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3 Bettencourt and Riberio (PloS One, 2008). See details for important
4 implementation notes."><meta property=
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5 Bettencourt and Riberio (PloS One, 2008). See details for important
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25 <ul class=
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"../articles/seq_bayes_post.html">Sequential Bayes: Utilizing the Posterior Distribution
</a></li>
26 <li><a class=
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</a></li>
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37 <main id=
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38 <img src=
"../logo.svg" class=
"logo" alt=
""><h1>Sequential Bayes (seqB)
</h1>
39 <small class=
"dont-index">Source:
<a href=
"https://github.com/MI2YorkU/Rnaught/blob/master/R/seq_bayes.R" class=
"external-link"><code>R/seq_bayes.R
</code></a></small>
40 <div class=
"d-none name"><code>seq_bayes.Rd
</code></div>
43 <div class=
"ref-description section level2">
44 <p>This function implements a sequential Bayesian estimation method of R0 due to
45 Bettencourt and Riberio (PloS One,
2008). See details for important
46 implementation notes.
</p>
49 <div class=
"section level2">
50 <h2 id=
"ref-usage">Usage
<a class=
"anchor" aria-label=
"anchor" href=
"#ref-usage"></a></h2>
51 <div class=
"sourceCode"><pre class=
"sourceCode r"><code><span><span class=
"fu">seq_bayes
</span><span class=
"op">(
</span><span class=
"va">cases
</span>,
<span class=
"va">mu
</span>, kappa
<span class=
"op">=
</span> <span class=
"fl">20</span>, post
<span class=
"op">=
</span> <span class=
"cn">FALSE
</span><span class=
"op">)
</span></span></code></pre></div>
54 <div class=
"section level2">
55 <h2 id=
"arguments">Arguments
<a class=
"anchor" aria-label=
"anchor" href=
"#arguments"></a></h2>
58 <dl><dt id=
"arg-cases">cases
<a class=
"anchor" aria-label=
"anchor" href=
"#arg-cases"></a></dt>
59 <dd><p>Vector of case counts. The vector must only contain non-negative
60 integers, and have at least two positive integers.
</p></dd>
63 <dt id=
"arg-mu">mu
<a class=
"anchor" aria-label=
"anchor" href=
"#arg-mu"></a></dt>
64 <dd><p>Mean of the serial distribution. This must be a positive number.
65 The value should match the case counts in time units. For example, if case
66 counts are weekly and the serial distribution has a mean of seven days,
67 then
<code>mu
</code> should be set to
<code>1</code>. If case counts are daily and the serial
68 distribution has a mean of seven days, then
<code>mu
</code> should be set to
<code>7</code>.
</p></dd>
71 <dt id=
"arg-kappa">kappa
<a class=
"anchor" aria-label=
"anchor" href=
"#arg-kappa"></a></dt>
72 <dd><p>Largest possible value of the uniform prior (defaults to
<code>20</code>).
73 This must be a number greater than or equal to
<code>1</code>. It describes the prior
74 belief on the ranges of R0, and should be set to a higher value if R0 is
75 believed to be larger.
</p></dd>
78 <dt id=
"arg-post">post
<a class=
"anchor" aria-label=
"anchor" href=
"#arg-post"></a></dt>
79 <dd><p>Whether to return the posterior distribution of R0 instead of the
80 estimate of R0 (defaults to
<code>FALSE
</code>). This must be a value identical to
81 <code>TRUE
</code> or
<code>FALSE
</code>.
</p></dd>
84 <div class=
"section level2">
85 <h2 id=
"value">Value
<a class=
"anchor" aria-label=
"anchor" href=
"#value"></a></h2>
86 <p>If
<code>post
</code> is identical to
<code>TRUE
</code>, a list containing the following
87 components is returned:
</p><ul><li><p><code>supp
</code> - the support of the posterior distribution of R0
</p></li>
88 <li><p><code>pmf
</code> - the probability mass function of the posterior distribution of R0
</p></li>
89 </ul><p>Otherwise, if
<code>post
</code> is identical to
<code>FALSE
</code>, only the estimate of R0 is
90 returned. Note that the estimate is equal to
<code>sum(supp * pmf)
</code> (i.e., the
93 <div class=
"section level2">
94 <h2 id=
"details">Details
<a class=
"anchor" aria-label=
"anchor" href=
"#details"></a></h2>
95 <p>The method sets a uniform prior distribution on R0 with possible values
96 between
<code>0</code> and
<code>kappa
</code>, discretized to a fine grid. The distribution of R0
97 is then updated sequentially, with one update for each new case count
98 observation. The final estimate of R0 is the mean of the (last) posterior
99 distribution. The prior distribution is the initial belief of the
100 distribution of R0, which is the uninformative uniform distribution with
101 values between
<code>0</code> and
<code>kappa
</code>. Users can change the value of
<code>kappa
</code> only
102 (i.e., the prior distribution cannot be changed from the uniform). As more
103 case counts are observed, the influence of the prior distribution should
104 lessen on the final estimate.
</p>
105 <p>This method is based on an approximation of the SIR model, which is most
106 valid at the beginning of an epidemic. The method assumes that the mean of
107 the serial distribution (sometimes called the serial interval) is known. The
108 final estimate can be quite sensitive to this value, so sensitivity testing
109 is strongly recommended. Users should be careful about units of time (e.g.,
110 are counts observed daily or weekly?) when implementing.
</p>
111 <p>Our code has been modified to provide an estimate even if case counts equal
112 to zero are present in some time intervals. This is done by grouping the
113 counts over such periods of time. Without grouping, and in the presence of
114 zero counts, no estimate can be provided.
</p>
116 <div class=
"section level2">
117 <h2 id=
"references">References
<a class=
"anchor" aria-label=
"anchor" href=
"#references"></a></h2>
118 <p><a href=
"https://doi.org/10.1371/journal.pone.0002185" class=
"external-link">Bettencourt and Riberio (PloS One,
2008)
</a></p>
120 <div class=
"section level2">
121 <h2 id=
"see-also">See also
<a class=
"anchor" aria-label=
"anchor" href=
"#see-also"></a></h2>
122 <div class=
"dont-index"><p><code><a href=
"../articles/seq_bayes_post.html">vignette("seq_bayes_post", package = "Rnaught")
</a></code> for examples of
123 using the posterior distribution.
</p></div>
126 <div class=
"section level2">
127 <h2 id=
"ref-examples">Examples
<a class=
"anchor" aria-label=
"anchor" href=
"#ref-examples"></a></h2>
128 <div class=
"sourceCode"><pre class=
"sourceCode r"><code><span class=
"r-in"><span><span class=
"co"># Weekly data.
</span></span></span>
129 <span class=
"r-in"><span><span class=
"va">cases
</span> <span class=
"op"><-
</span> <span class=
"fu"><a href=
"https://rdrr.io/r/base/c.html" class=
"external-link">c
</a></span><span class=
"op">(
</span><span class=
"fl">1</span>,
<span class=
"fl">4</span>,
<span class=
"fl">10</span>,
<span class=
"fl">5</span>,
<span class=
"fl">3</span>,
<span class=
"fl">4</span>,
<span class=
"fl">19</span>,
<span class=
"fl">3</span>,
<span class=
"fl">3</span>,
<span class=
"fl">14</span>,
<span class=
"fl">4</span><span class=
"op">)
</span></span></span>
130 <span class=
"r-in"><span></span></span>
131 <span class=
"r-in"><span><span class=
"co"># Obtain R0 when the serial distribution has a mean of five days.
</span></span></span>
132 <span class=
"r-in"><span><span class=
"fu">seq_bayes
</span><span class=
"op">(
</span><span class=
"va">cases
</span>, mu
<span class=
"op">=
</span> <span class=
"fl">5</span> <span class=
"op">/
</span> <span class=
"fl">7</span><span class=
"op">)
</span></span></span>
133 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
1]
1.026563</span>
134 <span class=
"r-in"><span></span></span>
135 <span class=
"r-in"><span><span class=
"co"># Obtain R0 when the serial distribution has a mean of three days.
</span></span></span>
136 <span class=
"r-in"><span><span class=
"fu">seq_bayes
</span><span class=
"op">(
</span><span class=
"va">cases
</span>, mu
<span class=
"op">=
</span> <span class=
"fl">3</span> <span class=
"op">/
</span> <span class=
"fl">7</span><span class=
"op">)
</span></span></span>
137 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
1]
1.015938</span>
138 <span class=
"r-in"><span></span></span>
139 <span class=
"r-in"><span><span class=
"co"># Obtain R0 when the serial distribution has a mean of seven days, and R0 is
</span></span></span>
140 <span class=
"r-in"><span><span class=
"co"># believed to be at most
4.
</span></span></span>
141 <span class=
"r-in"><span><span class=
"va">estimate
</span> <span class=
"op"><-
</span> <span class=
"fu">seq_bayes
</span><span class=
"op">(
</span><span class=
"va">cases
</span>, mu
<span class=
"op">=
</span> <span class=
"fl">1</span>, kappa
<span class=
"op">=
</span> <span class=
"fl">4</span><span class=
"op">)
</span></span></span>
142 <span class=
"r-in"><span></span></span>
143 <span class=
"r-in"><span><span class=
"co"># Same as above, but return the posterior distribution of R0 instead of the
</span></span></span>
144 <span class=
"r-in"><span><span class=
"co"># estimate.
</span></span></span>
145 <span class=
"r-in"><span><span class=
"va">posterior
</span> <span class=
"op"><-
</span> <span class=
"fu">seq_bayes
</span><span class=
"op">(
</span><span class=
"va">cases
</span>, mu
<span class=
"op">=
</span> <span class=
"fl">1</span>, kappa
<span class=
"op">=
</span> <span class=
"fl">4</span>, post
<span class=
"op">=
</span> <span class=
"cn">TRUE
</span><span class=
"op">)
</span></span></span>
146 <span class=
"r-in"><span></span></span>
147 <span class=
"r-in"><span><span class=
"co"># Display the support and probability mass function of the posterior.
</span></span></span>
148 <span class=
"r-in"><span><span class=
"va">posterior
</span><span class=
"op">$
</span><span class=
"va">supp
</span></span></span>
149 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
1]
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14</span>
150 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
16]
0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29</span>
151 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
31]
0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44</span>
152 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
46]
0.45 0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59</span>
153 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
61]
0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74</span>
154 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
76]
0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89</span>
155 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
91]
0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04</span>
156 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
106]
1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19</span>
157 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
121]
1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34</span>
158 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
136]
1.35 1.36 1.37 1.38 1.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49</span>
159 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
151]
1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64</span>
160 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
166]
1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79</span>
161 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
181]
1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94</span>
162 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
196]
1.95 1.96 1.97 1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09</span>
163 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
211]
2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24</span>
164 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
226]
2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39</span>
165 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
241]
2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54</span>
166 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
256]
2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69</span>
167 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
271]
2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.80 2.81 2.82 2.83 2.84</span>
168 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
286]
2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99</span>
169 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
301]
3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 3.13 3.14</span>
170 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
316]
3.15 3.16 3.17 3.18 3.19 3.20 3.21 3.22 3.23 3.24 3.25 3.26 3.27 3.28 3.29</span>
171 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
331]
3.30 3.31 3.32 3.33 3.34 3.35 3.36 3.37 3.38 3.39 3.40 3.41 3.42 3.43 3.44</span>
172 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
346]
3.45 3.46 3.47 3.48 3.49 3.50 3.51 3.52 3.53 3.54 3.55 3.56 3.57 3.58 3.59</span>
173 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
361]
3.60 3.61 3.62 3.63 3.64 3.65 3.66 3.67 3.68 3.69 3.70 3.71 3.72 3.73 3.74</span>
174 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
376]
3.75 3.76 3.77 3.78 3.79 3.80 3.81 3.82 3.83 3.84 3.85 3.86 3.87 3.88 3.89</span>
175 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
391]
3.90 3.91 3.92 3.93 3.94 3.95 3.96 3.97 3.98 3.99 4.00</span>
176 <span class=
"r-in"><span><span class=
"va">posterior
</span><span class=
"op">$
</span><span class=
"va">pmf
</span></span></span>
177 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
1]
4.396081e-14 6.866777e-14 1.069979e-13 1.663113e-13 2.578585e-13</span>
178 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
6]
3.987896e-13 6.151736e-13 9.465244e-13 1.452563e-12 2.223289e-12</span>
179 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
11]
3.393931e-12 5.167074e-12 7.845296e-12 1.187914e-11 1.793742e-11</span>
180 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
16]
2.700983e-11 4.055633e-11 6.072366e-11 9.065827e-11 1.349567e-10</span>
181 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
21]
2.003117e-10 2.964355e-10 4.373744e-10 6.433725e-10 9.435054e-10</span>
182 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
26]
1.379386e-09 2.010358e-09 2.920742e-09 4.229916e-09 6.106257e-09</span>
183 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
31]
8.786364e-09 1.260143e-08 1.801328e-08 2.566338e-08 3.643912e-08</span>
184 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
36]
5.156328e-08 7.271379e-08 1.021837e-07 1.430935e-07 1.996715e-07</span>
185 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
41]
2.776227e-07 3.846102e-07 5.308815e-07 7.300785e-07 1.000278e-06</span>
186 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
46]
1.365319e-06 1.856496e-06 2.514686e-06 3.393017e-06 4.560205e-06</span>
187 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
51]
6.104659e-06 8.139541e-06 1.080892e-05 1.429523e-05 1.882819e-05</span>
188 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
56]
2.469542e-05 3.225496e-05 4.194988e-05 5.432506e-05 7.004650e-05</span>
189 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
61]
8.992291e-05 1.149299e-04 1.462361e-04 1.852322e-04 2.335598e-04</span>
190 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
66]
2.931434e-04 3.662201e-04 4.553696e-04 5.635406e-04 6.940727e-04</span>
191 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
71]
8.507116e-04 1.037615e-03 1.259347e-03 1.520857e-03 1.827440e-03</span>
192 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
76]
2.184679e-03 2.598363e-03 3.074378e-03 3.618573e-03 4.236597e-03</span>
193 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
81]
4.933708e-03 5.714562e-03 6.582973e-03 7.541662e-03 8.591990e-03</span>
194 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
86]
9.733699e-03 1.096466e-02 1.228062e-02 1.367503e-02 1.513890e-02</span>
195 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
91]
1.666067e-02 1.822624e-02 1.981901e-02 2.142007e-02 2.300844e-02</span>
196 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
96]
2.456146e-02 2.605520e-02 2.746508e-02 2.876640e-02 2.993509e-02</span>
197 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
101]
3.094837e-02 3.178548e-02 3.242832e-02 3.286214e-02 3.307605e-02</span>
198 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
106]
3.306344e-02 3.282231e-02 3.235539e-02 3.167013e-02 3.077854e-02</span>
199 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
111]
2.969682e-02 2.844487e-02 2.704571e-02 2.552471e-02 2.390888e-02</span>
200 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
116]
2.222595e-02 2.050365e-02 1.876888e-02 1.704700e-02 1.536123e-02</span>
201 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
121]
1.373213e-02 1.217724e-02 1.071084e-02 9.343864e-03 8.083917e-03</span>
202 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
126]
6.935429e-03 5.899896e-03 4.976201e-03 4.160989e-03 3.449076e-03</span>
203 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
131]
2.833858e-03 2.307727e-03 1.862441e-03 1.489475e-03 1.180313e-03</span>
204 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
136]
9.266886e-04 7.207803e-04 5.553459e-04 4.238132e-04 3.203273e-04</span>
205 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
141]
2.397617e-04 1.777009e-04 1.304008e-04 9.473459e-05 6.812875e-05</span>
206 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
146]
4.849552e-05 3.416469e-05 2.381841e-05 1.643092e-05 1.121447e-05</span>
207 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
151]
7.572111e-06 5.057422e-06 3.340936e-06 2.182658e-06 1.410047e-06</span>
208 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
156]
9.006636e-07 5.687529e-07 3.550312e-07 2.190488e-07 1.335660e-07</span>
209 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
161]
8.047851e-08 4.791165e-08 2.817909e-08 1.637135e-08 9.394205e-09</span>
210 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
166]
5.323528e-09 2.978849e-09 1.645703e-09 8.975385e-10 4.831664e-10</span>
211 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
171]
2.566999e-10 1.345806e-10 6.961600e-11 3.552605e-11 1.788285e-11</span>
212 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
176]
8.878079e-12 4.346434e-12 2.098061e-12 9.984180e-13 4.683320e-13</span>
213 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
181]
2.165108e-13 9.863385e-14 4.427200e-14 1.957601e-14 8.526007e-15</span>
214 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
186]
3.657023e-15 1.544555e-15 6.422519e-16 2.628849e-16 1.059047e-16</span>
215 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
191]
4.198412e-17 1.637588e-17 6.283525e-18 2.371425e-18 8.801378e-19</span>
216 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
196]
3.211841e-19 1.152248e-19 4.063045e-20 1.407979e-20 4.794057e-21</span>
217 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
201]
1.603601e-21 5.268629e-22 1.699923e-22 5.385323e-23 1.674809e-23</span>
218 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
206]
5.112219e-24 1.531308e-24 4.500307e-25 1.297374e-25 3.668155e-26</span>
219 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
211]
1.016962e-26 2.764082e-27 7.363758e-28 1.922485e-28 4.917601e-29</span>
220 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
216]
1.232200e-29 3.023823e-30 7.265876e-31 1.709166e-31 3.935069e-32</span>
221 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
221]
8.865403e-33 1.954015e-33 4.212549e-34 8.880821e-35 1.830437e-35</span>
222 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
226]
3.687665e-36 7.260114e-37 1.396466e-37 2.623677e-38 4.813725e-39</span>
223 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
231]
8.622619e-40 1.507577e-40 2.572153e-41 4.281381e-42 6.950773e-43</span>
224 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
236]
1.100362e-43 1.698170e-44 2.554224e-45 3.743317e-46 5.343929e-47</span>
225 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
241]
7.429450e-48 1.005609e-48 1.324832e-49 1.698377e-50 2.118019e-51</span>
226 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
246]
2.568782e-52 3.029042e-53 3.471688e-54 3.866425e-55 4.182989e-56</span>
227 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
251]
4.394865e-57 4.482891e-58 4.438084e-59 4.263117e-60 3.972112e-61</span>
228 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
256]
3.588768e-62 3.143145e-63 2.667736e-64 2.193531e-65 1.746742e-66</span>
229 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
261]
1.346659e-67 1.004822e-68 7.254056e-70 5.065108e-71 3.419533e-72</span>
230 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
266]
2.231354e-73 1.406840e-74 8.567343e-76 5.037567e-77 2.859011e-78</span>
231 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
271]
1.565585e-79 8.268889e-81 4.210849e-82 2.066735e-83 9.773085e-85</span>
232 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
276]
4.450901e-86 1.951504e-87 8.234368e-89 3.342436e-90 1.304664e-91</span>
233 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
281]
4.895156e-93 1.764793e-94 6.110914e-96 2.031551e-97 6.481579e-99</span>
234 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
286]
1.983744e-100 5.821848e-102 1.637658e-103 4.413549e-105 1.139116e-106</span>
235 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
291]
2.814324e-108 6.652979e-110 1.504185e-111 3.251137e-113 6.714617e-115</span>
236 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
296]
1.324527e-116 2.494329e-118 4.482263e-120 7.682227e-122 1.255211e-123</span>
237 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
301]
1.954236e-125 2.897728e-127 4.090211e-129 5.493210e-131 7.015875e-133</span>
238 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
306]
8.517133e-135 9.822891e-137 1.075711e-138 1.117987e-140 1.102133e-142</span>
239 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
311]
1.030047e-144 9.121635e-147 7.649726e-149 6.072101e-151 4.559445e-153</span>
240 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
316]
3.236849e-155 2.171329e-157 1.375543e-159 8.224662e-162 4.638796e-164</span>
241 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
321]
2.466499e-166 1.235627e-168 5.828612e-171 2.587326e-173 1.080141e-175</span>
242 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
326]
4.238233e-178 1.562047e-180 5.404238e-183 1.754003e-185 5.337064e-188</span>
243 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
331]
1.521491e-190 4.061129e-193 1.014255e-195 2.368537e-198 5.168362e-201</span>
244 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
336]
1.053099e-203 2.002304e-206 3.550040e-209 5.865079e-212 9.022847e-215</span>
245 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
341]
1.291610e-217 1.719185e-220 2.126178e-223 2.441418e-226 2.600913e-229</span>
246 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
346]
2.568760e-232 2.350200e-235 1.990379e-238 1.559119e-241 1.128742e-244</span>
247 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
351]
7.546371e-248 4.655454e-251 2.647985e-254 1.387535e-257 6.692519e-261</span>
248 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
356]
2.968866e-264 1.210268e-267 4.529956e-271 1.555446e-274 4.895396e-278</span>
249 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
361]
1.410954e-281 3.720881e-285 8.970133e-289 1.975060e-292 3.968208e-296</span>
250 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
366]
7.268446e-300 1.212601e-303 1.840840e-307 2.540527e-311 3.184384e-315</span>
251 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
371]
3.621946e-319 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
252 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
376]
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
253 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
381]
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
254 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
386]
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
255 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
391]
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
256 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
396]
0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00</span>
257 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
401]
0.000000e+00</span>
258 <span class=
"r-in"><span></span></span>
259 <span class=
"r-in"><span><span class=
"co"># Note that the following always holds:
</span></span></span>
260 <span class=
"r-in"><span><span class=
"va">estimate
</span> <span class=
"op">==
</span> <span class=
"fu"><a href=
"https://rdrr.io/r/base/sum.html" class=
"external-link">sum
</a></span><span class=
"op">(
</span><span class=
"va">posterior
</span><span class=
"op">$
</span><span class=
"va">supp
</span> <span class=
"op">*
</span> <span class=
"va">posterior
</span><span class=
"op">$
</span><span class=
"va">pmf
</span><span class=
"op">)
</span></span></span>
261 <span class=
"r-out co"><span class=
"r-pr">#
></span> [
1] TRUE
</span>
264 </main><aside class=
"col-md-3"><nav id=
"toc" aria-label=
"Table of contents"><h2>On this page
</h2>
268 <footer><div class=
"pkgdown-footer-left">
269 <p>Developed by Naeem Model, Sawitree Boonpatcharanon, Jane Heffernan, Hanna Jankowski.
</p>
272 <div class=
"pkgdown-footer-right">
273 <p>Site built with
<a href=
"https://pkgdown.r-lib.org/" class=
"external-link">pkgdown
</a> 2.1.1.
</p>
git.nmode.ca / Rnaught / blob
