41 | 38 | <area shape="rect" href="classbdm_1_1migamma.html" title="Inverse-Gamma random walk." alt="" coords="16,239,139,265"><area shape="rect" href="classbdm_1_1mEF.html" title="Exponential family model." alt="" coords="35,161,120,188"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="32,84,123,111"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="21,7,133,33"></map> |
42 | 39 | <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> |
43 | | <div class="dynheader"> |
44 | | Collaboration diagram for bdm::migamma_fix:</div> |
45 | | <div class="dynsection"> |
46 | | <p><center><img src="classbdm_1_1migamma__fix__coll__graph.png" border="0" usemap="#bdm_1_1migamma__fix__coll__map" alt="Collaboration graph"></center> |
47 | | <map name="bdm_1_1migamma__fix__coll__map"> |
48 | | <area shape="rect" href="classbdm_1_1migamma.html" title="Inverse-Gamma random walk." alt="" coords="24,567,147,593"><area shape="rect" href="classbdm_1_1mEF.html" title="Exponential family model." alt="" coords="8,417,93,444"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="5,284,96,311"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="13,7,125,33"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="32,87,107,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="100,185,185,212"><area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="120,284,200,311"><area shape="rect" href="classbdm_1_1eigamma.html" title="Inverse-Gamma posterior density." alt="" coords="88,471,208,497"><area shape="rect" href="classbdm_1_1egamma.html" title="Gamma posterior density." alt="" coords="168,364,283,391"></map> |
49 | | <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> |
50 | | |
51 | | <p> |
52 | | <a href="classbdm_1_1migamma__fix-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0"> |
| 40 | |
| 41 | <p> |
| 42 | <a href="classbdm_1_1migamma__fix-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2> |
| 43 | Inverse-Gamma random walk around a fixed point. |
| 44 | <p> |
| 45 | Mean value, <img class="formulaInl" alt="$\mu$" src="form_14.png">, of this density is given by a geometric combination of <code>rvc</code> and given fixed point, <img class="formulaInl" alt="$p$" src="form_42.png">. <img class="formulaInl" alt="$l$" src="form_43.png"> is the coefficient of the geometric combimation <p class="formulaDsp"> |
| 46 | <img class="formulaDsp" alt="\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]" src="form_18.png"> |
| 47 | <p> |
| 48 | <p> |
| 49 | ==== Check == vv = Standard deviation of the random walk is proportional to one <img class="formulaInl" alt="$k$" src="form_41.png">-th the mean. This is achieved by setting <img class="formulaInl" alt="$\alpha=k$" src="form_11.png"> and <img class="formulaInl" alt="$\beta=k/\mu$" src="form_12.png">.<p> |
| 50 | The standard deviation of the walk is then: <img class="formulaInl" alt="$\mu/\sqrt(k)$" src="form_13.png">. <table border="0" cellpadding="0" cellspacing="0"> |
85 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b3aba7311038bf990d706a64cab60cf8"></a><!-- doxytag: member="bdm::migamma_fix::_rvc" ref="b3aba7311038bf990d706a64cab60cf8" args="() const " --> |
86 | | <a class="el" href="classbdm_1_1RV.html">RV</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#b3aba7311038bf990d706a64cab60cf8">_rvc</a> () const </td></tr> |
87 | | |
88 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">access function <br></td></tr> |
89 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="222d5280e309c5a053ba73841e98c151"></a><!-- doxytag: member="bdm::migamma_fix::_rv" ref="222d5280e309c5a053ba73841e98c151" args="() const " --> |
90 | | <a class="el" href="classbdm_1_1RV.html">RV</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#222d5280e309c5a053ba73841e98c151">_rv</a> () const </td></tr> |
91 | | |
92 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">access function <br></td></tr> |
| 84 | <tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr> |
| 85 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5571482d150fbcb72cc36f6694ce1a10"></a><!-- doxytag: member="bdm::migamma_fix::_rv" ref="5571482d150fbcb72cc36f6694ce1a10" args="()" --> |
| 86 | <a class="el" href="classbdm_1_1RV.html">RV</a> </td><td class="memItemRight" valign="bottom"><b>_rv</b> ()</td></tr> |
| 87 | |
| 88 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="26001264236846897bd11e4baad47245"></a><!-- doxytag: member="bdm::migamma_fix::_rvc" ref="26001264236846897bd11e4baad47245" args="()" --> |
| 89 | <a class="el" href="classbdm_1_1RV.html">RV</a> </td><td class="memItemRight" valign="bottom"><b>_rvc</b> ()</td></tr> |
| 90 | |
| 91 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1c2bae3e1e90874e72941863974ec0ed"></a><!-- doxytag: member="bdm::migamma_fix::dimension" ref="1c2bae3e1e90874e72941863974ec0ed" args="()" --> |
| 92 | int </td><td class="memItemRight" valign="bottom"><b>dimension</b> ()</td></tr> |
| 93 | |
| 94 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="35e135910aed187b7290742f50e61bc8"></a><!-- doxytag: member="bdm::migamma_fix::dimensionc" ref="35e135910aed187b7290742f50e61bc8" args="()" --> |
| 95 | int </td><td class="memItemRight" valign="bottom"><b>dimensionc</b> ()</td></tr> |
| 96 | |
98 | | <a class="el" href="classbdm_1_1epdf.html">epdf</a> * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#05e843fd11c410a99dad2b88c55aca80">_e</a> ()</td></tr> |
99 | | |
100 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">access function <br></td></tr> |
| 101 | <a class="el" href="classbdm_1_1epdf.html">epdf</a> * </td><td class="memItemRight" valign="bottom"><b>_e</b> ()</td></tr> |
| 102 | |
| 103 | <tr><td colspan="2"><div class="groupHeader">Connection to other objects</div></td></tr> |
| 104 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7631a5570e4ade1420065e8df78f4401"></a><!-- doxytag: member="bdm::migamma_fix::set_rvc" ref="7631a5570e4ade1420065e8df78f4401" args="(const RV &rvc0)" --> |
| 105 | void </td><td class="memItemRight" valign="bottom"><b>set_rvc</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &rvc0)</td></tr> |
| 106 | |
| 107 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18ac26bc2f96ae01ef4eb06178abbd75"></a><!-- doxytag: member="bdm::migamma_fix::set_rv" ref="18ac26bc2f96ae01ef4eb06178abbd75" args="(const RV &rv0)" --> |
| 108 | void </td><td class="memItemRight" valign="bottom"><b>set_rv</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &rv0)</td></tr> |
| 109 | |
| 110 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f8e3798150b42fd1f3e16ddbbe0e7045"></a><!-- doxytag: member="bdm::migamma_fix::isnamed" ref="f8e3798150b42fd1f3e16ddbbe0e7045" args="()" --> |
| 111 | bool </td><td class="memItemRight" valign="bottom"><b>isnamed</b> ()</td></tr> |
| 112 | |
118 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4825c0ef11a148bad9b802a496f56f96"></a><!-- doxytag: member="bdm::migamma_fix::_beta" ref="4825c0ef11a148bad9b802a496f56f96" args="" --> |
119 | | vec * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1migamma.html#4825c0ef11a148bad9b802a496f56f96">_beta</a></td></tr> |
| 130 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c9847093da59a9ba0ebb68d2c592f5dc"></a><!-- doxytag: member="bdm::migamma_fix::_alpha" ref="c9847093da59a9ba0ebb68d2c592f5dc" args="" --> |
| 131 | vec & </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1migamma.html#c9847093da59a9ba0ebb68d2c592f5dc">_alpha</a></td></tr> |
| 132 | |
| 133 | <tr><td class="mdescLeft"> </td><td class="mdescRight">cache of epdf.alpha <br></td></tr> |
| 134 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0d854c047001b5465cf1ba21f52904b5"></a><!-- doxytag: member="bdm::migamma_fix::_beta" ref="0d854c047001b5465cf1ba21f52904b5" args="" --> |
| 135 | vec & </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1migamma.html#0d854c047001b5465cf1ba21f52904b5">_beta</a></td></tr> |
122 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b6c265b132ff79963bf51dff4c3ef252"></a><!-- doxytag: member="bdm::migamma_fix::_alpha" ref="b6c265b132ff79963bf51dff4c3ef252" args="" --> |
123 | | vec * </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1migamma.html#b6c265b132ff79963bf51dff4c3ef252">_alpha</a></td></tr> |
124 | | |
125 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">chaceh of epdf.alpha <br></td></tr> |
126 | | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bcfb45435d30983f436d41c298cbb51"></a><!-- doxytag: member="bdm::migamma_fix::rv" ref="9bcfb45435d30983f436d41c298cbb51" args="" --> |
127 | | <a class="el" href="classbdm_1_1RV.html">RV</a> </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#9bcfb45435d30983f436d41c298cbb51">rv</a></td></tr> |
128 | | |
129 | | <tr><td class="mdescLeft"> </td><td class="mdescRight">modeled random variable <br></td></tr> |
| 138 | <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7c1900976ff13dbc09c9729b3bbff9e6"></a><!-- doxytag: member="bdm::migamma_fix::dimc" ref="7c1900976ff13dbc09c9729b3bbff9e6" args="" --> |
| 139 | int </td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#7c1900976ff13dbc09c9729b3bbff9e6">dimc</a></td></tr> |
| 140 | |
| 141 | <tr><td class="mdescLeft"> </td><td class="mdescRight">dimension of the condition <br></td></tr> |
139 | | <hr><a name="_details"></a><h2>Detailed Description</h2> |
140 | | Inverse-Gamma random walk around a fixed point. |
141 | | <p> |
142 | | Mean value, <img class="formulaInl" alt="$\mu$" src="form_14.png">, of this density is given by a geometric combination of <code>rvc</code> and given fixed point, <img class="formulaInl" alt="$p$" src="form_42.png">. <img class="formulaInl" alt="$l$" src="form_43.png"> is the coefficient of the geometric combimation <p class="formulaDsp"> |
143 | | <img class="formulaDsp" alt="\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]" src="form_18.png"> |
144 | | <p> |
145 | | <p> |
146 | | ==== Check == vv = Standard deviation of the random walk is proportional to one <img class="formulaInl" alt="$k$" src="form_41.png">-th the mean. This is achieved by setting <img class="formulaInl" alt="$\alpha=k$" src="form_11.png"> and <img class="formulaInl" alt="$\beta=k/\mu$" src="form_12.png">.<p> |
147 | | The standard deviation of the walk is then: <img class="formulaInl" alt="$\mu/\sqrt(k)$" src="form_13.png">. <hr><h2>Member Function Documentation</h2> |
| 151 | <hr><h2>Member Function Documentation</h2> |