thbf{x}_n &gt; \mathbf{0}\}\)</span> and <span class="math inline">\(\mathbf{1}\{\mathbf{x}_n &lt; \mathbf{0}\}\)</span> denote, respectively, the event that it is positive and the event that it is negative. A positive observation <span class="math inline">\(\mathbf{x}_n=(x_{n1},\ldots,x_{nP})\)</span> means that each element <span class="math inline">\(x_{nj}\)</span> is positive; likewise for a negative observation. Each component of <span class="math inline">\(\mathbf{x}_n\)</span> is IID according to th