| | 76 | <hr/><a name="_details"></a><h2>Detailed Description</h2> |
| | 77 | <p>Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities. </p> |
| | 78 | <p>This object represents exact or approximate evaluation of the Bayes rule: </p> |
| | 79 | <p class="formulaDsp"> |
| | 80 | <img class="formulaDsp" alt="\[ f(\theta_t | d_1,\ldots,d_t) = \frac{f(y_t|\theta_t,\cdot) f(\theta_t|d_1,\ldots,d_{t-1})}{f(y_t|d_1,\ldots,d_{t-1})} \]" src="form_8.png"/> |
| | 81 | </p> |
| | 82 | <p>Access to the resulting posterior density is via function <code>posterior()</code>.</p> |
| | 83 | <p>As a "side-effect" it also evaluates log-likelihood of the data, which can be accessed via function _ll(). It can also evaluate predictors of future values of <img class="formulaInl" alt="$y_t$" src="form_9.png"/>, see functions <a class="el" href="classbdm_1_1BM.html#a688d7a2aced1e06aa1c468d73a9e5eba" title="Constructs a predictive density .">epredictor()</a> and <a class="el" href="classbdm_1_1BM.html#a598b25e3f3d96a5bc00a5faeb5b3c912" title="Constructs conditional density of 1-step ahead predictor .">predictor()</a>.</p> |
| | 84 | <p>Alternatively, it can evaluate posterior density conditioned by a known constant, <img class="formulaInl" alt="$ c_t $" src="form_10.png"/>: </p> |
| | 85 | <p class="formulaDsp"> |
| | 86 | <img class="formulaDsp" alt="\[ f(\theta_t | c_t, d_1,\ldots,d_t) \propto f(y_t,\theta_t|c_t,\cdot, d_1,\ldots,d_{t-1}) \]" src="form_11.png"/> |
| | 87 | </p> |
| | 88 | <p>The value of <img class="formulaInl" alt="$ c_t $" src="form_10.png"/> is set by function <a class="el" href="classbdm_1_1BM.html#a6799f4b16a6a59ed58b1d0d6e17116f4" title="Substitute val for rvc.">condition()</a>. </p> |
| 175 | | <hr/><a name="_details"></a><h2>Detailed Description</h2> |
| 176 | | <p>Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities. </p> |
| 177 | | <p>This object represents exact or approximate evaluation of the Bayes rule: </p> |
| 178 | | <p class="formulaDsp"> |
| 179 | | <img class="formulaDsp" alt="\[ f(\theta_t | d_1,\ldots,d_t) = \frac{f(y_t|\theta_t,\cdot) f(\theta_t|d_1,\ldots,d_{t-1})}{f(y_t|d_1,\ldots,d_{t-1})} \]" src="form_8.png"/> |
| 180 | | </p> |
| 181 | | <p>Access to the resulting posterior density is via function <code>posterior()</code>.</p> |
| 182 | | <p>As a "side-effect" it also evaluates log-likelihood of the data, which can be accessed via function _ll(). It can also evaluate predictors of future values of <img class="formulaInl" alt="$y_t$" src="form_9.png"/>, see functions <a class="el" href="classbdm_1_1BM.html#a688d7a2aced1e06aa1c468d73a9e5eba" title="Constructs a predictive density .">epredictor()</a> and <a class="el" href="classbdm_1_1BM.html#a598b25e3f3d96a5bc00a5faeb5b3c912" title="Constructs conditional density of 1-step ahead predictor .">predictor()</a>.</p> |
| 183 | | <p>Alternatively, it can evaluate posterior density conditioned by a known constant, <img class="formulaInl" alt="$ c_t $" src="form_10.png"/>: </p> |
| 184 | | <p class="formulaDsp"> |
| 185 | | <img class="formulaDsp" alt="\[ f(\theta_t | c_t, d_1,\ldots,d_t) \propto f(y_t,\theta_t|c_t,\cdot, d_1,\ldots,d_{t-1}) \]" src="form_11.png"/> |
| 186 | | </p> |
| 187 | | <p>The value of <img class="formulaInl" alt="$ c_t $" src="form_10.png"/> is set by function <a class="el" href="classbdm_1_1BM.html#a6799f4b16a6a59ed58b1d0d6e17116f4" title="Substitute val for rvc.">condition()</a>. </p> |
