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chapter3Bayes_ex5and6.html
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<h1 id="chapter-3---bayesian-statistics---exercises-5-6">Chapter 3 - Bayesian Statistics - Exercises 5 & 6</h1>
<p>Daniel Piqué<br />2016-09-05</p>
<h3 id="test-of-a-proportion">5. Test of a proportion</h3>
<ul>
<li>In the standard Rhine test of extra-sensory perception (ESP), a set of cards is used where each card has a circle, a square, wavy lines, a cross, or a star. A card is selected at random from the deck, and a person tries to guess the symbol on the card. This experiment is repeated 20 times, and the number of correct guesses y is recorded. Let p denote the probability that the person makes a correct guess, where p = .2 if the person does not have ESP and is just guessing at the card symbol. To see if the person truly has some ESP, we would like to test the hypothesis H : p = .2.</li>
</ul>
<h4 id="a-if-the-person-identifies-y-8-cards-correctly-compute-the-p-value.">A) If the person identifies y = 8 cards correctly, compute the p-value.</h4>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">library</span>(LearnBayes)
<span class="co">#HO: p = 0.2</span>
<span class="co">#HA: p != 0.2</span>
<span class="co">#We are dealing with a binomial distribution (ie a certain number of successes)</span>
<span class="co">#y = 8 successes</span>
<span class="dv">1</span> -<span class="st"> </span><span class="kw">pbinom</span>(<span class="dv">8</span>, <span class="dv">20</span>, <span class="fl">0.2</span>)</code></pre>
<pre><code>## [1] 0.009981786</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(<span class="dv">1</span>:<span class="dv">20</span>, <span class="dv">1</span>-<span class="kw">pbinom</span>(<span class="dv">1</span>:<span class="dv">20</span>, <span class="dv">20</span>, <span class="fl">0.2</span>), <span class="dt">xlab =</span> <span class="st">"Number of correct guesses"</span>, <span class="dt">ylab =</span> <span class="st">"p-value"</span>, <span class="dt">main=</span> <span class="st">"P-values for ESP hypothesis testing </span><span class="ch">\n</span><span class="st"> by the number of correct guesses"</span>)
<span class="kw">abline</span>(<span class="dt">v =</span> <span class="dv">8</span>,<span class="dt">lty=</span><span class="dv">2</span>, <span class="dt">col=</span> <span class="st">'red'</span>)
<span class="kw">text</span>(<span class="dt">x =</span> <span class="dv">13</span>, <span class="fl">0.2</span>, <span class="dt">labels =</span> <span class="st">"p-value for the scenario </span><span class="ch">\n</span><span class="st"> with 8 correct guesses"</span>)</code></pre>
<p><img src="data:image/png;base64,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" /></p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">plot</span>(<span class="dv">0</span>:<span class="dv">20</span>, <span class="kw">dbinom</span>(<span class="dv">0</span>:<span class="dv">20</span>, <span class="dv">20</span>, <span class="fl">0.2</span>), <span class="dt">xlab=</span> <span class="st">"Number of Correct Guesses"</span>, <span class="dt">ylab =</span> <span class="st">"Probability Density"</span>)</code></pre>
<p><img 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" /></p>
<h4 id="b-suppose-you-believe-a-priori-that-the-probability-that-p-.2-is-.5-and-if-p-.2-you-assign-a-beta1-4-prior-on-the-proportion.-using-the-function-pbetat-compute-the-posterior-probability-of-the-hypothesis-h.-compare-your-answer-with-the-p-value-computed-in-part-a.">B) Suppose you believe a priori that the probability that p = .2 is .5 and if p != .2 you assign a beta(1, 4) prior on the proportion. Using the function pbetat, compute the posterior probability of the hypothesis H. Compare your answer with the p-value computed in part (a).</h4>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">pbetat</span>(.<span class="dv">2</span>, .<span class="dv">5</span>, <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">4</span>), <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">12</span>))</code></pre>
<pre><code>## $bf
## [1] 0.5175417
##
## $post
## [1] 0.3410395</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co">#$bf [1] 0.5175417 (Bayes Factor, in support of the null)</span>
<span class="co">#$post [1] 0.3410395 (posterior probability of null)</span>
<span class="co">#p=0.34 is much higher than that derived from the binomial. Basically, under the Bayesian framework, we are more skeptial about rejecting the null hypothesis that there is no ESP than under the frequentist framework.</span>
### pbetat function ###
<span class="co">#function (p0, prob, ab, data) </span>
<span class="co">#{</span>
<span class="co"># a = ab[1]</span>
<span class="co"># b = ab[2]</span>
<span class="co"># s = data[1]</span>
<span class="co"># f = data[2]</span>
<span class="co"># lbf = s * log(p0) + f * log(1 - p0) + lbeta(a, b) - lbeta(a + </span>
<span class="co"># s, b + f)</span>
<span class="co"># bf = exp(lbf)</span>
<span class="co"># post = prob * bf/(prob * bf + 1 - prob)</span>
<span class="co"># return(list(bf = bf, post = post))</span>
<span class="co">#}</span></code></pre>
<h4 id="c-the-posterior-probability-computed-in-part-b-depended-on-your-belief-about-plausible-values-of-the-proportion-p-when-p-.2.-for-each-of-the-following-priors-compute-the-posterior-probability-of-h-1-p-beta.5-2-2-p-beta2-8-3-p-beta8-32.">C) The posterior probability computed in part (b) depended on your belief about plausible values of the proportion p when p != .2. For each of the following priors, compute the posterior probability of H: (1) p ∼ beta(.5, 2), (2) p ∼ beta(2, 8), (3) p ∼ beta(8, 32).</h4>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">pbetat</span>(.<span class="dv">2</span>, .<span class="dv">5</span>, <span class="kw">c</span>(<span class="fl">0.5</span>,<span class="dv">2</span>), <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">12</span>)) <span class="co">#[1] 0.3900752</span></code></pre>
<pre><code>## $bf
## [1] 0.6395464
##
## $post
## [1] 0.3900752</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">pbetat</span>(.<span class="dv">2</span>, .<span class="dv">5</span>, <span class="kw">c</span>(<span class="dv">2</span>,<span class="dv">8</span>), <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">12</span>)) <span class="co">#0.328591</span></code></pre>
<pre><code>## $bf
## [1] 0.4894051
##
## $post
## [1] 0.328591</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">pbetat</span>(.<span class="dv">2</span>, .<span class="dv">5</span>, <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">32</span>), <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">12</span>)) <span class="co">#0.3855337</span></code></pre>
<pre><code>## $bf
## [1] 0.6274287
##
## $post
## [1] 0.3855337</code></pre>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co">#show the 4 different beta distributions</span>
<span class="kw">par</span>(<span class="dt">mfrow=</span><span class="kw">c</span>(<span class="dv">2</span>,<span class="dv">2</span>))
x <-<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>, <span class="dv">1</span>, <span class="dt">by =</span> <span class="fl">0.01</span>)
<span class="kw">plot</span>(x, <span class="kw">dbeta</span>(x, <span class="dt">shape1 =</span> <span class="dv">1</span>, <span class="dt">shape2 =</span> <span class="dv">4</span>), <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">1</span>, <span class="dt">xlab=</span><span class="st">""</span>, <span class="dt">ylab=</span><span class="st">"Density"</span>, <span class="dt">main=</span><span class="st">"Beta(1,4) Distribution"</span>)
<span class="kw">plot</span>(x, <span class="kw">dbeta</span>(x, <span class="dt">shape1 =</span> <span class="fl">0.5</span>, <span class="dt">shape2 =</span> <span class="dv">2</span>), <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">1</span>, <span class="dt">xlab=</span><span class="st">""</span>, <span class="dt">ylab=</span><span class="st">"Density"</span>, <span class="dt">main=</span><span class="st">"Beta(0.5,2) Distribution"</span>)
<span class="kw">plot</span>(x, <span class="kw">dbeta</span>(x, <span class="dt">shape1 =</span> <span class="dv">2</span>, <span class="dt">shape2 =</span> <span class="dv">8</span>), <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">1</span>, <span class="dt">xlab=</span><span class="st">""</span>, <span class="dt">ylab=</span><span class="st">"Density"</span>, <span class="dt">main=</span><span class="st">"Beta(2,8) Distribution"</span>)
<span class="kw">plot</span>(x, <span class="kw">dbeta</span>(x, <span class="dt">shape1 =</span> <span class="dv">8</span>, <span class="dt">shape2 =</span> <span class="dv">32</span>), <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">1</span>, <span class="dt">xlab=</span><span class="st">""</span>, <span class="dt">ylab=</span><span class="st">"Density"</span>, <span class="dt">main=</span><span class="st">"Beta(8,32) Distribution"</span>)</code></pre>
<p><img 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" /></p>
<h4 id="d-on-the-basis-of-your-bayesian-computations-do-you-think-that-y-8-is-convincing-evidence-that-the-person-really-has-some-esp-explain.">D) On the basis of your Bayesian computations, do you think that y =8 is convincing evidence that the person really has some ESP? Explain.</h4>
<ul>
<li>No. Given a sensible prior with the probability density centered around the null hypothesis that the proportion of correct guesses equals 0.2, I wouldn't expect this person to have ESP.</li>
</ul>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co">#robustness to different values of alpha</span>
postGrid <-<span class="st"> </span><span class="kw">matrix</span>(<span class="ot">NA</span>, <span class="dt">nrow =</span> <span class="dv">100</span>, <span class="dt">ncol=</span><span class="dv">100</span>)
<span class="kw">colnames</span>(postGrid) <-<span class="st"> </span><span class="dv">1</span>:<span class="dv">100</span>
<span class="kw">rownames</span>(postGrid) <-<span class="st"> </span><span class="dv">1</span>:<span class="dv">100</span>
for(i in <span class="kw">seq</span>(<span class="dv">1</span>, <span class="dv">100</span>, <span class="dt">by=</span><span class="dv">1</span>)){
for (j in <span class="kw">seq</span>(<span class="dv">1</span>,<span class="dv">100</span>, <span class="dt">by=</span><span class="dv">1</span>)){
post <-<span class="st"> </span><span class="kw">unlist</span>(<span class="kw">pbetat</span>(.<span class="dv">2</span>, .<span class="dv">5</span>, <span class="kw">c</span>(i,j), <span class="kw">c</span>(<span class="dv">8</span>,<span class="dv">12</span>))[<span class="dv">2</span>])
postGrid[i, j] <-<span class="st"> </span>post
}
}
<span class="kw">library</span>(gplots)
<span class="kw">heatmap.2</span>(postGrid, <span class="dt">dendrogram=</span><span class="st">'none'</span>, <span class="dt">Rowv=</span><span class="ot">FALSE</span>, <span class="dt">Colv=</span><span class="ot">FALSE</span>,<span class="dt">trace=</span><span class="st">'none'</span>, , <span class="dt">xlab =</span> <span class="st">"beta"</span>, <span class="dt">ylab =</span> <span class="st">"alpha"</span>)</code></pre>
<p><img src="data:image/png;base64,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" /></p>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">min</span>(postGrid)</code></pre>
<pre><code>## [1] 0.1154475</code></pre>
<h3 id="suppose-you-drive-on-a-particular-interstate-roadway-and-typically-drive-at-a-constant-speed-of-70-mph.-one-day-you-pass-one-car-and-get-passed-by-17-cars.-suppose-that-the-speeds-are-normally-distributed-with-unknown-mean-mu-and-standard-deviation--10.-if-you-pass-s-cars-and-f-cars-pass-you-the-likelihood-of-mu-is-given-by">6. Suppose you drive on a particular interstate roadway and typically drive at a constant speed of 70 mph. One day, you pass one car and get passed by 17 cars. Suppose that the speeds are normally distributed with unknown mean mu and standard deviation σ = 10. If you pass s cars and f cars pass you, the likelihood of mu is given by</h3>
<p>L(mu) ∝ Φ(70,mu,σ)^s * (1 − Φ(70,mu,σ))^f, ### where Φ(y, mu, σ) is the cdf of the normal distribution with mean mu and standard deviation σ. Assign the unknown mean mu a flat prior density.</p>
<h4 id="a-if-s-1-and-f-17-plot-the-posterior-density-of-mu.">A) If s = 1 and f = 17, plot the posterior density of mu.</h4>
<pre class="sourceCode r"><code class="sourceCode r">s=<span class="dv">1</span>
f=<span class="dv">17</span>
sigma=<span class="dv">10</span>
x =<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dt">length=</span><span class="dv">200</span>)
prior =<span class="st"> </span><span class="kw">dbeta</span>(x,<span class="dv">1</span> ,<span class="dv">1</span>)
mu=<span class="dv">1</span>:<span class="dv">200</span>
likelihood =<span class="st"> </span><span class="kw">pnorm</span>(<span class="dv">70</span>, mu, sigma)^s *<span class="st"> </span>(<span class="dv">1</span> -<span class="st"> </span><span class="kw">pnorm</span>(<span class="dv">70</span>, mu, sigma))^f
posterior =<span class="st"> </span>prior*likelihood/<span class="kw">sum</span>(prior*likelihood)
<span class="kw">plot</span>(mu, posterior, <span class="dt">type =</span> <span class="st">'l'</span>, <span class="dt">ylab =</span> <span class="st">"posterior"</span>, <span class="dt">main =</span> <span class="st">"Posterior Density of mu"</span>)</code></pre>
<p><img src="data:image/png;base64,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" /></p>
<ol>
<li>Using the density found in part (a), find the posterior mean of mu.</li>
</ol>
<pre class="sourceCode r"><code class="sourceCode r"><span class="co">#how to find the posterior mean? Get a weighted average of all your points.</span>
<span class="kw">sum</span>(mu *<span class="st"> </span>posterior) <span class="co">#87.11109</span></code></pre>
<pre><code>## [1] 87.11109</code></pre>
<ol>
<li>Find the probability that the average speed of the cars on this interstate roadway exceeds 80 mph.</li>
</ol>
<pre class="sourceCode r"><code class="sourceCode r"><span class="kw">sum</span>(posterior[<span class="dv">80</span>:<span class="dv">200</span>]) <span class="co">#probability that average speed exceeds 80 mph</span></code></pre>
<pre><code>## [1] 0.9468573</code></pre>
<pre class="sourceCode r"><code class="sourceCode r">like <-<span class="st"> </span>function(mu, sigma, s,f){
likelihood =<span class="st"> </span><span class="kw">pnorm</span>(<span class="dv">70</span>, mu, sigma)^s *<span class="st"> </span>(<span class="dv">1</span> -<span class="st"> </span><span class="kw">pnorm</span>(<span class="dv">70</span>, mu, sigma))^f
}
cord.x <-<span class="st"> </span><span class="kw">c</span>(<span class="dv">80</span>,<span class="kw">seq</span>(<span class="dv">80</span>,<span class="dv">200</span>,<span class="fl">0.01</span>),<span class="dv">200</span>)
cord.y <-<span class="st"> </span><span class="kw">c</span>(<span class="dv">0</span>,<span class="kw">like</span>(<span class="kw">seq</span>(<span class="dv">80</span>,<span class="dv">200</span>,<span class="fl">0.01</span>), sigma, s, f),<span class="dv">0</span>)
<span class="kw">curve</span>(<span class="kw">like</span>(x, sigma, s, f), <span class="dt">xlim=</span><span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">200</span>), <span class="dt">xlab =</span> <span class="st">"mu (Avg. Speed)"</span>, <span class="dt">ylab =</span> <span class="st">"posterior probability"</span>, <span class="dt">main =</span> <span class="st">"Posterior Density of mu (Avg. Speed)"</span>)
<span class="kw">polygon</span>(cord.x,cord.y,<span class="dt">col=</span><span class="st">'skyblue'</span>)</code></pre>
<p><img 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" 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