function <span class="math inline">\(L\)</span> in our example as follows:</p>
|
||||
<p><span class="math display">\[L(\pi|y=1) = f(y=1|\pi) = {6 \choose 1}\pi^1(1-\pi)^{6-1}\]</span> <span class="math display">\[ = 6\pi(1 - \pi)^5\]</span></p>
|
||||
<p>We can test this out</p>
|
||||
<div class="cell">
|
||||
<div class="sourceCode cell-code" id="cb26"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a><span class="dv">6</span> <span class="sc">*</span> .<span class="dv">2</span> <span class="sc">*</span> (.<span class="dv">8</span> <span class="sc">^</span> <span class="dv">5</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<div class="cell-output cell-output-stdout">
|
||||
<pre><code>[1] 0.393216</code></pre>
|
||||
</div>
|
||||
</div>
|
||||
<p>which is the value we get as .2 in the bar plot above.</p>
|
||||
<p>the likelihood values for <span class="math inline">\(Y = 1\)</span> are here:</p>
|
||||
<div class="cell">
|
||||
<div class="sourceCode cell-code" id="cb28"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb28-1"><a href="#cb28-1" aria-hidden="true" tabindex="-1"></a>d <span class="sc">|></span></span>
|
||||
<span id="cb28-2"><a href="#cb28-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">filter</span>(ys <span class="sc">==</span> <span class="dv">1</span>)<span class="sc">|></span></span>
|
||||
<span id="cb28-3"><a href="#cb28-3" aria-hidden="true" tabindex="-1"></a> <span class="fu">select</span>(<span class="sc">-</span>display_pi) <span class="sc">|></span></span>
|
||||
<span id="cb28-4"><a href="#cb28-4" aria-hidden="true" tabindex="-1"></a> knitr<span class="sc">::</span><span class="fu">kable</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||||
<div class="cell-output-display">
|
||||
<table class="table table-sm table-striped">
|
||||
<thead>
|
||||
<tr class="header">
|
||||
<th style="text-align: right;">pies</th>
|
||||
<th style="text-align: right;">ys</th>
|
||||
<th style="text-align: right;">fys</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr class="odd">
|
||||
<td style="text-align: right;">0.1</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.354294</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: right;">0.2</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.393216</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: right;">0.3</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.302526</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: right;">0.4</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.186624</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: right;">0.5</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.093750</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: right;">0.6</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.036864</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: right;">0.7</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.010206</td>
|
||||
</tr>
|
||||
<tr class="even">
|
||||
<td style="text-align: right;">0.8</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.001536</td>
|
||||
</tr>
|
||||
<tr class="odd">
|
||||
<td style="text-align: right;">0.9</td>
|
||||
<td style="text-align: right;">1</td>
|
||||
<td style="text-align: right;">0.000054</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
</main>
|
||||
|
|
|
|||
23
R/ch2.qmd
23
R/ch2.qmd
|
|
@ -543,4 +543,27 @@ are likelihoods. We are determining how likely each value of
|
|||
$\pi$ is given that we have observed $Y = 1$.
|
||||
:::
|
||||
|
||||
We can formalize the likelihood function $L$ in our example
|
||||
as follows:
|
||||
|
||||
$$L(\pi|y=1) = f(y=1|\pi) = {6 \choose 1}\pi^1(1-\pi)^{6-1}$$
|
||||
$$ = 6\pi(1 - \pi)^5$$
|
||||
|
||||
We can test this out
|
||||
|
||||
```{r}
|
||||
6 * .2 * (.8 ^ 5)
|
||||
```
|
||||
which is the value we get as .2 in the bar plot above.
|
||||
|
||||
the likelihood values for $Y = 1$ are here:
|
||||
|
||||
```{r}
|
||||
d |>
|
||||
filter(ys == 1)|>
|
||||
select(-display_pi) |>
|
||||
knitr::kable()
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Binary file not shown.
|
Before Width: | Height: | Size: 16 KiB After Width: | Height: | Size: 16 KiB |
Binary file not shown.
|
Before Width: | Height: | Size: 12 KiB After Width: | Height: | Size: 12 KiB |
|
|
@ -1,4 +1,5 @@
|
|||
@import url('https://fonts.googleapis.com/css?family=Lora&display=swap');
|
||||
@import url('https://fonts.googleapis.com/css?family=Source+Code+Pro&display=swap');
|
||||
|
||||
body {
|
||||
font-family: 'Lora';
|
||||
|
|
|
|||
Loading…
Reference in New Issue